The lectures gathered in this volume present some of the different aspects of Mathematical Control Theory. Adopting the point of view of Geometric Control Theory and of Nonlinear Control Theory, the lectures focus on some aspects of the Optimization and Control of nonlinear, not necessarily smooth, dynamical systems. Specifically, three of the five lectures discuss respectively: logic-based switching control, sliding mode control and the input to the state stability paradigm for the control and stability of nonlinear systems. The remaining two lectures are devoted to Optimal Control: one investigates the connections between Optimal Control Theory, Dynamical Systems and Differential Geometry, while the second presents a very general version, in a non-smooth context, of the Pontryagin Maximum Principle. The arguments of the whole volume are self-contained and are directed to everyone working in Control Theory. They offer a sound presentation of the methods employed in the control and optimization of nonlinear dynamical systems.

Research in robust control theory has been one of the most active areas of mainstream systems theory since the late 70s. This research activity has been at the confluence of dynamical systems theory, functional analysis, matrix analysis, numerical methods, complexity theory, and engineering applications. The discipline has involved interactions between diverse research groups including pure mathematicians, applied mathematicians, computer scientists and engineers. This research effort has produced a rather extensive set of approaches using a wide variety of mathematical techniques, and applications of robust control theory are spreading to areas as diverse as control of fluids, power networks, and the investigation of feddback mechanisms in biology. During the 90's the theory has seen major advances and achieved a new maturity, centered around the notion of convexity. The goal of this book is to give a graduate-level course on robust control theory that emphasizes these new developments, but at the same time conveys the main principles and ubiquitous tools at the heart of the subject. Its pedagogical objectives are to introduce a coherent and unified framework for studying robust control theory, to provide students with the control-theoretic background required to read and contribute to the research literature, and to present the main ideas and demonstrations of the major results of robust control theory. The book will be of value to mathematical researchers and computer scientists wishing to learn about robust control theory, graduate students planning to do research in the area, and engineering practitioners requiring advanced control techniques.

This book includes selected peer-reviewed papers presented at the International Conference on Modeling, Simulation and Optimization (CoMSO 2022), organized by National Institute of Technology, Silchar, Assam, India, during December 21–23, 2022. The book covers topics of modeling, simulation, and optimization, including computational modeling and simulation, system modeling and simulation, device/VLSI modeling and simulation, control theory and applications, and modeling and simulation of energy systems and optimization. The book disseminates various models of diverse systems and includes solutions of emerging challenges of diverse scientific fields.

In a mathematical programming problem, an optimum (maxi­ mum or minimum) of a function is sought, subject to con­ straints on the values of the variables. In the quarter century since G. B. Dantzig introduced the simplex method for linear programming, many real-world problems have been modelled in mathematical programming terms. Such problems often arise in economic planning - such as scheduling industrial production or transportation - but various other problems, such as the optimal control of an interplanetary rocket, are of similar kind. Often the problems involve nonlinear func­ tions, and so need methods more general than linear pro­ gramming. This book presents a unified theory of nonlinear mathe­ matical programming. The same methods and concepts apply equally to 'nonlinear programming' problems with a finite number of variables, and to 'optimal control' problems with e. g. a continuous curve (i. e. infinitely many variables).

This book is an introduction to the mathematical theory of optimal control of processes governed by ordinary differential eq- tions. It is intended for students and professionals in mathematics and in areas of application who want a broad, yet relatively deep, concise and coherent introduction to the subject and to its relati- ship with applications. In order to accommodate a range of mathema- cal interests and backgrounds among readers, the material is arranged so that the more advanced mathematical sections can be omitted wi- out loss of continuity. For readers primarily interested in appli- tions a recommended minimum course consists of Chapter I, the sections of Chapters II, III, and IV so recommended in the introductory sec­ tions of those chapters, and all of Chapter V.

The book presents some recent specialized theoretical and practical works in the field of process control based on the model predictive control (MPC) method. It includes seven chapters that present studies on the application of MPC in various technical processes, such as the atmospheric plasma spray process, permanent magnet synchronous motors, monitoring of the pose of a walking person, monitoring of the heat treatment process of raw materials, discrete event processes, control of passenger vehicles, and natural gas sweetening processes.

Modelling and Control of Mini-Flying Machines is an exposition of models developed to assist in the motion control of various types of mini-aircraft:

Textbooks in the field of control engineering have, in the main, been written for electrical engineers and the standard of the mathematics used has been relatively high. The purpose of this work is to provide a course of study in elementary control theory which is self-contained and suitable for students of all branches of engineering and of applied physics. The book assumes that the student has a knowledge of mathematics of A-level or 0-2 level standard only. All other necessary pure and applied mathematics is covered for reference purposes in chapters 2-6. As a students' textbook it contains many fully worked numerical examples and sets of examples are provided at the end of all chapters except the first. The answers to these examples are given at the end of the book. The book covers the majority of the control theory likely to be encountered on H. N. C. , H. N. D. and degree courses in electrical, mechanical, chemical and production engineering and in applied physics. It will also provide a primer in specialist courses in instru­ mentation and control engineering at undergraduate and post­ graduate level. Furthermore, it covers much of the control theory encountered in the graduateship examinations of the professional institutions, for example I. E. E. Part III (Advanced Electrical Engineer­ ing and Instrumentation and Control), I. E. R. E. Part 5 (Control Engineering) and the new c. E. I. Part 2 (Mechanics of Machines and Systems and Control Engineering).

This book presents the separation principle which is also known as the principle of separation of estimation and control and states that, under certain assumptions, the problem of designing an optimal feedback controller for a stochastic system can be solved by designing an optimal observer for the system's state, which feeds into an optimal deterministic controller for the system. Thus, the problem may be divided into two halves, which simplifies its design. In the context of deterministic linear systems, the first instance of this principle is that if a stable observer and stable state feedback are built for a linear time-invariant system (LTI system hereafter), then the combined observer and feedback are stable. The separation principle does not true for nonlinear systems in general. Another instance of the separation principle occurs in the context of linear stochastic systems, namely that an optimum state feedback controller intended to minimize a quadratic cost is optimal for the stochastic control problem with output measurements. The ideal solution consists of a Kalman filter and a linear-quadratic regulator when both process and observation noise are Gaussian. The term for this is linear-quadratic-Gaussian control. More generally, given acceptable conditions and when the noise is a martingale (with potential leaps), a separation principle, also known as the separation principle in stochastic control, applies when the noise is a martingale (with possible jumps).

The book gives an introduction to networked control systems and describes new modeling paradigms, analysis methods for event-driven, digitally networked systems, and design methods for distributed estimation and control. Networked model predictive control is developed as a means to tolerate time delays and packet loss brought about by the communication network. In event-based control the traditional periodic sampling is replaced by state-dependent triggering schemes. Novel methods for multi-agent systems ensure complete or clustered synchrony of agents with identical or with individual dynamics.

This book introduces the reader to the hottest topics in current control sciences and robotics, as seen by scientists from Poland and other European countries.