103,99 €
Mehr erfahren.
- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
An Introduction to Data-Driven Control Systems An introduction to the emerging dominant paradigm in control design Model-based approaches to control systems design have long dominated the control systems design methodologies. However, most models require substantial prior or assumed information regarding the plant's structure and internal dynamics. The data-driven paradigm in control systems design, which has proliferated rapidly in recent decades, requires only observed input-output data from plants, making it more flexible and broadly applicable. An Introduction to Data-Driven Control Systems provides a foundational overview of data-driven control systems methodologies. It presents key concepts and theories in an accessible way, without the need for the complex mathematics typically associated with technical publications in the field, and raises the important issues involved in applying these approaches. The result is a highly readable introduction to what promises to become the dominant control systems design paradigm. Readers will also find: * An overview of philosophical-historical issues accompanying the emergence of data-driven control systems * Design analysis of several conventional data-driven control systems design methodologies * Algorithms and simulation results, with numerous examples, to facilitate the implementation of methods An Introduction to Data-Driven Control Systems is ideal for students and researchers in control theory or any other research area related to plant design and production.
Sie lesen das E-Book in den Legimi-Apps auf:
Seitenzahl: 561
Veröffentlichungsjahr: 2023
Ähnliche
Table of Contents
Cover
Table of Contents
Title Page
Copyright
Preface
Acknowledgements
List of Acronyms
1 Introduction
1.1 Model‐Based Control System Design Approach
1.2 Data‐driven Control System Design Approach
1.3 Data‐Driven Control Schemes
1.4 Outline of the Book
References
2 Philosophical Perspectives of the Paradigm Shift in Control Systems Design and the Re‐Emergence of Data‐Driven Control
2.1 Introduction
2.2 Background Materials
2.3 Paradigm Shifts in Control Systems Design
2.4 Uncertainty Combat Paradigm
2.5 The Paradigm Shift Towards Data‐driven Control Methodologies
2.6 Conclusions
References
3 Unfalsified Adaptive Switching Supervisory Control
3.1 Introduction
3.2 A Philosophical Perspective
3.3 Principles of the Unfalsified Adaptive Switching Control
3.4 The Non‐Minimum Phase Controller
3.5 The DAL Phenomena
3.6 Performance Improvement Techniques
3.7 Increasing Cost Level Algorithms in UASC
3.8 Time‐varying Systems in the UASC
3.9 Conclusion
Problems
References
Notes
4 Multi‐Model Unfalsified Adaptive Switching Supervisory Control
4.1 Introduction
4.2 The Multi‐Model Adaptive Control
4.3 Principles of the Multi‐Model Unfalsified Adaptive Switching Control
4.4 Performance Enhancement Techniques in the MMUASC
4.5 Input‐constrained Multi‐Model Unfalsified Switching Control Design
4.6 Conclusion
Problems
References
Note
5 Data‐Driven Control System Design Based on the Virtual Reference Feedback Tuning Approach
5.1 Introduction
5.2 The Basic VRFT Methodology
5.3 The Measurement Noise Effect
5.4 The Non‐Minimum Phase Plants Challenge in the VRFT Design Approach
5.5 Extensions of the VRTF Methodology to Multivariable Plants
5.6 Optimal Reference Model Selection in the VRFT Methodology
5.7 Closed‐loop Stability of the VRFT‐Based Data‐Driven Control Systems
5.8 Conclusions
References
Notes
6 The Simultaneous Perturbation Stochastic Approximation‐Based Data‐Driven Control Design
6.1 Introduction
6.2 The Essentials of the SPSA Algorithm
6.3 Data‐Driven Control Design Based on the SPSA Algorithm
6.4 A Case Study: Data‐Driven Control of Under‐actuated Systems
6.5 Conclusions
Problems
References
7 Data‐driven Control System Design Based on the Fundamental Lemma
7.1 Introduction
7.2 The Fundamental Lemma
7.3 System Representation and Identification of LTI Systems
7.4 Data‐driven State‐feedback Stabilisation
7.5 Robust Data‐driven State‐feedback Stabilisation
7.6 Data‐driven Predictive Control
7.7 Conclusion
Problems
References
Notes
8 Koopman Theory and Data‐driven Control System Design of Nonlinear Systems
8.1 Introduction
8.2 Fundamentals of Koopman Theory for Data‐driven Control System Design
8.3 Koopman‐based Data‐driven Control of Nonlinear Systems
8.4 A Case Study: Data‐driven Koopman Predictive Control of the ACUREX Parabolic Solar Collector Field
8.5 Conclusion
Problems
References
Notes
9 Model‐free Adaptive Control Design
9.1 Introduction
9.2 The Dynamic Linearisation Methodologies
9.3 Extensions of the Dynamic Linearisation Methodologies to Multivariable Plants
9.4 Design of Model‐free Adaptive Control Systems for Unknown Nonlinear Plants
9.5 Extensions of the Model‐free Adaptive Control Methodologies to Multivariable Plants
9.6 A Combined MFAC–SPSA Data‐driven Control Strategy
9.7 Conclusions
References
Notes
Appendix
A Norms
B Lyapunov Equation
C Incremental Stability
D Switching and the Dwell‐time
E Inverse Moments
F Least Squares Estimation
G Linear Matrix Inequalities
H Linear Fractional Transformations
References
Index
End User License Agreement
List of Tables
Chapter 2
Table 2.1 Summary of the main features of control systems design paradigm s...
Chapter 4
Table 4.1 Different choices of
F
i
.
Table 4.2 Performance comparison of different cost functions.
Chapter 6
Table 6.1 SPSA main specifications for data‐driven control.
Table 6.2 Model parameters of the liquid slosh system [8].
Table 6.3 Model parameters of the ball and beam system [12].
Chapter 8
Table 8.1 Model parameters and variables of the solar collector field.
Table 8.2 Parameters measured of the ACUREX parabolic collector field.
List of Illustrations
Chapter 1
Figure 1.1 The structure of a model‐based control system design.
Figure 1.2 The structure of a data‐driven control system design.
Figure 1.3 The unfalsified control structure.
Figure 1.4 The VRFT general structure. (a) Model reference scheme of VRFT, (...
Figure 1.5 A SPSA‐based data‐driven control system.
Figure 1.6 The model‐based cycle of the Koopman‐based linear controller desi...
Figure 1.7 The data‐driven design cycle of the Koopman‐based linear controll...
Figure 1.8 The model‐free adaptive control.
Chapter 2
Figure 2.1 The first paradigm shift.
Figure 2.2 The modelling cycle.
Figure 2.3 Inductive reasoning versus deductive reasoning.
Figure 2.4 The second paradigm shift.
Figure 2.5 The third paradigm shift.
Figure 2.6 The fourth paradigm shift.
Figure 2.7 A two‐dimensional picture of paradigm shifts versus plant classif...
Figure 2.8 A general overview of the paradigm shifts in control system desig...
Chapter 3
Figure 3.1 The concept of the controllers' falsification.
Figure 3.2 The virtual reference signal in the potential loop.
Figure 3.3 General structure of a switching supervisory control.
Figure 3.4 The output and reference input.
Figure 3.5 (a) The switching signal and (b) the cost functions.
Figure 3.6 The new potential loop for a non‐minimum phase controller.
Figure 3.7 The switching signal, control input signal and output for differe...
Figure 3.8 (a) Output signal, (b) control input signal and (c) reference inp...
Figure 3.9 Cost function: (a) norm 2 versus (b) norm ∞.
Figure 3.10 THSA algorithm: (a) output and reference input, (b) control inpu...
Figure 3.11 UASC algorithm: (a) output and reference input, (b) control inpu...
Figure 3.12 The cost functions for the THSA algorithm.
Figure 3.13 The cost functions for the UASC algorithm.
Figure 3.14 SIHSA algorithm: (a) Output and reference input, (b) control inp...
Figure 3.15 The cost functions for the SIHSA algorithm.
Figure 3.16 LICLA algorithm: (a) Output and reference input, (b) control inp...
Figure 3.17 The cost functions for the LICLA algorithm.
Figure 3.18 The closed‐loop output: (a) UASC, (b) UASC‐R.
Figure 3.19 The control selection signal
σ
(
t
)
and the reset time signal...
Figure 3.20 The cost functions: (a) UASC, (b) UASC‐R.
Chapter 4
Figure 4.1 Multi‐model supervisory control structure.
Figure 4.2 General structure of the multi‐model adaptive switching superviso...
Figure 4.3 Typical switching control structure.
Figure 4.4 (a) Time‐varying closed‐loop switching system, (b) the potential ...
Figure 4.5 Error of the closed‐loop system and the control candidate loop.
Figure 4.6 The MMUASC block diagram structure.
Figure 4.7 The connected two carts with a spring.
Figure 4.8 The MMUASC reference input and closed‐loop output.
Figure 4.9 The MMUASC switching signal.
Figure 4.10 The MMUASC cost functions.
Figure 4.11 New control candidate loop.
Figure 4.12 The output and reference: (a) MMUASC, (b) MMUASC‐R.
Figure 4.13 The switching signal: (a) MMUASC, (b) MMUASC‐R.
Figure 4.14 The cost functions: (a) MMUASC, (b) MMUASC‐R.
Figure 4.15 The adaptive memory
M
(
t
) and reset time
t
k
for the MMUASC‐R.
Figure 4.16 Comparison between potential and reference loops both driven by
Figure 4.17 LTI case (from top to bottom): reference and plant outputs, cont...
Figure 4.18 Time‐varying case (from top to bottom): reference input and plan...
Figure 4.19 The MMUCGPC structure.
Figure 4.20 The predictive control tuned loop.
Figure 4.21 (a) Reference and output, (b) control signal, (c) cost value.
Figure 4.22 (a) Controller selection signal, (b) virtual reference convergen...
Chapter 5
Figure 5.1 The VRFT general structure.
Figure 5.2 Bode magnitude plots: the plant (solid line) and the reference mo...
Figure 5.3 Step responses of the control system with
θ
(solid line) and...
Figure 5.4 Bode plots of the closed‐loop system with
θ
(solid line) and...
Figure 5.5 Step responses of the closed‐loop system with
θ
(solid line)...
Figure 5.6 The closed‐loop step responses of the control system with
θ
...
Figure 5.7 Closed‐loop output responses and control signals of the decentral...
Figure 5.8 Closed‐loop output responses and control signals of the decentral...
Figure 5.9 The closed‐loop performance with the optimal controller parameter...
Figure 5.10 A feedback control and disturbance rejection feedforward scheme....
Chapter 6
Figure 6.1 The SPSA algorithm design steps.
Figure 6.2 The SPSA data‐driven control flowchart.
Figure 6.3 (a) The output
y
, (b) the control effort.
Figure 6.4 PI controller parameters.
Figure 6.5 The cost function
J
.
Figure 6.6 The liquid slosh system is modelled by a set of rigid masses and ...
Figure 6.7 The PID control scheme.
Figure 6.8 (a)
y
1
the trolley position, (b)
y
2
the slosh angle of the liquid...
Figure 6.9 (a) Control input
u
,
(b) the cost function
J
for the liquid slosh...
Figure 6.10 The PID controllers' parameters for the liquid slosh.
Figure 6.11 The ball and beam system.
Figure 6.12 (a)
y
1
the ball position, (b)
y
2
the beam angle of the ball and ...
Figure 6.13 (a) Control input
u
, (b) the cost function
J
for the ball and be...
Figure 6.14 PID controllers' parameters for the ball and beam.
Chapter 7
Figure 7.1 A schematic representation of the controllability property.
Figure 7.2 The open‐loop and closed‐loop system states with data‐driven stat...
Figure 7.3 The open‐loop and closed‐loop system states with data‐driven robu...
Figure 7.4 The basic structure of a classical MPC.
Figure 7.5
N
‐step data‐enabled predictive control responses.
Figure 7.6 The schematic presentation of artificial steady state and artific...
Figure 7.7 N‐step data‐enabled nonlinear predictive control responses.
Chapter 8
Figure 8.1 Schematic diagram of the Koopman operator in action.
Figure 8.2 The output responses of the nonlinear system and its linear equiv...
Figure 8.3 Comparison of the DMD‐based Koopman model output with the actual ...
Figure 8.4 Comparison of the EDMD‐ and DMD‐based Koopman model outputs with ...
Figure 8.5 Block diagram of the model‐based Koopman predictive control syste...
Figure 8.6 Block diagram of the data‐driven Koopman predictive control syste...
Figure 8.7 Output of the bilinear DC motor by applying the proposed data‐dri...
Figure 8.8 A schematic diagram of the ACUREX solar collector field.
Figure 8.9 Persistently excitation signal
u
d
.
Figure 8.10 Output temperature of the ACUREX solar collector field distribut...
Figure 8.11 Irradiance from 12 : 30 to 15 : 18.
Figure 8.12 HTF flow of the ACUREX solar collector field model by applying t...
Figure 8.13 Ambient Temperature from 12 : 30 to 15 : 18.
Chapter 9
Figure 9.1 Different modelling boxes in control systems identification, mode...
Figure 9.2 The MFAC closed‐loop plant based on the PPD identification.
Figure 9.3 The MFAC closed‐loop plant based on the PFDL data model identific...
Figure 9.4 The MFAC closed‐loop plant based on the FFDL data model identific...
Figure 9.5 Closed‐loop responses of the three MFAC approaches.
Figure 9.6 The MFAC control signals.
Figure 9.7 (a) PPD of CLFD‐MFAC scheme, (b) PG of PFDL‐MFAC scheme and (c) P...
Figure 9.8 Schematic diagram of the gas turbine.
Figure 9.9 The closed‐loop outputs.
Figure 9.10 The control signals (a) first input and (b) second input.
Figure 9.11 The PJM in the CFDL–MFAC approach.
Figure 9.12 The PPJM in the PFDL–MFAC approach.
Figure 9.13 The PPJM in the FFDL–MFAC approach.
Figure 9.14 Schematic diagram of a cascade of two continuous stirred tank re...
Figure 9.15 (a) Closed‐loop responses and (b) control signals.
Figure 9.16 The PJM in the CFDL–MFAC approach.
Figure 9.17 The PPJM in the PFDL–MFAC approach.
Figure 9.18 The PPJM in the FFDL–MFAC approach.
Figure 9.19 The general combined MFAC–SPSA control system.
Figure 9.20 The open‐loop responses (a) the trolley position and (b) the slo...
Figure 9.21 The closed‐loop responses with two PIDs (a) the trolley position...
Figure 9.22 Combination of SPSA and CFDL–MFAC systems with two degrees of fr...
Figure 9.23 (a)
y
1
the trolley position and (b)
y
2
the slosh angle of the liq...
Figure 9.24 (a) Control input
u
and (b) the cost function
J
for the liquid s...
Figure 9.25 PID controllers' parameters for the combined MFAC–SPSA scheme.
Figure 9.26 (a) The first and (b) the second element of the PJM estimate f...
Figure 9.27 The liquid slosh's modified reference input for the combined M...
Figure 9.28 Performance of the inner loop PID controllers after disconnectin...
Figure 9.29 Control signal of the liquid slosh inner loop PID control after ...
Appendix
Figure D.1
Figure E.1
Figure E.2
Figure E.3
Figure E.4
Figure E.5
Figure E.6
Figure H.1
Guide
Cover
Table of Contents
Title Page
Copyright
Preface
Acknowledgements
List of Acronyms
Begin Reading
Appendix
Index
End User License Agreement
Pages
ii
iii
iv
xi
xii
xiii
xiv
xv
xvi
xvii
xviii
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
357
358
359
360
361
362
363
364
365
366
367
IEEE Press
445 Hoes Lane
Piscataway, NJ 08854
IEEE Press Editorial Board
Sarah Spurgeon, Editor in Chief
Jón Atli Benediktsson
Anjan Bose
James Duncan
Amin Moeness
Desineni Subbaram Naidu
Behzad Razavi
Jim Lyke
Hai Li
Brian Johnson
Jeffrey Reed
Diomidis Spinellis
Adam Drobot
Tom Robertazzi
Ahmet Murat Tekalp
An Introduction to Data‐Driven Control Systems
Ali Khaki‐Sedigh
K.N. Toosi University of TechnologyIran
Copyright © 2024 by The Institute of Electrical and Electronics Engineers, Inc.All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per‐copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750‐8400, fax (978) 750‐4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748‐6011, fax (201) 748‐6008, or online at http://www.wiley.com/go/permission.
Trademarks: Wiley and the Wiley logo are trademarks or registered trademarks of John Wiley & Sons, Inc. and/or its affiliates in the United States and other countries and may not be used without written permission. All other trademarks are the property of their respective owners. John Wiley & Sons, Inc. is not associated with any product or vendor mentioned in this book.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.
For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762‐2974, outside the United States at (317) 572‐3993 or fax (317) 572‐4002.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com.
Library of Congress Cataloging‐in‐Publication Data Applied for:
Hardback ISBN: 9781394196401
Cover Design: WileyCover Image: © zf L/Getty Images
Preface
Model‐based control systems. Model‐based control system analysis and design approaches have been the dominant paradigm in control system education and the cornerstone of control system design for decades. These methodologies rely on accurate mathematical models and assumptions to achieve the desired system behaviour. In the early decades of the last century, despite the tremendous interest in model‐based control approaches, many PID controllers in the industry were designed based on the data‐driven technique of Ziegler–Nichols PID parameter tuning, which is considered the first data‐driven control approach. Later, the advanced adaptive and robust model‐based control techniques evolved to combat the uncertainty challenge in the established model‐based techniques. These advanced control techniques successfully controlled many real‐world and industrial plants. Yet, both strategies require mathematical models and prior plant assumptions mandated by the theory.
Data‐driven control methodologies. The limitations and uncertainties associated with models and assumptions, on the one hand, and the emergence of progressively complex systems, on the other hand, have sparked a paradigm shift towards data‐driven control methodologies. The exponentially increasing number of research papers in this field and the growing number of courses offered in universities worldwide on the subject clearly show this trend. The new data‐driven control system design paradigm has re‐emerged to circumvent the necessity of deriving offline or online plant models. Many plants regularly generate and store huge amounts of operating data at specific instants of time. Such data encompasses all the relevant plant information required for control, estimation, performance assessment, decision‐making and fault diagnosis. This data availability has facilitated the design of data‐driven control systems.
Intended audience. This book is an introduction to data‐driven control systems and attempts to provide an overview of the mainstream design approaches in the field. The selected approaches may be called with caution the conventional approaches, not including the approaches based on soft computing techniques. A unique chapter is devoted to philosophical–historical issues regarding the emergence of data‐driven control systems as the future dominant control design paradigm. This chapter will be particularly appealing to readers interested in gaining insights into the philosophical and historical aspects of control system design methodologies. Concepts from the philosophy of science and historical discussions are presented to show the inevitable prevalence of data‐driven techniques in the face of emerging complex adaptive systems. This book can cover a graduate course on data‐driven control and can also be used by any student or researcher who wishes to start working in the field of data‐driven control systems. This book will present the primary material, and the reader can perceive a general overview of the developing data‐driven control theory. The book presentation avoids detailed mathematical relations and derivations that are available in the cited technical papers on each subject. However, algorithms for easy implementation of the methods with numerical and simulation examples are provided. The software codes are available upon request from the author. Data‐driven control is also a hot research topic; many final‐year undergraduate and postgraduate students are interested in starting a research project in its different areas. The available reading sources are the technical papers and the limited number of research monographs and books on the subject. However, the technical papers are very specialised and involve deep mathematical derivations. The limited number of published monographs and books also specialise in specific subject areas and do not provide a general introduction and overview of different methodologies for a first‐time reader in data‐driven control. The selected topics in this book can be individually taught in many different courses on advanced control theory. Also, for an interested researcher in any of the covered fields, it would be beneficial to learn about the basics of other alternative methodologies to plan a research programme.
Prerequisites. The book is designed for graduate‐level courses and researchers specialising in control systems across various engineering disciplines. The book assumes that the reader possesses a solid understanding of feedback control systems as well as familiarity with the principles of discrete‐time control systems and optimisation problems. Moreover, a basic understanding of system identification, adaptive control and robust control can enhance the reader's comprehension and appreciation of data‐driven control methodologies.
Overview of the book. The book is organised as follows. Chapter 1 introduces both the model‐based and data‐driven control system design approaches. It discusses the early developments and the current status quo of model‐based control systems, as well as the challenges they face. The chapter also explores adaptive and robust control methodologies as a means to overcome some of these challenges. Subsequently, the data‐driven control system design approach is presented, and the technical aspects of different data‐driven control schemes are discussed.
Chapter 2 takes a philosophical perspective to analyse the paradigm shifts in control system design. It presents scientific theory, revolutions and paradigm shifts, drawing parallels to the evolution of control system design methodologies. The historical development of control systems design paradigms and their philosophical foundations is introduced, and a general classification of control systems is given. The chapter concludes with an exploration of the paradigm shifts towards data‐driven control methodologies, with a focus on the influence of the unfalsified philosophy.
Chapters 3 and 4 present data‐driven adaptive switching supervisory control and multi‐model adaptive switching supervisory control, respectively. The philosophical backbone of the presented methodologies is Popper's falsification theory, which is introduced in a data‐driven control context by Safonov. It is shown in Chapter 3 that the unfalsified adaptive switching supervisory control can effectively control unknown plants with guaranteed closed‐loop stability under the minimum assumption of the existence of a stabilising controller. Although several closed‐loop transient improvement techniques are presented in Chapter 3, the multi‐model unfalsified adaptive switching control is introduced in Chapter 4 to ensure a superior closed‐loop transient performance. It is shown that performance improvement is achieved by utilising a model set to select the appropriate controller based on the falsifying theory. The adaptive memory concept, input‐constrained design problems and quadratic inverse optimal control notion are also discussed.
Chapter 5 presents the virtual reference feedback tuning approach. It is shown that by formulating the controller tuning problem as a controller parameter identification problem, a data‐based controller design methodology is derived. In this approach, a virtual reference signal is introduced, and it is assumed that the controller structure is known a priori. After introducing the basic concepts and methodology, the problems of appropriate filter design, measurement noise, non‐minimum phase zero challenges, closed‐loop stability and extensions to multivariable plants are addressed in this chapter.
The simultaneous perturbation stochastic approximation optimisation technique is introduced and utilised in Chapter 6 for the design of data‐driven control systems. It is shown that this circumvents the necessity of an analytical closed‐form solution to the control optimisation problems that require almost exact mathematical models of the true plant. The essentials of the technique are presented for plants with unknown exact mathematical models. Then, after selecting a controller with a fixed known structure but unknown parameters, by minimising a cost function, the controller parameters are derived. The presented data‐driven control methodology is then applied to unknown, under‐actuated systems as a practical case study.
Chapter 7 presents a class of data‐driven controllers based on Willem's Fundamental Lemma. It is initially shown that persistently exciting data can be used to represent the input–output behaviour of a linear system without the need to identify the linear system's matrices. The derived so‐called equivalent data‐based representations of a linear time invariant (LTI) system are subsequently utilised to design data‐driven state‐feedback stabilisers and predictive controllers called Data‐enabled Predictive Control, or DeePC for short. Results with measurement noise and nonlinear systems are also given in this chapter.
Chapter 8 presents data‐driven controllers based on Koopman's theory and the Fundamental Lemma presented in Chapter 7. The fundamentals of Koopman's theory are briefly reviewed for data‐driven control. It is shown that nonlinear dynamical systems are presented by higher dimensional linear approximations. The main notions of lifting or embedding and the effective tools of (extended) dynamic mode decompositions are introduced and a data‐driven Koopman‐based predictive control scheme is presented by incorporating Willem's Fundamental Lemma of Chapter 7. A robust stability analysis is provided, and the results are finally applied to the ACUREX solar collector field.
The model‐free adaptive control design is a data‐driven control design approach based on dynamic linearisation methodologies and is presented in Chapter 9. The three main dynamic linearisations discussed in this chapter are shown to capture the system's behaviour by investigating the output variations resulting from input signals. These data models are utilised for controller design and their virtual nature makes them inappropriate for other system analysis purposes. Also, in Chapter 9, the virtual data model results and their corresponding model‐free adaptive controllers are extended to multivariable plants.
Some preliminary concepts that are useful for the chapters are presented in the Appendix. The chapters are accompanied by problem sets that provide readers with the opportunity to reinforce their understanding and apply the concepts discussed. A solution manual is also provided for instructors teaching a class on data‐driven control using this book by contacting the author.
October 2023
Ali Khaki‐Sedigh
Department of Electrical EngineeringK.N. Toosi University of Technology
Acknowledgements
The preparation of this book has greatly benefited from the invaluable contributions and support of numerous postgraduate students and colleagues who generously dedicated their time to share expertise, valuable suggestions and corrections throughout the process. I extend my sincere gratitude to the following individuals, whose significant efforts have greatly enriched the content of this book:
Amirehsan Karbasizadeh from the Department of Philosophy at the University of Isfahan, for his insightful discussions on the philosophy of science and his invaluable comments that notably enhanced
Chapter 2
.
Mojtaba Nooi Manzar from Faculty of Electrical and Computer Engineering, Shahid Beheshti University, for his contributions to the initial draft of
Chapters 3
and
4
, as well as corrections and the simulation results for these chapters.
Mohammad Moghadasi, Mehran Soleymani and Maedeh Alimohamadi, my master's students in the Advanced Control Laboratory, for their diligent proofreading of
Chapter 3
.
Bahman Sadeghi and Maedeh Alimohamadi, my master's students in the Advanced Control Laboratory, for their valuable contributions to
Chapter 4
.
Mohammad Jeddi and Fatemeh Hemati Kheirabadi, my master's students in the Advanced Control Laboratory, for their insightful contributions to
Chapter 5
.
Sepideh Nasrollahi, my PhD student in the Advanced Control Laboratory, for her contributions to
Chapter 6
, as well as her valuable contributions to other chapters and the creation of numerous figures throughout the book.
Tahereh Gholaminejad, my PhD student in the Advanced Control Laboratory, for her significant contributions to
Chapters 7
and
8
.
Sara Iman, PhD student from Iran University of Science and Technology, for her meticulous proofreading and useful comments on
Chapters 7
and
8
.
Ali Rezaei, my master's student in the Advanced Control Laboratory, for his valuable contributions to
Chapter 9
and the effort he dedicated to simulations throughout the book.
Finally, I would like to express my sincere appreciation to the anonymous reviewers who provided invaluable feedback during the review process of this book, and special thanks to Wiley‐IEEE Press for their exceptional professionalism, dedication, industry knowledge and seamless coordination that exceeded my expectations. Last but not least, I am also grateful to my family for their collaboration and support, allowing me to dedicate most of my holidays, weekends and evenings to completing this book.
List of Acronyms
ASSC
Adaptive switching supervisory control
BIBO
Bounded‐input bounded‐output
CFDL
Compact‐form dynamic linearisation
CSP
Concentrated solar power
DAL
Dehghani–Anderson–Lanzon
DDKPC
Data‐driven Koopman predictive control
DeePC
D
ata‐
e
nabl
e
d
P
redictive
C
ontrol
DFT
Discrete Fourier transform
DMD
Dynamic mode decomposition
EDMD
Extended dynamic mode decomposition
ETFE
Empirical transfer function estimate
FFDL
Full‐form dynamic linearisation
GLA
Generalised Laplace analysis
GPC
Generalised predictive control
ICLA
Increasing cost level algorithm
IFAC
International Federation of Automatic Control
LFT
Linear fractional transformation
LICLA
Linearly increasing cost level algorithm
LLC
Linearisation length constant
LMI
Linear matrix inequality
LQG
Linear quadratic Gaussian
LQR
Linear quadratic regulator
LSTM
Long short‐term memory
LTI
Linear time‐invariant
MFAC
Model‐free adaptive control
MMUASC
Multi‐model unfalsified adaptive switching control
MMUASC‐R
MMUASC with reset time
MMUCGPC
Multi‐model unfalsified constrained GPC
MPC
Model predictive control
MPUM
Most powerful unfalsified model
PE
Persistence of excitation, persistently exciting
PFDL
Partial‐form dynamic linearisation
PG
Pseudo‐gradient
PID
Proportional integral derivative
PJM
Pseudo‐Jacobian matrix
PPD
Pseudo‐partial derivative
PPJM
Pseudo‐partitioned‐Jacobian matrix
PSO
Particle swarm optimisation
QFT
Quantitative feedback theory
SA
Stochastic approximation
SCLI
Stably causally left invertible
SICE
Society of Instrument and Control Engineering
SIHSA
Scale‐independent hysteresis algorithm
SISO
Single‐input‐single‐output
SNR
Signal‐to‐noise ratio
SPSA
Simultaneous perturbation stochastic approximation
SVD
Singular value decomposition
THSA
Threshold hysteresis algorithm
UASC
Unfalsified adaptive switching control
UASC‐R
UASC with reset‐time
UASSC
Unfalsified adaptive switching supervisory control
VRFT
Virtual reference feedback tuning
1Introduction
1.1 Model‐Based Control System Design Approach
1.1.1 The Early Developments
The advent of models in control systems theory and design is rooted in the seminal paper of Maxwell On Governers[1]. Norbert Wiener, in introducing the word cybernetics in Ref. [2] describes the Maxwell paper as ‘… the first significant paper on feedback mechanisms is an article on governors, which was published by Clerk Maxwell in 1868’ and in Ref. [3], Maxwell is recognised as the ‘father of control theory’. The Maxwell magic was to introduce differential equations in modelling the behaviour of the flyball governor feedback control system invented by James Watt in 1788. This ground‐breaking contribution by Maxwell introduced the concept of mathematical modelling in the stability analysis of a closed‐loop control system, an idea that soon found many applications and advocates and solved many until then unsolved stability analysis problems. The differential equations encountered in the flyball governor model were nonlinear. By linearising these nonlinear equations, Maxwell managed to introduce the notions of what is today called real poles, imaginary poles and the significance of pole position in the right half plane. This model‐based approach to the analysis of a control system through the differential equations of motion was performed for the first time in the history of control theory. Hence, it is plausible to introduce Maxwell as the pioneer of the model‐based control theory.
In the early twentieth century, control system design methodologies such as the classical control techniques initiated by Bode, Nyquist, Evans and Nichols were all model‐based approaches to control design since the transfer function knowledge of the controlled system is required. The transfer function can be derived from a set of algebraic and differential equations that analytically relate inputs and outputs, or it could be obtained from simple tests performed on the plant with the assumptions of linearity and time invariance. Later in the 1960s, Kalman introduced the model‐based state‐space approach that was more detailed and mathematical.
The only notable data‐driven technique of the first half of the last century is the Ziegler–Nichols proportional‐integral‐derivative (PID) parameter tuning proposed in Ref. [4], which became a widely used control technique in the industry [5]. It is stated in Ref. [4] that “A purely mathematical approach to the study of automatic control is certainly the most desirable course from a standpoint of accuracy and brevity. Unfortunately, however, the mathematics of control involves such a bewildering assortment of exponential and trigonometric functions that the average engineer cannot afford the time necessary to plow through them to a solution of his current problem.” This statement from the eminent control engineers of that time shows the long‐lasting influence of mathematical model‐based design techniques on the control systems design community. In describing their work, they immediately state that ‘the purpose of this paper is to examine the action of the three principal control effects found in present‐day instruments, assign practical values to each effect, see what adjustment of each does to the final control, and give a method for arriving quickly at the optimum settings of each control effect. The paper will thus first endeavor to answer the question: “How can the proper controller adjustments be quickly determined on any control application?”’ This statement can enlighten aspects of the philosophy of the data‐driven control systems that evolved in the late twentieth century onwards.
1.1.2 Model‐based Control System Status Quo
Model‐based control system design is the dominant paradigm in control system education and design. This approach is based on derived analytical models from basic physical laws and equations or models from an identification process. Models are only approximations of reality and cannot capture all the features and characteristics of a plant under control. High‐frequency un‐modelled dynamics are an example, as in robotic and spacecraft applications where the residual vibration modes are not included in the model [6]. The structure of a model‐based control system is shown in Figure 1.1. In the case of adaptive control strategies, the approximate plant model is updated using the input–output data.
Figure 1.1 The structure of a model‐based control system design.
As is shown in Figure 1.1, the plant model, derived from first principles or identified from plant‐measured data, is used to design a fixed‐order controller satisfying the specified closed‐loop requirements. However, the designed controller does not necessarily satisfy the pre‐defined requirements when connected to the real plant, and the closed‐loop performance is limited by the modelling errors. Modelling errors can have many root causes, such as un‐modelled dynamics, unknown or varying plant parameters resulting from changing operating points, equipment ageing or faults and inappropriate model structures.
Modelling errors due to un‐modelled dynamics are justified in the standard practice of model‐based control design when the system is complex and is of a high order, and a low‐order model is employed to facilitate the control design. On the other hand, there can be a tendency to increase the model order to find a suitable model. It is shown in Ref. [7] that this is not generally true if the model has to be used for control design. In fact, the order of a real system is a badly defined concept, and even the most accurate models are only an approximation of the real plant. In the real world, a full‐order model does not exist, and any description is, by definition, an approximation [7]. Model‐based control design can only be employed with confidence in real‐world applications if the model structure is perfectly known.
The issue of model‐based control system design and the paradigm shifts to and from model‐based approaches is further elaborated in Chapter 2.
1.1.3 Challenges of Models in Control Systems Design
The introduction of the state‐space concept by Kalman in 1960, together with the newly established notion of optimality, resulted in a remarkable development of model‐based control design methods. Before Kalman's state‐space theory, most of the control design was based on transfer function models, as is in the Bode and Nyquist plots or the root‐locus method and the Nichols charts for lead–lag compensator design.
In the cases where reliable models were unavailable, or in the case of varying parameters and changing operating conditions, the application of the model‐based control was severely limited. In the mid‐1960s, the system identification strategy evolved. The proposed Maximum Likelihood framework for the identification of input–output models resulted in the prediction error‐type identifiers. The advent of identification theory solved the problem of controlling complex time‐varying plants using model‐based control design methodologies.
Initially, control scientists working on the identification methods aimed at developing sophisticated models and methodologies with the elusive goal of converging to the true system, under the assumption that the true system was in the defined model set. Later, they realised that the theory could best achieve an approximation of the true system and characterise this approximation in terms of bias and variance error on the identified models. Finally, system identification was guided towards a control‐oriented identification. In all the modelling strategies, modelling by first principles or by identification from data, modelling errors are unescapable, and explicit quantification of modelling errors is practically impossible. Hence, the modelling strategies cannot provide adequate practical uncertainty descriptions for control design purposes. Therefore, the first modelling principle given in Ref. [8], that arbitrarily small modelling errors can lead to arbitrarily bad closed‐loop performance, is seriously alarming for control systems designers.
Application of the certainty equivalence principle (see Chapter 2) was based on the early optimistic assumption that it is possible to almost perfectly model the actual plant and the mathematical model obtained from the first principles or by identification from input–output data is valid enough to represent the true system. However, applications in real‐world problems did not meet the expectations of the control scientists and designers. Therefore, an obvious need prevailed to guarantee closed‐loop stability and performance in the model‐based control design approaches. This led to the development of the model‐based approaches of fixed‐parameter robust control and adaptive control system design [9].
The mathematical models derived from the physical laws have been effectively used in practical applications, provided that the following assumptions hold:
Accurately model the actual plant.
Priori bounds on the noise and modelling errors are available.
Also, identification models have been employed in many practical applications. The identified model can capture the main features of the plant, provided that
Compatibility of the selected model structure and parameterisation with the actual plant's characteristics is assumed.
The experiment design is appropriate; that is, for control problems, the selection of the input signal is in accordance with the actual plant's characteristics or the
persistence of excitation
(
PE
) condition.
It is important to note that even in the case of an accurately modelled plant, if the assumptions about the plant characteristics are not met, the mathematical theorems rigorously proving closed‐loop robust stability and performance and parameter convergence are not of practical value.
Hence, in summary, if
An accurate model is unavailable, or
The assumptions regarding the plant do not hold,
the designed model‐based controller, validated by simulations, can lead to an unstable closed‐loop plant or poor closed‐loop performance.
1.1.4 Adaptive and Robust Control Methodologies
Adaptive and robust control systems have successfully controlled many real‐world and industrial plants. However, both strategies require many prior plant assumptions to be mandated by the theory. The key questions are the closed‐loop robust stability and robust performance issues in practical implementations. The assessment of these specifications is not possible a priori, as unforeseen events may occur in practice. Hence, the control engineer must resort to ad hoc methods for a safe and reliable closed‐loop operation. This is often done by performing many tests for many different variations of uncertainties and operating scenarios in the Monte Carlo simulations. However, with the growing plant complexity and the possible test situations, the cost of these heuristic tests increases. Hence, the limitations inherent in the adaptive and robust controllers are clearly observed. Parameter adjustments and robust control and their synergistic design packages are the ultimate solutions of the model‐based control scientists for the utmost guarantee of safe and reliable closed‐loop control.
A closed‐loop system's performance degradation and even instability are almost inevitable when the plant uncertainty is too large or when the parameter changes or structural variations are too large or occur abruptly. The adaptive switching control was introduced as one of the robust adaptive control techniques to handle such situations and lessen the required prior assumptions. This led to the switching supervisory control methods, where a supervisor controller selects the appropriate controller from a controller bank, similar to their ancestor, the gain‐scheduling methodology, which has been and still is widely used in many applications. This mindset and the recently developed selection process based on the falsification theory are regarded as the first attempt towards truly data‐driven, almost plant‐independent adaptive control algorithms [10].
1.2 Data‐driven Control System Design Approach
To circumvent the necessity of deriving offline or online plant models, an alternative approach to control system design is to use the plant data to directly design the controller. This is the data‐driven approach, which appeared at the end of the 1990s. Many plants regularly generate and store huge amounts of operating data at specific instants of time. Such data encompass all the relevant plant information required for control, estimation, performance assessment, decision makings and fault diagnosis. This facilitates the design of data‐driven control systems. The term data‐driven was initially used in computer science and has entered the control system science literature in the past two decades. Although data‐driven control was actually introduced in the first decades of the twentieth century (see Chapter 2), the approach was not called data‐driven at that time. The data‐driven control and data‐based control concepts are differentiated in Ref. [11]. Also, Ref. [12] has elaborated on the difference between data‐based and data‐driven control. It is stated in Ref. [12] that ‘data‐driven control only refers to a closed loop control that starting point and destination are both data. Data‐based control is then a more general term that controllers are designed without directly making use of parametric models, but based on knowledge of the plant input‐output data. Sorted according to the relationship between the control strategy and the measurements, data based control can be summarized as four types: post‐identification control, direct data‐driven control, learning control, and observer integrated control.’
The main features of the data‐driven control approaches can be categorised as follows:
Control system design and analysis employ only the measured plant input–output data. Such data are the controller design's starting point and end criteria for control system performance.
No priori information and assumptions on the plant's dynamics or structure are required.
The controller structure can be predetermined.
The closed‐loop stability, convergence and safe operation issues should be addressed in a data‐driven context.
A designer‐specified cost function is minimised using the measured data to derive the controller parameters.
The structure of a data‐driven control system design is shown in Figure 1.2.
Figure 1.2 The structure of a data‐driven control system design.
Several definitions for data‐driven control are proposed in the literature. The following definition from Ref. [11] is presented.
Definition 1.1 Data‐driven control includes all control theories and methods in which the controller is designed by directly using online or offline input–output data of the controlled system or knowledge from the data processing but not any explicit information from a mathematical model of the controlled process and whose stability, convergence and robustness can be guaranteed by rigorous mathematical analysis under certain reasonable assumptions.
The three key points of this definition are the direct use of the measured input–output data, data modelling rather than first principles modelling or identified modelling, and the guarantee of the results by theoretical analysis.
1.2.1 The Designer Choice: Model‐based or Data‐driven Control?
In general, systems encountered in control systems design can be categorised as simple, complicated, complex and complex adaptive (see Chapter 2 for definitions and more details). In real‐world applications, the controlled plants and all the conditions that they may confront in terms of models and assumptions can be categorised into the following classes:
Class 1
: In this class, it is possible to derive accurate mathematical models from the first principles or the identification‐based schemes, and it can be anticipated that the theoretically indispensable plant assumptions hold. This class includes simple plants and certain well‐modelled complicated systems.
Class 2
: In this class, for some even simple plants, many complicated systems, and a few complex systems, models derived from the first principles or the identification‐based schemes are crudely accurate, but uncertainties can be used to compensate for the modelling error with known bounds, and it can be anticipated that the theoretically indispensable plant assumptions hold.
Class 3
: In this class, conditions are similar to those of class 2, but with the difference that the theoretically indispensable plant assumptions may not be guaranteed to hold.
Class 4
: In this class, for some complicated systems and most complex systems, models derived from the first principles or the identification‐based schemes models are crudely accurate, and the uncertainties used to describe the modelling errors are difficult to obtain accurately, and it can be anticipated that the theoretically indispensable plant assumptions may not hold.
Class 5
: In this class, for a few complicated, some complex, and complex adaptive systems, derivation of models from the first principles or the identification‐based schemes, and reliable uncertainty descriptions are difficult or practically unavailable, and it can be anticipated that the theoretically indispensable plant assumptions do not hold.
The plants falling into the class 1 category have been successfully controlled by the well‐established and well‐documented model‐based control strategies from the classical and state‐space schools of thought. For the plants falling into the class 2 category, both adaptive and robust control schools are well developed and have been successfully implemented in practice. Although there are still many open problems in the adaptive and robust control approaches to reliably control all such plants, solutions are conceivable in the future with the present theoretical tools or some extensions and modifications. Adaptive and robust control methodologies must be selected with much hesitation for the control of the real‐world plants falling into the class 3 category. In such cases, a data‐driven approach would be the recommended choice. For the plants falling into the class 4 category, the data‐driven approach is the strongly recommended choice. Although some of the present adaptive and robust control techniques may be employed in a few class 4 category plants, their application is difficult, time‐consuming and with no guaranteed safety and reliability. In the case of plants falling into the class 5 category, data‐driven control is the sole choice. Many of the future real‐world plants are going in this direction [13], and the control scientist's community must be equipped with a well‐established and strong sufficient theoretical background of data‐driven control theory to handle these control problems. The final point to note is that practical controllers should not be too complex, difficult or non‐economical to use.
To summarise, the main characteristics of data‐driven control systems that make them appealing to selection by a designer are given as follows:
In the data‐driven control approaches, the design methodologies do not explicitly include any parts or the whole of the plant model or are not restricted by the assumptions following the traditional modelling processes. Hence, they are basically
model‐free
designs.
The stability and convergence derivations of the data‐driven approach do not depend on the model and uncertainty modelling accuracy.
In the data‐driven control framework, the inherently born concepts of un‐modelled dynamics and robustness in the model‐based control methodologies are non‐applicable.
1.2.2 Technical Remarks on the Data‐Driven Control Methodologies
The following remarks are important to clarify certain ambiguities and concepts in the current data‐driven control literature:
Remark 1
: In the control literature, the control design techniques that
implicitly
utilise the plant model, such as the direct adaptive control and the subspace‐identification‐based predictive control methods, are sometimes categorised as data‐driven control. However, their controller design, stability and convergence analysis are fundamentally model‐based and also require fulfilling strong assumptions on different model characteristics such as the model order, relative degree, time delay, noise, uncertainty characteristics and bounds. Hence, this book categorises such techniques as model‐based rather than data‐driven.
Remark 2
: In dealing with mathematical models, issues such as nonlinearity, time‐varying parameters and time‐varying model structures cause serious limitations and require complex theoretical handling. However, such issues at the input–output data level are non‐existent. In fact, a truly data‐driven control approach should be able to deal with the above control problems.
Remark 3
: The concepts of robustness and persistency of excitation that appear in adaptive and robust control methodologies are general notions that must also be dealt with in the data‐driven control approach. However, new definitions and frameworks are necessary to pursue these concepts in the data‐driven control context.
Remark 4
: The theory–practice gap in the model‐based approaches is greatly alleviated in the data‐driven approach as the implementations are directly field‐based.
Remark 5
: A very rich literature on the mathematical system theory and immensely valuable experiences in the implementation of model‐based control techniques is available. It would not be desirable or wise to ignore such valuable information. The fact is that plant models can play a vital role in the design of control systems. One aspect is the application of model‐based controller design techniques, if possible. The other aspect would be the cooperation of data‐driven control with other control theories and methods. The relationship between data‐driven and model‐based control should be complementary, and data‐driven approaches can learn and benefit from the established model‐based concepts. The effective employment of existing accurate information about the plant by the data‐driven approach is an open problem for further research.
Remark 6
: Data‐driven control is predicted to be the dominant paradigm of control design science, complementing and substituting the present model‐based paradigm.
1.3 Data‐Driven Control Schemes
In this section, six different data‐driven control schemes are briefly introduced. A classification and a brief survey on the available data‐driven approaches are given in Ref. [11].
1.3.1 Unfalsified Adaptive Control
Unfalsified control was proposed by Safonov in 1995 [14]. The underlying philosophy of unfalsified control is Popper's falsification theory proposed for the demarcation problem in the philosophy of science (see Chapter 2).
Unfalsified control is a data‐driven control theory that utilises physical data to learn or select the appropriate controller via a falsification or elimination process. In the unfalsified feedback control configuration, the goal is to determine a control law C for plant P such that the closed‐loop system T satisfies the desired specifications, where the plant is either unknown or only partially known, and the input–output data are utilised in selecting the control law C. In the unfalsified control, the control system learns when new input–output information enables it to eliminate the candidate controllers from the control bank. The three elements that form the unfalsified control problem are as follows:
Plant input–output data.
The bank of candidate controllers.
Desired closed‐loop performance specification denoted by
T
spec
consisting of the 3‐tuples of the reference input, output and input signals
(
r
,
y
,
u
)
.
Definition 1.2 [15] A controller C is said to be falsified by measurement information if this information is sufficient to deduce that the performance specification (r, y, u) ∈ Tspec ∀ r ∈ ℝ would be violated if that controller were in the feedback loop. Otherwise, the control law C is said to be unfalsified.
Figure 1.3 shows the general structure of the closed‐loop unfalsified control system. The inputs to the falsification logic and algorithm are the plant input–output data, the set of candidate controllers in a control bank or set, and the desired closed‐loop performance. The controllers are verified using a falsification logic and algorithm with performance goals and physical data as its inputs. Note that no plant models are required in the verification process. However, in the design of the controller members of the set of candidate controllers, a plant model can be beneficial. This is, of course, before the selection of the candidate controllers.
Figure 1.3 The unfalsified control structure.
The selection process recursively falsifies candidate controllers that fail to satisfy the desired performance specification. The whole process is designed by the input–output data rather than the mathematical model of controlled plants. The candidate controllers set can be generated utilising priori model information or can be generated or updated based on the plant input–output data.
1.3.1.1 Unfalsified Control: Selected Applications
Model‐based control techniques are the dominant control design methodologies utilised in marine systems. However, as stated in Ref. [16], the emerging field of smart sensors has provided a unique opportunity to have access to online plant measurements at a low price. Data‐driven control algorithms are applied to marine systems by presenting the results of the application of unfalsified control to the problem of dynamic positioning of marine vessels subjected to environmental forces in Ref. [16]. Also, in Ref. [17], robust switching controllers are developed by applying the unfalsified control concept to the autopilot design of extremely manoeuvrable missiles. It is claimed that this can overcome challenging problems of highly nonlinear dynamics, wide variations in plant parameters and strong performance requirements in missiles.
Controlling the flight of micro‐aerial vehicles is a highly challenging task due to the inherent nonlinearities and highly varying longitudinal and lateral derivatives. In Ref. [18], the application of unfalsified control theory is presented for such systems. Also, the unfalsified control concept is employed for the automatic adaptation of linear single‐loop controllers and is successfully implemented in a continuous non‐minimum phase stirred tank reactor model with the Van de Vusse reaction scheme in Ref. [19]. Finally, in Ref. [20], an application of the unfalsified control theory to the design of an adaptive switching controller for a nonlinear robot manipulator is presented, where the manipulator has many factors that are not accurately characterised in a model, such as link flexibility and the effects of actuator dynamics, saturation, friction and mechanical backlash.
1.3.2 Virtual Reference Feedback Tuning
Virtual Reference Feedback Tuning (VRFT) is a general methodology for the controller design of a plant with no available mathematical models. It is a non‐iterative or one‐shot direct method that minimises the control cost in the 2‐norm type by utilising a batch of input–output data collected from the plant, where the optimisation variables are the controller parameters.
VRFT formulates a controller tuning problem as a controller parameter identification problem by introducing a virtual reference signal. It is therefore called a data‐based controller design method in Ref. [21], indicating it is an adaptive method where the adaptation is performed offline. In VRFT, a controller class is selected, and a specific controller is chosen based on the collected data. The selection is performed offline. Initially, a batch of input–output data is collected from the plant, and utilising this data and the virtual reference concept, a controller is selected. The selected controller is then placed in the loop without any further adaptation. Note that the designed controller is verified for stability and performance requirements before its placement in the loop.
To further elaborate on the one‐shot direct data‐based nature of VRFT, it returns a controller without requiring iterations and/or further access to the plant for experiments after the batch input–output plant data collection. This is possible because the design engine inside VRFT is intrinsically global, and no gradient‐descent techniques are involved. The input signals must be exciting enough, and in the case of poor excitation, the selected controller can be inappropriate with non‐satisfactory closed‐loop responses. The results obtained by VRFT are related to the information content present in the given batch of input–output data. The one‐shot feature of VRFT is practically attractive because [21]:
It is low‐demanding, i.e. access to the plant for multiple experiments is not necessary, and therefore the normal operation of the plant is not halted.
It does not suffer from local minima and initialisation problems.
The virtual reference concept is fundamental to VRFT; its basic idea is presented in Ref. [22]. Let the controller C(z; θ) be such that the closed‐loop system transfer function is as a desired reference model M(z). Consider any reference signal r(t), the model reference output will be M(z)r(t). Hence, a necessary condition for the closed‐loop system to have the same transfer function as the reference model is that the output of the two systems is the same for a given . In typical model reference controllers, such as the model reference adaptive control, for a given reference input and reference model, the controller C(z; θ) is designed to satisfy the above condition. However, in the model reference designs, it is assumed that the plant model is available or its structure is known with certain given assumptions.
The basic idea of the virtual reference approach is an intelligent selection of
