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​Hybrid System Identification helps readers to build mathematical models of dynamical systems switching between different operating modes, from their experimental observations. It provides an overview of the interaction between system identification, machine learning and pattern recognition fields in explaining and analysing hybrid system identification. It emphasises the optimization and computational complexity issues that lie at the core of the problems considered and sets them aside from standard system identification problems. The book presents practical methods that leverage this complexity, as well as a broad view of state-of-the-art machine learning methods. The authors illustrate the key technical points using examples and figures to help the reader understand the material. The book includes an in-depth discussion and computational analysis of hybrid system identification problems, moving from the basic questions of the definition of hybrid systems and system identification to methods of hybrid system identification and the estimation of switched linear/affine and piecewise affine models. The authors also give an overview of the various applications of hybrid systems, discuss the connections to other fields, and describe more advanced material on recursive, state-space and nonlinear hybrid system identification. Hybrid System Identification includes a detailed exposition of major methods, which allows researchers and practitioners to acquaint themselves rapidly with state-of-the-art tools. The book is also a sound basis for graduate and undergraduate students studying this area of control, as the presentation and form of the book provides the background and coverage necessary for a full understanding of hybrid system identification, whether the reader is initially familiar with system identification related to hybrid systems or not.
Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.
This book is the first to present the application of the hybrid system theory to systems with EPCA (equations with piecewise continuous arguments). The hybrid system paradigm is a valuable modeling tool for describing a wide range of real-world applications. Moreover, although new technology has produced, and continues to produce highly hierarchical sophisticated machinery that cannot be analyzed as a whole system, hybrid system representation can be used to reduce the structural complexity of these systems. That is to say, hybrid systems have become a modeling priority, which in turn has led to the creation of a promising research field with several application areas. As such, the book explores recent developments in the area of deterministic and stochastic hybrid systems using the Lyapunov and Razumikhin–Lyapunov methods to investigate the systems’ properties. It also describes properties such as stability, stabilization, reliable control, H-infinity optimal control, input-to-state stability (ISS)/stabilization, state estimation, and large-scale singularly perturbed systems.
This book constitutes the refereed proceedings of the 10th International Conference on Hybrid Systems: Computation and Control, HSCC 2007, held in Pisa, Italy in April 2007. The 44 revised full papers and 39 revised short papers presented together with the abstracts of 3 keynote talks were carefully reviewed and selected from 167 submissions. Among the topics addressed are models of heterogeneous systems, computability and complexity issues, real-time computing and control, embedded and resource-aware control, control and estimation over wireless networks, tools for analysis, verification, control, and design, programming languages support and implementation, applications, including automotive, communication networks, avionics, energy systems, transportation networks, biology and other sciences, manufacturing, and robotics.
Because they incorporate both time- and event-driven dynamics, stochastic hybrid systems (SHS) have become ubiquitous in a variety of fields, from mathematical finance to biological processes to communication networks to engineering. Comprehensively integrating numerous cutting-edge studies, Stochastic Hybrid Systems presents a captivating treatment of some of the most ambitious types of dynamic systems. Cohesively edited by leading experts in the field, the book introduces the theoretical basics, computational methods, and applications of SHS. It first discusses the underlying principles behind SHS and the main design limitations of SHS. Building on these fundamentals, the authoritative contributors present methods for computer calculations that apply SHS analysis and synthesis techniques in practice. The book concludes with examples of systems encountered in a wide range of application areas, including molecular biology, communication networks, and air traffic management. It also explains how to resolve practical problems associated with these systems. Stochastic Hybrid Systems achieves an ideal balance between a theoretical treatment of SHS and practical considerations. The book skillfully explores the interaction of physical processes with computerized equipment in an uncertain environment, enabling a better understanding of sophisticated as well as everyday devices and processes.
A Relaxation Based Approach to Optimal Control of Hybrid and Switched Systems proposes a unified approach to effective and numerically tractable relaxation schemes for optimal control problems of hybrid and switched systems. The book gives an overview of the existing (conventional and newly developed) relaxation techniques associated with the conventional systems described by ordinary differential equations. Next, it constructs a self-contained relaxation theory for optimal control processes governed by various types (sub-classes) of general hybrid and switched systems. It contains all mathematical tools necessary for an adequate understanding and using of the sophisticated relaxation techniques. In addition, readers will find many practically oriented optimal control problems related to the new class of dynamic systems. All in all, the book follows engineering and numerical concepts. However, it can also be considered as a mathematical compendium that contains the necessary formal results and important algorithms related to the modern relaxation theory. - Illustrates the use of the relaxation approaches in engineering optimization - Presents application of the relaxation methods in computational schemes for a numerical treatment of the sophisticated hybrid/switched optimal control problems - Offers a rigorous and self-contained mathematical tool for an adequate understanding and practical use of the relaxation techniques - Presents an extension of the relaxation methodology to the new class of applied dynamic systems, namely, to hybrid and switched control systems
This book constitutes the refereed proceedings of the 11th International Conference on Hybrid Systems: Computation and Control, HSCC 2008, held in St. Louis, MO, USA, in April 2008. The 42 revised full papers and 20 revised short papers presented were carefully reviewed and selected from numerous submissions for inclusion in the book. The papers focus on research in embedded, reactive systems involving the interplay between symbolic/switching and continuous dynamical behaviors and feature the latest developments of applications and theoretical advancements in the design, analysis, control, optimization, and implementation of hybrid systems, with particular attention to embedded and networked control systems.
This book is a collection of contributions defining the state of current knowledge and new trends in hybrid systems – systems involving both continuous dynamics and discrete events – as described by the work of several well-known groups of researchers. Hybrid Dynamical Systems presents theoretical advances in such areas as diagnosability, observability and stabilization for various classes of system. Continuous and discrete state estimation and self-triggering control of nonlinear systems are advanced. The text employs various methods, among them, high-order sliding modes, Takagi–Sugeno representation and sampled-data switching to achieve its ends. The many applications of hybrid systems from power converters to computer science are not forgotten; studies of flexible-joint robotic arms and – as representative biological systems – the behaviour of the human heart and vasculature, demonstrate the wide-ranging practical significance of control in hybrid systems. The cross-disciplinary origins of study in hybrid systems are evident. Academic researchers and graduate students interested in hybrid and switched systems need look no further than Hybrid Dynamical Systems for a single source which will bring them up to date with work in this area from around the world.
Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost functional. This book, Continuous Time Dynamical Systems: State Estimation and Optimal Control with Orthogonal Functions, considers different classes of systems with quadratic performance criteria. It then attempts to find the optimal control law for each class of systems using orthogonal functions that can optimize the given performance criteria. Illustrated throughout with detailed examples, the book covers topics including: Block-pulse functions and shifted Legendre polynomials State estimation of linear time-invariant systems Linear optimal control systems incorporating observers Optimal control of systems described by integro-differential equations Linear-quadratic-Gaussian control Optimal control of singular systems Optimal control of time-delay systems with and without reverse time terms Optimal control of second-order nonlinear systems Hierarchical control of linear time-invariant and time-varying systems