This book presents analysis and design for a class of stochastic systems with semi-Markovian jump parameters. It explores systematic analysis of semi-Markovian jump systems via sliding mode control strategy which makes up the shortages in the analysis and design of stochastic systems. This text provides a novel estimation method to deal with the stochastic stability of semi-Markovian jump systems along with design of novel integral sliding surface. Finally, Takagi-Sugeno fuzzy model approach is brought to deal with system nonlinearities and fuzzy sliding mode control laws are provided to ensure the stabilization purpose.
Features:
- Presents systematic work on sliding mode control (SMC) of semi-Markvoain jump systems.
- Explores SMC methods, such as fuzzy SMC, adaptive SMC, with the presence of generally uncertain transition rates.
- Provides novel method in dealing with stochastic systems with unknown switching information.
- Proposes more general theories for semi-Markovian jump systems with generally uncertain transition rates.
- Discusses practical examples to verify the effectiveness of SMC theory in semi-Markovian jump systems.
This book aims at graduate and postgraduate students and for researchers in all engineering disciplines, including mechanical engineering, electrical engineering and applied mathematics, control engineering, signal processing, process control, control theory and robotics.
This book presents analysis and design for a class of stochastic systems with semi-Markovian jump parameters. It explores systematic analysis of semi-Markovian jump systems via sliding mode control strategy which makes up the shortages in the analysis and design of stochastic systems.
| Preface |
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ix | |
| Acknowledgment |
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xi | |
| Authors |
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xiii | |
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1 | (20) |
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1 | (4) |
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1.1.1 Basic Concepts of SMC |
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1 | (3) |
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1.1.2 Implementation of SMC |
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4 | (1) |
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1.1.2.1 Sliding Surface Design |
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5 | (1) |
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1.1.2.2 Sliding Mode Controller Design |
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5 | (1) |
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1.2 Semi-Markovian Jump Systems |
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5 | (6) |
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1.2.1 Review of Markovian Jump Systems |
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5 | (3) |
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1.2.2 Description of Semi-Markovian Jump Systems |
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8 | (3) |
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11 | (2) |
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1.4 Some Useful Definitions and Lemmas |
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13 | (1) |
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1.5 Abbreviations and Notations |
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14 | (7) |
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15 | (6) |
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Chapter 2 Stochastic Stability of Semi-Markovian Jump Systems with Generally Uncertain Transition Rates |
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21 | (18) |
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21 | (1) |
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22 | (4) |
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2.3 Stochastic Stability Analysis |
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26 | (8) |
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34 | (2) |
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36 | (3) |
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37 | (2) |
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Chapter 3 Fuzzy Integral Sliding Mode Control of Semi-Markovian Jump Systems |
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39 | (26) |
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39 | (1) |
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40 | (2) |
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42 | (13) |
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3.3.1 Sliding Surface Design |
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43 | (2) |
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3.3.2 Stochastic Stability Analysis |
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45 | (7) |
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3.3.4 Reachability of Sliding Surface |
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52 | (3) |
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55 | (6) |
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61 | (4) |
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61 | (4) |
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Chapter 4 Fuzzy Sliding Mode Control for Finite-Time Synthesis of Semi-Markovian Jump Systems |
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65 | (22) |
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65 | (1) |
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66 | (3) |
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69 | (12) |
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4.3.1 Finite-Time Reachability of Sliding Surface in T* |
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69 | (2) |
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4.3.2 Finite-Time Boundedness Analysis During [ 0, T*] |
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71 | (3) |
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4.3.3 Finite-Time Boundedness Analysis of Sliding Mode Dynamics |
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74 | (2) |
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4.3.4 Finite-Time Boundedness Analysis Over [ 0,T] |
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76 | (5) |
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81 | (5) |
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86 | (1) |
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86 | (1) |
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Chapter 5 Adaptive Fuzzy Sliding Mode Control of Semi-Markovian Jump Systems |
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87 | (28) |
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87 | (1) |
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88 | (3) |
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91 | (15) |
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5.3.1 Sliding Mode Observer Design |
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91 | (2) |
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5.3.2 Design of Sliding Surface |
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93 | (2) |
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5.3.3 Stochastic Stability and H-Infinity Performance Analysis |
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95 | (9) |
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5.3.4 Reachability Analysis |
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104 | (2) |
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106 | (5) |
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111 | (4) |
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112 | (3) |
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Chapter 6 Decentralized Adaptive Sliding Mode Control of Large-Scale Semi-Markovian Jump Systems |
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115 | (18) |
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115 | (1) |
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116 | (3) |
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119 | (8) |
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6.3.1 Sliding Surface Design |
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119 | (1) |
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6.3.2 Stability Analysis of Sliding Mode Dynamics |
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119 | (5) |
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6.3.3 Convergence of Sliding Surface |
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124 | (3) |
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127 | (4) |
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131 | (2) |
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131 | (2) |
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Chapter 7 Reduced-Order Adaptive Sliding Mode Control for Switching Semi-Markovian Jump Delayed Systems |
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133 | (24) |
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133 | (1) |
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134 | (2) |
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136 | (11) |
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136 | (1) |
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7.3.2 Mean-Square Exponential Stability Analysis |
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137 | (8) |
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7.3.3 Adaptive SMC Law Design |
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145 | (2) |
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147 | (8) |
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155 | (2) |
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155 | (2) |
| Outlook |
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157 | (2) |
| Index |
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159 | |
Dr. Baoping Jiang
School of Electronic and Information Engineering, Suzhou University of Science and Technology, Suzhou 215009, China (e-mails: baopingj@163.com).
Baoping Jiang received the Ph.D. degree in control theory from the Ocean University of China, Qingdao, China, in 2019. From 2017 to 2019, he was a joint training Ph.D. Candidate with the Department of Mechanical Engineering, Politecnico di Milano, Milan, Italy. In 2019, he joined the Suzhou University of Science and Technology, Suzhou, China, where he is an associate professor. His research interests include sliding mode control, stochastic systems, etc.
Dr. Hamid Reza Karimi
Department of Mechanical Engineering, Politecnico di Milano, 20156 Milan, Italy, Email: hamidreza.karimi@polimi.it
Hamid Reza Karimi received the B.Sc. (First Hons.) degree in power systems from the Sharif University of Technology, Tehran, Iran, in 1998, and the M.Sc. and Ph.D. (First Hons.) degrees in control systems engineering from the University of Tehran, Tehran, in 2001 and 2005, respectively. He is currently Professor of Applied Mechanics with the Department of Mechanical Engineering, Politecnico di Milano, Milan, Italy. From 2009-2016, he has been Full Professor of Mechatronics-Control Systems at University of Agder, Norway. His current research interests include control systems and mechatronics with applications to automotive control systems, robotics, vibration systems and wind energy.
Prof. Karimi is currently the Editor-in-Chief of the Journal of Cyber-Physical Systems, Editor-in-Chief of the Journal of Machines, Editor-in-Chief of the International Journal of Aerospace System Science and Engineering, Editor-in-Chief of the Journal of Designs, Subject Editor of the IET Journal of Electronics Letters, Section Editor-in-Chief of the Journal of Electronics, Subject Editor of the Journal of Science Progress, Subject Editor for Journal of The Franklin Institute and a Technical Editor or Associate Editor for some international journals. He is a member of Agder Academy of Science and Letters and also a member of the IEEE Technical Committee on Systems with Uncertainty, the Committee on Industrial Cyber-Physical Systems, the IFAC Technical Committee on Mechatronic Systems, the Committee on Robust Control, and the Committee on Automotive Control. Prof. Karimi has been awarded as the 2016-2020 Web of Science Highly Cited Researcher in Engineering, the 2020 IEEE Transactions on Circuits and Systems Guillemin-Cauer Best Paper Award, August-Wilhelm-Scheer Visiting Professorship Award, JSPS (Japan Society for the Promotion of Science) Research Award, and Alexander-von-Humboldt-Stiftung research Award, for instance. He has also participated as keynote/plenary speaker, distinguished speaker or program chair for many international conferences in the areas of Control Systems, Robotics and Mechatronics.
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