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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Serie: Wiley Series in Dynamics and Control of Electromechanical Systems
- Sprache: Englisch
- Unifies existing and emerging concepts concerning multi-objective control and stochastic control with engineering-oriented phenomena
- Establishes a unified theoretical framework for control and filtering problems for a class of discrete-time nonlinear stochastic systems with consideration to performance
- Includes case studies of several nonlinear stochastic systems
- Investigates the phenomena of incomplete information, including missing/degraded measurements, actuator failures and sensor saturations
- Considers both time-invariant systems and time-varying systems
- Exploits newly developed techniques to handle the emerging mathematical and computational challenges
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Veröffentlichungsjahr: 2015
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Table of Contents
Cover
Wiley Series in Dynamics and Control of Electromechanical Systems
Title Page
Copyright
Preface
Series Preface
Acknowledgements
List of Abbreviations
List of Figures
Chapter 1: Introduction
1.1 Analysis and Synthesis of Nonlinear Stochastic Systems
1.2 Multi-Objective Control and Filtering with Variance Constraints
1.3 Outline
Chapter 2: Robust H
∞
Control with Variance Constraints
2.1 Problem Formulation
2.2 Stability,
H
∞
Performance, and Variance Analysis
2.3 Robust Controller Design
2.4 Numerical Example
2.5 Summary
Chapter 3: Robust Mixed H
2
/H
∞
Filtering
3.1 System Description and Problem Formulation
3.2 Algebraic Characterizations for Robust
H
2
/
H
∞
Filtering
3.3 Robust
H
2
/
H
∞
Filter Design Techniques
3.4 An Illustrative Example
3.5 Summary
Chapter 4: Robust Variance-Constrained Filtering with Missing Measurements
4.1 Problem Formulation
4.2 Stability and Variance Analysis
4.3 Robust Filter Design
4.4 Numerical Example
4.5 Summary
Chapter 5: Robust Fault-Tolerant Control with Variance Constraints
5.1 Problem Formulation
5.2 Stability and Variance Analysis
5.3 Robust Controller Design
5.4 Numerical Example
5.5 Summary
Chapter 6: Robust H2 Sliding Mode Control
6.1 The System Model
6.2 Robust
H
2
Sliding Mode Control
6.3 Sliding Mode Controller
6.4 Numerical Example
6.5 Summary
Chapter 7: Variance-Constrained Dissipative Control with Degraded Measurements
7.1 Problem Formulation
7.2 Stability, Dissipativity, and Variance Analysis
7.3 Observer-Based Controller Design
7.4 Numerical Example
7.5 Summary
Chapter 8: Variance-Constrained H
∞
Control with Multiplicative Noises
8.1 Problem Formulation
8.2 Stability,
H
∞
Performance, and Variance Analysis
8.3 Robust State Feedback Controller Design
8.4 Numerical Example
8.5 Summary
Chapter 9: Robust H
∞
Control with Variance Constraints: the Finite-Horizon Case
9.1 Problem Formulation
9.2 Performance Analysis
9.3 Robust Finite-Horizon Controller Design
9.4 Numerical Example
9.5 Summary
Chapter 10: Error Variance-Constrained H
∞
Filtering with Degraded Measurements: The Finite-Horizon Case
10.1 Problem Formulation
10.2 Performance Analysis
10.3 Robust Filter Design
10.4 Numerical Example
10.5 Summary
Chapter 11: Mixed H
2
/H
∞
Control with Randomly Occurring Nonlinearities: The Finite-Horizon Case
11.1 Problem Formulation
11.2
H
∞
Performance
11.3 Mixed
H
2
/
H
∞
Controller Design
11.4 Numerical Example
11.5 Summary
Chapter 12: Mixed H
2
/H
∞
Control with Markovian Jump Parameters and Probabilistic Sensor Failures: The Finite-Horizon Case
12.1 Problem Formulation
12.2
H
∞
Performance
12.3 Mixed
H
2
/
H
∞
Controller Design
12.4 Numerical Example
12.5 Summary
Chapter 13: Robust Variance-Constrained H
∞
Control with Randomly Occurring Sensor Failures: The Finite-Horizon Case
13.1 Problem Formulation
13.2
H
∞
and Covariance Performance Analysis
13.3 Robust Finite-Horizon Controller Design
13.4 Numerical Example
13.5 Summary
Chapter 14: Mixed H
2
/H
∞
Control with Actuator Failures: the Finite-Horizon Case
14.1 Problem Formulation
14.2
H
∞
Performance
14.3 Multi-Objective Controller Design
14.4 Numerical Example
14.5 Summary
Chapter 15: Conclusions and Future Topics
15.1 Concluding Remarks
15.2 Future Research
References
Index
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Begin Reading
List of Illustrations
Chapter 1: Introduction
Figure 1.1 Architecture of surveyed contents.
Figure 1.2 The framework of this book
Chapter 2: Robust H
∞
Control with Variance Constraints
Figure 2.1 The white sequence
Figure 2.13 The state variance evolution for Case 3
Figure 2.14 The
H
∞
performance versus the optimal value
Figure 2.2 The state evolution of the uncontrolled system for Case 1
Figure 2.4 The state evolution of the uncontrolled system for Case 2
Figure 2.6 The state evolution of the uncontrolled system for Case 3
Figure 2.3 The state evolution of the controlled system for Case 1
Figure 2.5 The state evolution of the controlled system for Case 2
Figure 2.7 The state evolution of the controlled system for Case 3
Figure 2.8 The stochastic nonlinearity for Case 1,
Figure 2.9 The stochastic nonlinearity for Case 2,
Figure 2.10 The stochastic nonlinearity for Case 3,
Figure 2.11 The state variance evolution for Case 1
Figure 2.12 The state variance evolution for Case 2
Chapter 4: Robust Variance-Constrained Filtering with Missing Measurements
Figure 4.1 The actual state and its estimate for Case 1
Figure 4.13 The comparison between filtering error variance of different data missing rates
Figure 4.3 The actual state and its estimate for Case 1
Figure 4.5 The actual state and its estimate for Case 2
Figure 4.7 The actual state and its estimate for Case 2
Figure 4.9 The actual state and its estimate for Case 3
Figure 4.11 The actual state and its estimate for Case 3
Figure 4.4 The filtering error variances for Case 1
Figure 4.8 The filtering error variances for Case 2
Figure 4.12 The filtering error variances for Case 3
Figure 4.14 The stochastic nonlinearity for Case 1
Figure 4.16 The stochastic nonlinearity for Case 3
Chapter 5: Robust Fault-Tolerant Control with Variance Constraints
Figure 5.1 Single degree-of-freedom structure with active tendon control
Figure 5.2 The state responses of the uncontrolled system
Figure 5.4 The steady-state variances of the closed-loop system
Figure 5.3 The response of of the controlled system
Figure 5.5 The control input
Figure 5.7 The nonlinearity
Chapter 6: Robust H2 Sliding Mode Control
Figure 6.1 The trajectories of state
Figure 6.12 The matched nonlinearity
Chapter 7: Variance-Constrained Dissipative Control with Degraded Measurements
Figure 7.1 System state and its estimate
Figure 7.2 System state and its estimate
Figure 7.3 The individual steady state variance of each state
Figure 7.4 The controlled output signal
Chapter 9: Robust H
∞
Control with Variance Constraints: the Finite-Horizon Case
Figure 9.1 The variance upper bounds and actual variances
Figure 9.7 The stochastic nonlinearity
Chapter 10: Error Variance-Constrained H
∞
Filtering with Degraded Measurements: The Finite-Horizon Case
Figure 10.1 The state and its estimate for Case 1
Figure 10.9 The stochastic nonlinearity
Chapter 13: Robust Variance-Constrained H
∞
Control with Randomly Occurring Sensor Failures: The Finite-Horizon Case
Figure 13.1 The variance upper bound and actual variance
Figure 13.4 The system output
List of Tables
Chapter 9: Robust H
∞
Control with Variance Constraints: the Finite-Horizon Case
Table 9.1 The obtained controller parameters
Chapter 12: Mixed H
2
/H
∞
Control with Markovian Jump Parameters and Probabilistic Sensor Failures: The Finite-Horizon Case
Table 12.1 The random mode
Wiley Series in Dynamics and Control of Electromechanical Systems
Variance-Constrained Multi-Objective Stochastic Control and Filtering
Ma, Wang and Bo
April 2015
Sliding Mode Control of Uncertain Parameter-Switching Hybrid Systems
Wu, Shi and Su
July 2014
Algebraic Identification and Estimation Methods in Feedback Control Systems
Sira-Ramìrez, Garcìa Rodrìguez, Cortes Romero and Luviano Juárez
May 2014
Variance-Constrained Multi-Objective Stochastic Control and Filtering
Lifeng Ma
Nanjing University of Science and Technology, China
Zidong Wang
Brunel University, United Kingdom
Yuming Bo
Nanjing University of Science and Technology, China
This edition first published 2015
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ISBN: 9781118929490
Preface
Nonlinearity and stochasticity are arguably two of the main resources in reality that have resulted in considerable system complexity. Therefore, recently, control and filtering of nonlinear stochastic systems have been an active branch within the general research area of nonlinear control problems. In engineering practice, it is always desirable to design systems capable of simultaneously guaranteeing various performance requirements to meet the ever-increasing practical demands toward the simultaneous satisfaction of performances such as stability, robustness, precision, and reliability, among which the system covariance plays a vital role in system analysis and synthesis due to the fact that several design objectives, such as stability, time-domain and frequency-domain performance specifications, robustness, and reliability, can be directly related to steady-state covariance of the closed-loop systems.
In this book, we discuss the multi-objective control and filtering problems for a class of nonlinear stochastic systems with variance constraints. The stochastic nonlinearities taken into consideration are quite general and could cover several classes of well-studied nonlinear stochastic systems. The content of this book is divided mainly into two parts. In the first part, we focus on the variance-constrained control and filtering problems for time-invariant nonlinear stochastic systems subject to different kinds of complex situations, including measurements missing, actuator failures, output degradation, etc. Some sufficient conditions are derived for the existence of the desired controllers and filters in terms of the linear matrix inequalities (LMIs). The control and filtering problems with multiple performance specifications are considered in the second part for time-varying nonlinear stochastic systems. In this part, several design techniques including recursive linear matrix inequalities (RLMIs), game theory, and gradient method have been employed to develop the desired controllers and filters capable of simultaneously achieving multiple pre-specified performance requirements.
The compendious frame and description of the book are given as follows: Chapter 1 introduces the recent advances on variance-constrained multi-objective control and filtering problems for nonlinear stochastic systems and the outline of the book. Chapter 2 is concerned with the H∞ control problem for a class of nonlinear stochastic systems with variance constraints. Chapter 3 deals with the mixed H2/H∞ filtering problem for a type of time-invariant nonlinear stochastic systems. In Chapter 4, the variance-constrained filtering problem is solved in the case of missing measurements. Chapter 5 discusses the controller design problem with variance constraints when the actuator is confronted with possible failures. The sliding mode control problem is investigated in Chapter 6 for a class of nonlinear discrete-time stochastic systems with H2 specification. In Chapter 7, the dissipativity performance is taken into consideration with variance performance and the desired control scheme is given. For a special type of nonlinear stochastic system, namely, systems with multiplicative noises, Chapter 8 deals with the robust controller design problem with simultaneous consideration of variance constraints and H∞ requirement. For time-varying nonlinear stochastic systems, Chapters 9 and 10 investigate the H∞ control and filtering problems over a finite horizon, respectively. Chapters 11 and 12 discuss the mixed H2/H∞ control problems, taking the randomly occurring nonlinearities (RONs) and Markovian jump parameters into consideration, respectively. Chapters 13 and 14 give the solutions to the multi-objective control problems for time-varying nonlinear stochastic systems in the presence of sensor and actuator failures, respectively. Chapter 15 gives the conclusions and some possible future research topics.
This book is a research monograph whose intended audience is graduate and postgraduate students as well as researchers.
Series Preface
Electromechanical Systems permeate the engineering and technology fields in aerospace, automotive, mechanical, biomedical, civil/structural, electrical, environmental, and industrial systems. The Wiley Book Series on dynamics and control of electromechanical systems covers a broad range of engineering and technology in these fields. As demand increases for innovation in these areas, feedback control of these systems is becoming essential for increased productivity, precision operation, load mitigation, and safe operation. Furthermore, new applications in these areas require a reevaluation of existing control methodologies to meet evolving technological requirements. An example involves distributed control of energy systems. The basics of distributed control systems are well documented in several textbooks, but the nuances of its use for future applications in the evolving area of energy system applications, such as wind turbines and wind farm operations, solar energy systems, smart grids, and energy generation, storage and distribution, require an amelioration of existing distributed control theory to specific energy system needs. The book series serves two main purposes: (1) a delineation and explication of theoretical advancements in electromechanical system dynamics and control and (2) a presentation of application driven technologies in evolving electromechanical systems.
This book series embraces the full spectrum of dynamics and control of electromechanical systems from theoretical foundations to real world applications. The level of the presentation should be accessible to senior undergraduate and first-year graduate students, and should prove especially well suited as a self-study guide for practicing professionals in the fields of mechanical, aerospace, automotive, biomedical, and civil/structural engineering. The aim is to provide an interdisciplinary series ranging from high-level undergraduate/graduate texts, explanation and dissemination of science and technology and good practice, through to important research that is immediately relevant to industrial development and practical applications. It is hoped that this new and unique perspective will be of perennial interest to students, scholars, and employees in these engineering disciplines. Suggestions for new topics and authors for the series are always welcome.
This book, Variance-Constrained Multi-Objective Stochastic Control and Filtering, has the objective of providing a theoretical foundation as well as practical insights on the topic at hand. It is broken down into two essential parts: (1) variance-constrained control and filtering problems for time-invariant nonlinear stochastic systems and (2) designing controllers and filters capable of simultaneously achieving multiple pre-specified performance requirements. The book is accessible to readers who have a basic understanding of stochastic processes, control, and filtering theory. It provides detailed derivations from first principles to allow the reader to thoroughly understand the particular topic. It also provides several illustrative examples to bridge the gap between theory and practice. This book is a welcome addition to the Wiley Electromechanical Systems Series because no other book is focused on the topic of stochastic control and filtering with a specific emphasis on variance-constrained multi-objective systems.
Mark J. Balas, John L. Crassidis, and Florian Holzapfel
Acknowledgements
The authors would like to express their deep appreciation to those who have been directly involved in various aspects of the research leading to this book. Special thanks go to Professor James Lam from the University of Hong Kong and Professor Xiaohui Liu from Brunel University of the United Kingdom for their valuable suggestions, constructive comments, and support. We also extend our thanks to many colleagues who have offered support and encouragement throughout this research effort. In particular, we would like to acknowledge the contributions from Derui Ding, Hongli Dong, Xiao He, Jun Hu, Liang Hu, Xiu Kan, Zhenna Li, Jinling Liang, Qinyuan Liu,Yang Liu, Yurong Liu, Bo Shen, Guoliang Wei, Nianyin Zeng, Sunjie Zhang, and Lei Zou. Finally, the authors are especially grateful to their families for their encouragement and never-ending support when it was most required.
The writing of this book was supported in part by the National Natural Science Foundation of China under Grants 61304010, 61273156, 61134009, 61004067, and 61104125, the Natural Science Foundation of Jiangsu Province under Grant BK20130766, the Postdoctoral Science Foundation of China under Grant 2014M551598, the International Postdoctoral Exchange Fellowship Program from China Postdoctoral Council, the Engineering and Physical Sciences Research Council (EPSRC) of the UK, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany. The support of these organizations is gratefully acknowledged.
List of Abbreviations
The
-dimensional Euclidean space.
The set of non-negative integers.
The set of all
real matrices.
The Euclidean norm in
.
The space of square-integrable vector functions over
.
The spectral radius of matrix
.
The eigenvalue of matrix
.
The trace of matrix
.
The Kronecker product of matrices.
The stack that forms a vector out of the columns of matrix
.
Equal to
.
The occurrence probability of the event “
”.
The expectation of stochastic variable
.
The expectation of
conditional on
,
, and
are both stochastic variables.
The identity matrix of compatible dimension.
The
List of Figures
1.1
Architecture of surveyed contents
1.2
The framework of this book
2.1
The white sequence ω(
k
)
2.2
The state evolution
x
(
k
) of the uncontrolled system for Case 1
2.3
The state evolution
x
(
k
) of the controlled system for Case 1
2.4
The state evolution
x
(
k
) of the uncontrolled system for Case 2
2.5
The state evolution
x
(
k
) of the controlled system for Case 2
2.6
The state evolution
x
(
k
) of the uncontrolled system for Case 3
2.7
The state evolution
x
(
k
) of the controlled system for Case 3
2.8
The stochastic nonlinearity
f
(
x
(
k
)) for Case 1,
k
∈ [0, 100]
2.9
The stochastic nonlinearity
f
(
x
(
k
)) for Case 2,
k
∈ [0, 100]
2.10
The stochastic nonlinearity
f
(
x
(
k
)) for Case 3,
k
∈ [0, 100]
2.11
The state variance evolution for Case 1
2.12
The state variance evolution for Case 2
2.13
The state variance evolution for Case 3
2.14
The
H
∞
performance
versus the optimal value
4.1
The actual state
and its estimate
for Case 1
4.2
The actual state
and its estimate
for Case 1
4.3
The actual state
and its estimate
for Case 1
4.4
The filtering error variances for Case 1
4.5
The actual state
and its estimate
for Case 2
4.6
The actual state
and its estimate
for Case 2
4.7
The actual state
and its estimate
for Case 2
4.8
The filtering error variances for Case 2
4.9
The actual state
and its estimate
for Case 3
4.10
The actual state
and its estimate
for Case 3
4.11
The actual state
and its estimate
for Case 3
4.12
The filtering error variances for Case 3
4.13
The comparison between filtering error variance of different data missing rates
4.14
The stochastic nonlinearity
f
(
x
(
k
)) for Case 1
4.15
The stochastic nonlinearity
f
(
x
(
k
)) for Case 2
4.16
The stochastic nonlinearity
f
(
x
(
k
)) for Case 3
5.1
Single degree-of-freedom structure with active tendon control
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