A comprehensive overview of nonlinear H∞ control theory for both continuous-time and discrete-time systems, Nonlinear H∞-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear H∞-control, nonlinear H∞ -filtering, mixed H2/ H∞-nonlinear control and filtering, nonlinear H∞-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter. Recent progress in developing computational schemes for solving the Hamilton-Jacobi equation (HJE) has facilitated the application of Hamilton-Jacobi theory in both mechanics and control. As there is currently no efficient systematic analytical or numerical approach for solving them, the biggest bottle-neck to the practical application of the nonlinear equivalent of the H∞-control theory has been the difficulty in solving the Hamilton-Jacobi-Isaacs partial differential-equations (or inequalities). In light of this challenge, the author hopes to inspire continuing research and discussion on this topic via examples and simulations, as well as helpful notes and a rich bibliography. Nonlinear H∞-Control, Hamiltonian Systems and Hamilton-Jacobi Equations was written for practicing professionals, educators, researchers and graduate students in electrical, computer, mechanical, aeronautical, chemical, instrumentation, industrial and systems engineering, as well as applied mathematics, economics and management.

This book provides techniques to produce robust, stable and useable solutions to problems of H-infinity and H2 control in high-performance, non-linear systems for the first time. The book is of importance to control designers working in a variety of industrial systems. Case studies are given and the design of nonlinear control systems of the same caliber as those obtained in recent years using linear optimal and bounded-norm designs is explained.

Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also discusses Hamilton-Jacobi theory. By providing a sufficient and rigorous treatment of finite dimensional control problems, the book equips readers with the foundation to deal with other types of control problems, such as those governed by stochastic differential equations, partial differential equations, and differential games.

This textbook is intended for physics students at the senior and graduate level. The first chapter employs Huygens' theory of wavefronts and wavelets to derive Hamilton's equations and the Hamilton-Jacobi equation. The final section presents a step-by-step precedure for the quanitzation of a Hamiltonian system. The remarkable congruence between particle dynaics and wave packets is shown. The second chapter presents sufficiency conditions for the standard case, broken, and singular extremals. Chapter III presents four schemes that can yield formal integrals of of Hamilton's equations- Killing's, Noether's, Poisson's, and Jacobi's. Chapter IV discusses iterative, numerical algorithms that converge to extremals. Three discontinuous problems are solved in Chapter V - refraction, jump discontinuities specified for state variables, and inequality contrainsts on state variables. The book contains many exercises and examples, in particular the geodesics of a Riemannian manifold.

The performance of a process -- for example, how an aircraft consumes fuel -- can be enhanced when the most effective controls and operating points for the process are determined. This holds true for many physical, economic, biomedical, manufacturing, and engineering processes whose behavior can often be influenced by altering certain parameters or controls to optimize some desired property or output.

This book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamiltona "Jacobi type and its interplay with Bellmana (TM)s dynamic programming approach to optimal control and differential games, as it developed after the beginning of the 1980s with the pioneering work of M. Crandall and P.L. Lions. The book will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. In particular, it will appeal to system theorists wishing to learn about a mathematical theory providing a correct framework for the classical method of dynamic programming as well as mathematicians interested in new methods for first-order nonlinear PDEs. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book. "The exposition is self-contained, clearly written and mathematically precise. The exercises and open problemsa ]will stimulate research in the field. The rich bibliography (over 530 titles) and the historical notes provide a useful guide to the area." a " Mathematical Reviews "With an excellent printing and clear structure (including an extensive subject and symbol registry) the book offers a deep insight into the praxis and theory of optimal control for the mathematically skilled reader. All sections close with suggestions for exercisesa ]Finally, with more than 500 cited references, an overview on the history and the main works of this modern mathematical discipline is given." a " ZAA "The minimal mathematical background...the detailed and clear proofs, the elegant style of presentation, and the sets of proposed exercises at the end of each section recommend this book, in the first place, as a lecture course for graduate students and as a manual for beginners in the field. However, this status is largely extended by the presence of many advanced topics and results by the fairly comprehensive and up-to-date bibliography and, particularly, by the very pertinent historical and bibliographical comments at the end of each chapter. In my opinion, this book is yet another remarkable outcome of the brilliant Italian School of Mathematics." a " Zentralblatt MATH "The book is based on some lecture notes taught by the authors at several universities...and selected parts of it can be used for graduate courses in optimal control. But it can be also used as a reference text for researchers (mathematicians and engineers)...In writing this book, the authors lend a great service to the mathematical community providing an accessible and rigorous treatment of a difficult subject." a " Acta Applicandae Mathematicae

The central focus of this book is the control of continuous-time/continuous-space nonlinear systems. Using new techniques that employ the max-plus algebra, the author addresses several classes of nonlinear control problems, including nonlinear optimal control problems and nonlinear robust/H-infinity control and estimation problems. Several numerical techniques are employed, including a max-plus eigenvector approach and an approach that avoids the curse-of-dimensionality. The max-plus-based methods examined in this work belong to an entirely new class of numerical methods for the solution of nonlinear control problems and their associated Hamilton–Jacobi–Bellman (HJB) PDEs; these methods are not equivalent to either of the more commonly used finite element or characteristic approaches. Max-Plus Methods for Nonlinear Control and Estimation will be of interest to applied mathematicians, engineers, and graduate students interested in the control of nonlinear systems through the implementation of recently developed numerical methods.