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Analysis and Design of Markov Jump Discrete Systems

Analysis and Design of Markov Jump Discrete Systems
Author: Yonggui Kao
Publisher: Springer Nature
Total Pages: 200
Release: 2023-11-15
Genre: Technology & Engineering
ISBN: 9819957486

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This book proposes analysis and design techniques for Markov jump systems (MJSs) using Lyapunov function and sliding mode control techniques. It covers a range of topics including stochastic stability, finite-time boundedness, actuator-fault problem, bumpless transfer scheme, and adaptive sliding mode fault-tolerant control for uncertain MJSs. Notably, the book presents a new model for deception attacks (DAs), establishing the correlation between attacks and time delays, which should be of particular interest due to the recent increase in such attacks. The book's content is presented in a comprehensive, progressive manner, with fundamental principles introduced first before addressing more advanced techniques. The book features illustrations and tables, providing readers with a practical and intuitive approach to applying these methods in their own research. This book will prove invaluable to researchers and graduate students in control engineering and applied mathematics with an interest in the latest developments in MJSs.


Analysis and Design of Markov Jump Systems with Complex Transition Probabilities

Analysis and Design of Markov Jump Systems with Complex Transition Probabilities
Author: Lixian Zhang
Publisher: Springer
Total Pages: 263
Release: 2016-01-19
Genre: Technology & Engineering
ISBN: 3319288474

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The book addresses the control issues such as stability analysis, control synthesis and filter design of Markov jump systems with the above three types of TPs, and thus is mainly divided into three parts. Part I studies the Markov jump systems with partially unknown TPs. Different methodologies with different conservatism for the basic stability and stabilization problems are developed and compared. Then the problems of state estimation, the control of systems with time-varying delays, the case involved with both partially unknown TPs and uncertain TPs in a composite way are also tackled. Part II deals with the Markov jump systems with piecewise homogeneous TPs. Methodologies that can effectively handle control problems in the scenario are developed, including the one coping with the asynchronous switching phenomenon between the currently activated system mode and the controller/filter to be designed. Part III focuses on the Markov jump systems with memory TPs. The concept of σ-mean square stability is proposed such that the stability problem can be solved via a finite number of conditions. The systems involved with nonlinear dynamics (described via the Takagi-Sugeno fuzzy model) are also investigated. Numerical and practical examples are given to verify the effectiveness of the obtained theoretical results. Finally, some perspectives and future works are presented to conclude the book.


Discrete-Time Markov Jump Linear Systems

Discrete-Time Markov Jump Linear Systems
Author: O.L.V. Costa
Publisher: Springer Science & Business Media
Total Pages: 287
Release: 2006-03-30
Genre: Mathematics
ISBN: 1846280826

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This will be the most up-to-date book in the area (the closest competition was published in 1990) This book takes a new slant and is in discrete rather than continuous time


Discrete-Time Markov Jump Linear Systems

Discrete-Time Markov Jump Linear Systems
Author: O.L.V. Costa
Publisher: Springer Science & Business Media
Total Pages: 304
Release: 2005-02-02
Genre: Computers
ISBN: 9781852337612

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This will be the most up-to-date book in the area (the closest competition was published in 1990) This book takes a new slant and is in discrete rather than continuous time


Analysis and Design of Singular Markovian Jump Systems

Analysis and Design of Singular Markovian Jump Systems
Author: Guoliang Wang
Publisher: Springer
Total Pages: 287
Release: 2014-07-17
Genre: Technology & Engineering
ISBN: 3319087231

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This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H∞ control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat’s Lemma, among other techniques. Features of the book include: · study of the stability problem for SMJSs with general transition rate matrices (TRMs); · stabilization for SMJSs by TRM design, noise control, proportional-derivative and partially mode-dependent control, in terms of LMIs with and without equation constraints; · mode-dependent and mode-independent H∞ control solutions with development of a type of disordered controller; · observer-based controllers of SMJSs in which both the designed observer and controller are either mode-dependent or mode-independent; · consideration of robust H∞ filtering in terms of uncertain TRM or filter parameters leading to a method for totally mode-independent filtering · development of LMI-based conditions for a class of adaptive state feedback controllers with almost-certainly-bounded estimated error and almost-certainly-asymptotically-stable corres ponding closed-loop system states · applications of Markov process on singular systems with norm bounded uncertainties and time-varying delays Analysis and Design of Singular Markovian Jump Systems contains valuable reference material for academic researchers wishing to explore the area. The contents are also suitable for a one-semester graduate course.


Analysis and Design for Positive Stochastic Jump Systems

Analysis and Design for Positive Stochastic Jump Systems
Author: Wenhai Qi
Publisher: Springer Nature
Total Pages: 219
Release: 2022-09-19
Genre: Technology & Engineering
ISBN: 9811954909

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The book focuses on analysis and design for positive stochastic jump systems. By using multiple linear co-positive Lyapunov function method and linear programming technique, a basic theoretical framework is formed toward the issues of analysis and design for positive stochastic jump systems. This is achieved by providing an in-depth study on several major topics such as stability, time delay, finite-time control, observer design, filter design, and fault detection for positive stochastic jump systems. The comprehensive and systematic treatment of positive systems is one of the major features of the book, which is particularly suited for readers who are interested to learn non-negative theory. By reading this book, the reader can obtain the most advanced analysis and design techniques for positive stochastic jump systems.


Analysis and Synthesis of Fault-Tolerant Control Systems

Analysis and Synthesis of Fault-Tolerant Control Systems
Author: Magdi S. Mahmoud
Publisher: John Wiley & Sons
Total Pages: 451
Release: 2013-10-28
Genre: Technology & Engineering
ISBN: 111870035X

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In recent years, control systems have become more sophisticated in order to meet increased performance and safety requirements for modern technological systems. Engineers are becoming more aware that conventional feedback control design for a complex system may result in unsatisfactory performance, or even instability, in the event of malfunctions in actuators, sensors or other system components. In order to circumvent such weaknesses, new approaches to control system design have emerged which can tolerate component malfunctions while maintaining acceptable stability and performance. These types of control systems are often known as fault-tolerant control systems (FTCS). More precisely, FTCS are control systems which possess the ability to accommodate component failure automatically. Analysis and Synthesis of Fault-Tolerant Control Systems comprehensively covers the analysis and synthesis methods of fault tolerant control systems. It unifies the methods for developing controllers and filters for a wide class of dynamical systems and reports on the recent technical advances in design methodologies. MATLAB® is used throughout the book, to demonstrate methods of analysis and design. Key features: • Provides advanced theoretical methods and typical practical applications • Provides access to a spectrum of control design methods applied to industrial systems • Includes case studies and illustrative examples • Contains end-of-chapter problems Analysis and Synthesis of Fault-Tolerant Control Systems is a comprehensive reference for researchers and practitioners working in this area, and is also a valuable source of information for graduates and senior undergraduates in control, mechanical, aerospace, electrical and mechatronics engineering departments.


Multi-model Jumping Systems: Robust Filtering and Fault Detection

Multi-model Jumping Systems: Robust Filtering and Fault Detection
Author: Shuping He
Publisher: Springer Nature
Total Pages: 188
Release: 2021-03-01
Genre: Technology & Engineering
ISBN: 9813364742

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This book focuses on multi-model systems, describing how to apply intelligent technologies to model complex multi-model systems by combining stochastic jumping system, neural network and fuzzy models. It focuses on robust filtering, including finite-time robust filtering, finite-frequency robust filtering and higher order moment robust filtering schemes, as well as fault detection problems for multi-model jump systems, such as observer-based robust fault detection, filtering-based robust fault detection and neural network-based robust fault detection methods. The book also demonstrates the validity and practicability of the theoretical results using simulation and practical examples, like circuit systems, robot systems and power systems. Further, it introduces readers to methods such as finite-time filtering, finite-frequency robust filtering, as well as higher order moment and neural network-based fault detection methods for multi-model jumping systems, allowing them to grasp the modeling, analysis and design of the multi-model systems presented and implement filtering and fault detection analysis for various systems, including circuit, network and mechanical systems.


Continuous-Time Markov Jump Linear Systems

Continuous-Time Markov Jump Linear Systems
Author: Oswaldo Luiz do Valle Costa
Publisher: Springer Science & Business Media
Total Pages: 295
Release: 2012-12-18
Genre: Mathematics
ISBN: 3642341004

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It has been widely recognized nowadays the importance of introducing mathematical models that take into account possible sudden changes in the dynamical behavior of a high-integrity systems or a safety-critical system. Such systems can be found in aircraft control, nuclear power stations, robotic manipulator systems, integrated communication networks and large-scale flexible structures for space stations, and are inherently vulnerable to abrupt changes in their structures caused by component or interconnection failures. In this regard, a particularly interesting class of models is the so-called Markov jump linear systems (MJLS), which have been used in numerous applications including robotics, economics and wireless communication. Combining probability and operator theory, the present volume provides a unified and rigorous treatment of recent results in control theory of continuous-time MJLS. This unique approach is of great interest to experts working in the field of linear systems with Markovian jump parameters or in stochastic control. The volume focuses on one of the few cases of stochastic control problems with an actual explicit solution and offers material well-suited to coursework, introducing students to an interesting and active research area. The book is addressed to researchers working in control and signal processing engineering. Prerequisites include a solid background in classical linear control theory, basic familiarity with continuous-time Markov chains and probability theory, and some elementary knowledge of operator theory. ​


Discrete-Time Markov Chains

Discrete-Time Markov Chains
Author: G. George Yin
Publisher: Springer Science & Business Media
Total Pages: 354
Release: 2005-10-04
Genre: Mathematics
ISBN: 0387268715

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This book focuses on two-time-scale Markov chains in discrete time. Our motivation stems from existing and emerging applications in optimization and control of complex systems in manufacturing, wireless communication, and ?nancial engineering. Much of our e?ort in this book is devoted to designing system models arising from various applications, analyzing them via analytic and probabilistic techniques, and developing feasible compu- tionalschemes. Ourmainconcernistoreducetheinherentsystemcompl- ity. Although each of the applications has its own distinct characteristics, all of them are closely related through the modeling of uncertainty due to jump or switching random processes. Oneofthesalientfeaturesofthisbookistheuseofmulti-timescalesin Markovprocessesandtheirapplications. Intuitively,notallpartsorcom- nents of a large-scale system evolve at the same rate. Some of them change rapidly and others vary slowly. The di?erent rates of variations allow us to reduce complexity via decomposition and aggregation. It would be ideal if we could divide a large system into its smallest irreducible subsystems completely separable from one another and treat each subsystem indep- dently. However, this is often infeasible in reality due to various physical constraints and other considerations. Thus, we have to deal with situations in which the systems are only nearly decomposable in the sense that there are weak links among the irreducible subsystems, which dictate the oc- sional regime changes of the system. An e?ective way to treat such near decomposability is time-scale separation. That is, we set up the systems as if there were two time scales, fast vs. slow. xii Preface Followingthetime-scaleseparation,weusesingularperturbationmeth- ology to treat the underlying systems.