Alexander B. Kurzhanski - Böcker

This work presents overviews of Soviet research on nonlinear dynamics, particularly as applied to uncertain systems in a deterministic setting. The book concentrates on the three main branches of uncertain dynamics: differential games; evolution, estimation and control; and robust stabilization.

Dynamic Programming for Impulse Feedback and Fast Controls offers a description of feedback control in the class of impulsive inputs. This book deals with the problem of closed-loop impulse control based on generalization of dynamic programming techniques in the form of variational inequalities of the Hamilton–Jacobi–Bellman type. It provides exercises and examples in relation to software, such as techniques for regularization of ill-posed problems. It also gives an introduction to applications such as hybrid dynamics, control in arbitrary small time, and discontinuous trajectories.This book walks the readers through:the design and description of feedback solutions for impulse controls;the explanation of impulses of higher order that are derivatives of delta functions;the description of their physically realizable approximations - the fast controls and their approximations;the treatment of uncertaintyin impulse control and the applications of impulse feedback.Of interest to both academics and graduate students in the field of control theory and applications, the book also protects users from common errors , such as inappropriate solution attempts, by indicating Hamiltonian techniques for hybrid systems with resets.

The purpose of this volume is to present a coherent collection of overviews of recent Russian research in Control Theory and Nonlinear Dynamics written by active investigators in these fields. It is needless to say that the contribution of the scientists of the former Soviet Union to the development of nonlinear dynamics and control was significant and that their scientific schools and research community have highly evolved points of view, accents and depth which complemented, enhanced and sometimes inspired research directions in the West. With scientific exchange strongly increasing, there is still a consider­ able number of Eastern publications unknown to the Western community. We have therefore encouraged the authors to produce extended bibliogra­ phies in their papers. The particular emphasis of this volume is on the treatment of uncer­ tain systems in a deterministic setting-a field highly developed in the former Soviet Union and actively investigated in the West. The topics are concentrated around the three main branches of un­ certain dynamics which are the theory of Differential Games, the set­ membership approach to Evolution, Estimation and Control and the the­ ory of Robust Stabilization. The application of these techniques to non­ linear systems as well as the global optimization of the latter are also among the issues treated in this volume.

This monograph presents theoretical methods involving the Hamilton–Jacobi–Bellman formalism in conjunction with set-valued techniques of nonlinear analysis to solve significant problems in dynamics and control. The emphasis is on issues of reachability, feedback control synthesis under complex state constraints, hard or double bounds on controls, and performance in finite time. Guaranteed state estimation, output feedback control, and hybrid dynamics are also discussed. Although the focus is on systems with linear structure, the authors indicate how to apply each approach to nonlinear and nonconvex systems. The main theoretical results lead to computational schemes based on extensions of ellipsoidal calculus that provide complete solutions to the problems. These computational schemes in turn yield software tools that can be applied effectively to high-dimensional systems. Ellipsoidal Techniques for Problems of Dynamics and Control: Theory and Computation will interest graduate and senior undergraduate students, as well as researchers and practitioners interested in control theory, its applications, and its computational realizations.

This monograph presents theoretical methods involving the Hamilton–Jacobi–Bellman formalism in conjunction with set-valued techniques of nonlinear analysis to solve significant problems in dynamics and control. The emphasis is on issues of reachability, feedback control synthesis under complex state constraints, hard or double bounds on controls, and performance in finite time. Guaranteed state estimation, output feedback control, and hybrid dynamics are also discussed. Although the focus is on systems with linear structure, the authors indicate how to apply each approach to nonlinear and nonconvex systems. The main theoretical results lead to computational schemes based on extensions of ellipsoidal calculus that provide complete solutions to the problems. These computational schemes in turn yield software tools that can be applied effectively to high-dimensional systems. Ellipsoidal Techniques for Problems of Dynamics and Control: Theory and Computation will interest graduate and senior undergraduate students, as well as researchers and practitioners interested in control theory, its applications, and its computational realizations.

The investigation of special topics in systems dynamics -uncertain dynamic processes, viability theory, nonlinear dynamics in models for biomathematics, inverse problems in control systems theory-has become a major issue at the System and Decision Sciences Research Program of the International Insti­ tute for Applied Systems Analysis. The above topics actually reflect two different perspectives in the investigation of dynamic processes. The first, motivated by control theory, is concerned with the properties of dynamic systems that are stable under vari­ ations in the systems' parameters. This allows us to specify classes of dynamic systems for which it is possible to construct and control a whole "tube" of trajectories assigned to a system with uncertain parameters and to resolve some inverse problems of control theory within numerically stable solution schemes. The second perspective is to investigate generic properties of dynamic systems that are due to nonlinearity (as bifurcations theory, chaotic behavior, stability properties, and related problems in the qualitative theory of differential systems). Special stress is given to the applications of non­ linear dynamic systems theory to biomathematics and ecoloey.

Research in discrete systems is expanding rapidly, and specialized languages are proliferating. This book is a remarkable attempt to bring together researchers from a diverse range of application areas. This is the proceeding of a workshop on Discrete Event Systems Models. The 30 participants included researchers working in communication networks, manufacturing, digital signal processing, Markov decision theory, and automatic control. The purpose of the workshop was to establish the common features of the mathematical models, techniques and goals pursued in these diverse areas. The papers demonstrate that there is a large common core underlying these efforts, that researchers in one area can benefit from advances in other areas of discrete systems, and that it is not difficult to translate results expressed in one discrete event formation into another. The papers cover formal description methods, logical verification, simulation, performance evaluation, and optimization. Techniques covered include finite state machines, Petri nets, communicating sequential processes, queuing analysis, and perturbation analysis.

This volume is the proceedings of an IIASA conference held in Sopron, Hungary, whose purpose was to bring together prominent control theorists and practitioners from the east and west in order to focus on fundamental systems and control problems arising in the areas of modelling and adaptive control.