Variance-Constrained Multi-Objective Stochastic Control and Filtering

Lifeng Ma received the Ph.D. degree in Control Science and Engineering in 2010 from Nanjing University of Science and Technology, Nanjing, China. From August 2008 to February 2009, he was a Visiting Scholar in the Department of Information Systems and Computing, Brunel University, London, UK. From January 2010 to March 2010 and from May 2011 to September 2011, he was a Research Associate in the Department of Mechanical Engineering, the University of Hong Kong. He is now a Lecturer with the School of Automation, Nanjing University of Science and Technology, Nanjing, China. Dr. Ma's current research interests include nonlinear control and stochastic control. He is a very active reviewer for many international journals.Zidong Wang is currently Professor of Dynamical Systems and Computing in the Department of Information Systems and Computing, Brunel University, UK. From 1990 to 2002, he held teaching and research appointments in universities in China, Germany and the UK. Prof. Wang's research interests include dynamical systems, signal processing, bioinformatics, control theory and applications. He has published more than 280 papers in refereed international journals. He is a holder of the Alexander von Humboldt Research Fellowship of Germany, the JSPS Research Fellowship of Japan, William Mong Visiting Research Fellowship of Hong Kong. He serves as the Executive Editor for Systems Science and Control Engineering (Taylor and Francis) and an Associate Editor for 11 international journals including five IEEE Transactions. Prof. Wang is a Fellow of the IEEE, a Fellow of the Royal Statistical Society and a member of the program committee for many international conferences.Yuming Bo received his BSc degree in Automatic Control in 1984, his MSc degree in Automatic Control in 1987 and PhD degree in Control Theory and Control Engineering in 2005, all from Nanjing University of Science and Technology, Nanjing, China. He is now a Professor of Control Theory and Control Engineering in the School of Automation at Nanjing University of Science and Technology, Nanjing, China. His research interests include stochastic control and estimation, computer communication and programming. He has published more than 20 papers in refereed journals and served as an associate editor for two journals.

• Preface viiAcknowledgements ixList of Abbreviations xi1 Introduction 11.1 Analysis and Synthesis of Nonlinear Stochastic Systems 21.1.1 Nonlinear Systems 31.1.2 Stochastic Systems 41.2 Multi-Objective Control and Filtering with Variance Constraints 51.2.1 Covariance Control Theory 51.2.2 Multiple Performance Requirements 71.2.3 Design Techniques for Nonlinear Stochastic Systems with Variance Constraints 91.2.4 A Special Case of Multi-Objective Design: Mixed H2/H1 Control/Filtering 111.3 Outline 122 Robust H1 Control with Variance Constraints 172.1 Problem Formulation 182.2 Stability, H1 Performance and Variance Analysis 202.2.1 Stability, H1 Performance Analysis 212.2.2 Variance Analysis 232.3 Robust Controller Design 272.4 Numerical Example 302.5 Summary 333 Robust Mixed H2=H1 Filtering 413.1 System Description and Problem Formulation 423.2 Algebraic Characterizations for Robust H2=H1 Filtering 443.2.1 Robust H2 Filtering 443.2.2 Robust H1 Filtering 503.3 Robust H2=H1 Filter Design Techniques 513.4 An Illustrative Example 603.5 Summary 624 Filtering with Missing Measurements 634.1 Problem Formulation 644.2 Stability and Variance Analysis 674.3 Robust Filter Design 714.4 Numerical Example 754.5 Summary 785 Robust Fault-Tolerant Control 875.1 Problem Formulation 885.2 Stability and Variance Analysis 905.3 Robust Controller Design 925.4 Numerical Example 985.5 Summary 1036 Robust H2 SMC 1056.1 The System Model 1066.2 Robust H2 Sliding Mode Control 1076.2.1 Switching Surface 1076.2.2 Performances of the Sliding Motion 1086.2.3 Computational Algorithm 1146.3 Sliding Mode Controller 1156.4 Numerical Example 1166.5 Summary 1187 Dissipative Control with Degraded Measurements 1257.1 Problem Formulation 1267.2 Stability, Dissipativity and Variance Analysis 1297.3 Observer-Based Controller Design 1347.3.1 Solvability of Multi-Objective Control Problem 1347.3.2 Computational Algorithm 1397.4 Numerical Example 1407.5 Summary 1428 Variance-Constrained H1 Control with Multiplicative Noises 1458.1 Problem Formulation 1468.2 Stability, H1 Performance, Variance Analysis 1478.2.1 Stability 1488.2.2 H1 performance 1508.2.3 Variance analysis 1528.3 Robust State Feedback Controller Design 1538.4 A Numerical Example 1568.5 Summary 1579 Robust Finite-Horizon H1 Control 1599.1 Problem Formulation 1609.2 Performance Analysis 1629.2.1 H1 Performance 1629.2.2 Variance Analysis 1649.3 Robust Finite Horizon Controller Design 1679.4 Numerical Example 1719.5 Summary 17310 Finite-Horizon Filtering with Degraded Measurements 17710.1 Problem Formulation 17810.2 Performance Analysis 18110.2.1 H1 Performance Analysis 18110.2.2 System Covariance Analysis 18610.3 Robust Filter Design 18710.4 Numerical Example 19010.5 Summary 19111 Mixed H2=H1 Control with Randomly Occurring Nonlinearities: the Finite-Horizon Case 19711.1 Problem Formulation 19911.2 H1 Performance 20011.3 Mixed H2=H1 Controller Design 20411.3.1 State-Feedback Controller Design 20411.3.2 Computational Algorithm 20711.4 Numerical Example 20711.5 Summary 21112 Finite-Horizon H2=H1 Control of MJSs with Sensor Failures 21312.1 Problem Formulation 21412.2 H1 Performance 21612.3 Mixed H2=H1 Controller Design 22012.3.1 Controller Design 22012.3.2 Computational Algorithm 22412.4 Numerical Example 22412.5 Summary 22713 Finite-Horizon Control with ROSF 22913.1 Problem Formulation 23013.2 H1 And Covariance Performances Analysis 23413.2.1 H1 Performance 23413.2.2 Covariance Analysis 23813.3 Robust Finite-Horizon Controller Design 24013.3.1 Controller Design 24013.3.2 Computational Algorithm 24313.4 Numerical Example 24313.5 Summary 24414 Finite-Horizon H2=H1 Control with Actuator Failures 24714.1 Problem Formulation 24814.2 H1 Performance 25114.3 Multi-Objective Controller Design 25314.3.1 Controller Design 25314.3.2 Computational Algorithm 25614.4 Numerical Example 25714.5 Summary 25915 Conclusions and Future Topics 261References 263