Ebook: Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems

Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems begins with an introduction and extensive literature survey. The text proceeds to cover the field of H∞ time-delay linear systems where the issues of stability and L2−gain are presented and solved for nominal and uncertain stochastic systems, via the input-output approach. It presents solutions to the problems of state-feedback, filtering, and measurement-feedback control for these systems, for both the continuous- and the discrete-time settings. In the continuous-time domain, the problems of reduced-order and preview tracking control are also presented and solved. The second part of the monograph concerns non-linear stochastic state- multiplicative systems and covers the issues of stability, control and estimation of the systems in the H∞ sense, for both continuous-time and discrete-time cases. The book also describes special topics such as stochastic switched systems with dwell time and peak-to-peak filtering of nonlinear stochastic systems. The reader is introduced to six practical engineering- oriented examples of noisy state-multiplicative control and filtering problems for linear and nonlinear systems. The book is rounded out by a three-part appendix containing stochastic tools necessary for a proper appreciation of the text: a basic introduction to stochastic control processes, aspects of linear matrix inequality optimization, and MATLAB codes for solving the L2-gain and state-feedback control problems of stochastic switched systems with dwell-time. Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems will be of interest to engineers engaged in control systems research and development, to graduate students specializing in stochastic control theory, and to applied mathematicians interested in control problems. The reader is expected to have some acquaintance with stochastic control theory and state-space-based optimal control theory and methods for linear and nonlinear systems.

Table of Contents

Cover

Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems

ISBN 9781447150695 ISBN 9781447150701

Preface

Contents

1 Introduction

1.1 Stochastic State-Multiplicative Time Delay Systems
1.2 The Input-Output Approach for Delayed Systems
1.2.1 Continuous-Time Case
1.2.2 Discrete-Time Case
1.3 Non Linear Control of Stochastic State-Multiplicative Systems
1.3.1 The Continuous-Time Case
1.3.2 Stability
1.3.3 Dissipative Stochastic Systems
1.3.4 The Discrete-Time-Time Case
1.3.5 Stability
1.3.6 Dissipative Discrete-Time Nonlinear Stochastic Systems
1.4 Stochastic Processes - Short Survey
1.5 Mean Square Calculus
1.6 White Noise Sequences and Wiener Process
1.6.1 Wiener Process
1.6.2 White Noise Sequences
1.7 Stochastic Differential Equations
1.8 Ito Lemma
1.9 Nomenclature
1.10 Abbreviations

2 Time Delay Systems - H-infinity Control and General-Type Filtering

2.1 Introduction
2.2 Problem Formulation and Preliminaries
2.2.1 The Nominal Case
2.2.2 The Robust Case - Norm-Bounded Uncertain Systems
2.2.3 The Robust Case - Polytopic Uncertain Systems
2.3 Stability Criterion
2.3.1 The Nominal Case - Stability
2.3.2 Robust Stability - The Norm-Bounded Case
2.3.3 Robust Stability - The Polytopic Case
2.4 Bounded Real Lemma
2.4.1 BRL for Delayed State-Multiplicative Systems - The Norm-Bounded Case
2.4.2 BRL - The Polytopic Case
2.5 Stochastic State-Feedback Control
2.5.1 State-Feedback Control - The Nominal Case
2.5.2 Robust State-Feedback Control - The Norm-Bounded Case
2.5.3 Robust Polytopic State-Feedback Control
2.5.4 Example - State-Feedback Control
2.6 Stochastic Filtering for Delayed Systems
2.6.1 Stochastic Filtering - The Nominal Case
2.6.2 Robust Filtering - The Norm-Bounded Case
2.6.3 Robust Polytopic Stochastic Filtering
2.6.4 Example - Filtering
2.7 Stochastic Output-Feedback Control for Delayed Systems
2.7.1 Stochastic Output-Feedback Control - The Nominal Case
2.7.2 Example - Output-Feedback Control
2.7.3 Robust Stochastic Output-Feedback Control - The Norm-Bounded Case
2.7.4 Robust Polytopic Stochastic Output-Feedback Control
2.8 Static Output-Feedback Control
2.9 Robust Polytopic Static Output-Feedback Control
2.10 Conclusions

3 Reduced-Order H-infinity Output-Feedback Control

3.1 Introduction
3.2 Problem Formulation
3.3 The Delayed Stochastic Reduced-Order H Control 8
3.4 Conclusions

4 Tracking Control with Preview

4.1 Introduction
4.2 Problem Formulation
4.3 Stability of the Delayed Tracking System
4.4 The State-Feedback Tracking
4.5 Example
4.6 Conclusions
4.7 Appendix

5 H-infinity Control and Estimation of Retarded Linear Discrete-Time Systems

5.1 Introduction
5.2 Problem Formulation
5.3 Mean-Square Exponential Stability
5.3.1 Example - Stability
5.4 The Bounded Real Lemma
5.4.1 Example - BRL
5.5 State-Feedback Control
5.5.1 Example - Robust State-Feedback
5.6 Delayed Filtering
5.6.1 Example - Filtering
5.7 Conclusions

6 H-infinity-Like Control for Nonlinear Stochastic Syste8 ms

6.1 Introduction
6.2 Stochastic H-infinity SF Control
6.3 The In.nite-Time Horizon Case: A Stabilizing Controller
6.3.1 Example
6.4 Norm-Bounded Uncertainty in the Stationary Case
6.4.1 Example
6.5 Conclusions

7 Non Linear Systems - H-infinity-Type Estimation

7.1 Introduction
7.2 Stochastic H-infinity Estimation
7.2.1 Stability
7.3 Norm-Bounded Uncertainty
7.3.1 Example
7.4 Conclusions

8 Non Linear Systems - Measurement Output-Feedback Control

8.1 Introduction and Problem Formulation
8.2 Stochastic H-infinity OF Control
8.2.1 Example
8.2.2 The Case of Nonzero G2
8.3 Norm-Bounded Uncertainty
8.4 In.nite-Time Horizon Case: A Stabilizing H Controller 8
8.5 Conclusions

9 l2-Gain and Robust SF Control of Discrete-Time NL Stochastic Systems

9.1 Introduction
9.2 Su.cient Conditions for l2-Gain= .:ASpecial Case
9.3 Norm-Bounded Uncertainty
9.4 Conclusions

10 H-infinity Output-Feedback Control of Discrete-Time Systems

10.1 Su.cient Conditions for l2-Gain= .:ASpecial Case
10.1.1 Example
10.2 The OF Case
10.2.1 Example
10.3 Conclusions

11 H-infinity Control of Stochastic Switched Systems with Dwell Time

11.1 Introduction
11.2 Problem Formulation
11.3 Stochastic Stability
11.4 Stochastic L2-Gain
11.5 H-infinity State-Feedback Control
11.6 Example - Stochastic L2-Gain Bound
11.7 Conclusions

12 Robust L-infinity-Induced Control and Filtering

12.1 Introduction
12.2 Problem Formulation and Preliminaries
12.3 Stability and P2P Norm Bound of Multiplicative Noisy Systems
12.4 P2P State-Feedback Control
12.5 P2P Filtering
12.6 Conclusions

13 Applications

13.1 Reduced-Order Control
13.2 Terrain Following Control
13.3 State-Feedback Control of Switched Systems
13.4 Non Linear Systems: Measurement Output-Feedback Control
13.5 Discrete-Time Non Linear Systems: l2-Gain
13.6 L-infinity Control and Estimation

A Appendix: Stochastic Control Processes - Basic Concepts

B The LMI Optimization Method

C Stochastic Switching with Dwell Time - Matlab Scripts

References

Index