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.

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.