Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations

Based on a decade of research, this reference provides comprehensive mathematical treatment of nonlinear robust control, particularly nonlinear H-infinity control. To be used as a textbook and reference, it covers topics ranging from singular nonlinear H-infinity control, nonlinear H-infinity filtering, mixed H2/H-infinity nonlinear control and filtering, and nonlinear H-infinity-almost-disturbance-decoupling. Continuous-time and discrete-time systems are discussed as well. One chapter focuses on algorithms for the solution of the Hamiltonian – Jacobi equations. The authors employ examples, figures, and simulations to ensure comprehension. They include more than 2,000 equations throughout the book.

A comprehensive overview of nonlinear H₈ control theory for both continuous-time and discrete-time systems, Nonlinear H₈-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear H₈-control, nonlinear H₈ -filtering, mixed H₂/ H₈-nonlinear control and filtering, nonlinear H₈-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 H₈-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 H₈-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.