Optimal Control Of Differential And Functional Equations

Optimal Control of Differential and Functional Equations

Optimal Control of Differential and Functional Equations presents a mathematical theory of deterministic optimal control, with emphasis on problems involving functional-integral equations and functional restrictions. The book reviews analytical foundations, and discusses deterministic optimal control problems requiring original, approximate, or relaxed solutions. Original solutions involve mathematicians, and approximate solutions concern engineers. Relaxed solutions yield a complete theory that encompasses both existence theorems and necessary conditions. The text also presents general optimal control problems, optimal control of ordinary differential equations, and different types of functional-integral equations. The book discusses control problems defined by equations in Banach spaces, the convex cost functionals, and the weak necessary conditions for an original minimum. The text illustrates a class of ordinary differential problems with examples, and explains some conflicting control problems with relaxed adverse controls, as well as conflicting control problems with hyper-relaxed adverse controls. The book is intended for mature mathematicians, graduate students in analysis, and practitioners of optimal control whose primary interests and training are in science or engineering.

Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control

* A comprehensive and systematic exposition of the properties of semiconcave functions and their various applications, particularly to optimal control problems, by leading experts in the field * A central role in the present work is reserved for the study of singularities * Graduate students and researchers in optimal control, the calculus of variations, and PDEs will find this book useful as a reference work on modern dynamic programming for nonlinear control systems

Optimal Control of Systems Governed by Partial Differential Equations