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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
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. ​
This book presents state-of-the-art solution methods and applications of stochastic optimal control. It is a collection of extended papers discussed at the traditional Liverpool workshop on controlled stochastic processes with participants from both the east and the west. New problems are formulated, and progresses of ongoing research are reported. Topics covered in this book include theoretical results and numerical methods for Markov and semi-Markov decision processes, optimal stopping of Markov processes, stochastic games, problems with partial information, optimal filtering, robust control, Q-learning, and self-organizing algorithms. Real-life case studies and applications, e.g., queueing systems, forest management, control of water resources, marketing science, and healthcare, are presented. Scientific researchers and postgraduate students interested in stochastic optimal control,- as well as practitioners will find this book appealing and a valuable reference. ​
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.
In the past two decades, the number of applications that make use of supervisory algorithms to control complex continuous-time or discrete-time systems has increased steadily. Typical examples include air traffic management, digital control systems over networks, and flexible manufacturing systems. A common feature of these applications is the intermixing of the continuous dynamics of the controlled plant with the logical and discrete dynamics of the supervising algorithms. These so-called hybrid systems are the focus of much ongoing research. To improve the performance of these systems, it is important to analyze the interactions between the supervising algorithms and the plant. Few papers have studied this interaction when the plant is represented by a discrete-time system. Thus, this dissertation fixes this deficiency by addressing the following three main objectives: to introduce a new modeling framework for discrete-time stochastic hybrid systems suitable for stability analysis; to derive testable stability conditions for these models; and to demonstrate that these models are suitable to study real-world applications. To achieve the first objective, the Hybrid Jump Linear System model is introduced. Although it has many of the same modeling capabilities as other formalisms in the literature (e.g., Discrete Stochastic Hybrid Automata), it possesses the unique advantage of representing the dynamics of both the controlled plant and the supervising algorithm in the same analytical framework: stochastic difference equations. This enables the study of their joint properties such as, for example, mean square stability. The second objective is addressed by developing a collection of testable sufficient mean square stability conditions. These tests are developed by applying, successively, switched systems' techniques, singular value analysis, a second moment lifting technique, and Mark off kernel methods. The final objective is achieved by developing a hybrid jump linear system model of an AFTI-F16 flight controller deployed on a fault tolerant computer with rollback and cold-restart capabilities, and analyzing its stability properties.
This paper presents a comprehensive study of continuous-time Positive Markov Jump Linear Systems (PMJLS). A PMJLS can be seen as a dynamical system that switches within a finite set of linear time-invariant subsystems according to a stochastic switching signal modelled as a Markov chain, and describes the time-evolution of nonnegative variables under nonnegative inputs. Contrary to the well-studied general class of Markov Jump Linear Systems (MJLS), positivity endows the model with peculiar properties. The paper collects some existing results together with original developments on the stability analysis of PMJLS and the study of their input-output properties. In particular, conditions for stability of PMJLS are discussed, mainly based on Linear Programming problems. Similar computational tools are derived to analyze performance measures, such as L1, L2 and L8 costs and the respective input-output induced gains. The second part of the paper is devoted to the class of Dual switching Positive Markov Jump Linear Systems (D-PMJLS), namely PMJLS affected by an additional switching variable which can be either an unknown disturbance or a control signal available to the designer for stabilization and performance optimization. We discuss several problems, including stability, performance analysis, stabilization via switching control, and optimization. Some application examples are introduced to motivate the interest in PMJLS and D-PMJLS.
This book discusses analysis and design techniques for linear feedback control systems using MATLAB® software. By reducing the mathematics, increasing MATLAB working examples, and inserting short scripts and plots within the text, the authors have created a resource suitable for almost any type of user. The book begins with a summary of the properties of linear systems and addresses modeling and model reduction issues. In the subsequent chapters on analysis, the authors introduce time domain, complex plane, and frequency domain techniques. Their coverage of design includes discussions on model-based controller designs, PID controllers, and robust control designs. A unique aspect of the book is its inclusion of a chapter on fractional-order controllers, which are useful in control engineering practice.