Ebook: Mathematical methods in optimization of differential systems

I: Generalized Gradients and Optimality -- 1. Fundamentals of Convex Analysis -- 2. Generalized Gradients -- 3. The Ekeland Variational Principle -- References -- II: Optimal Control of Ordinary Differential Systems -- 1. Formulation of the Problem and Existence -- 2. The Maximum Principle -- 3. Applications of the Maximum Principle -- References -- III: The Dynamic Programming Method -- 1. The Dynamic Programming Equation -- 2. Variational and Viscosity Solutions to the Equation of Dynamic Programming -- 3. Constructive Approaches to Synthesis Problem -- References -- IV: Optimal Control of Parameter Distributed Systems -- 1. General Description of Parameter Distributed Systems -- 2. Optimal Convex Control Problems -- 3. The H? -Control Problem -- 4. Optimal Control of Nonlinear Parameter Distributed Systems -- References.;This work is a revised and enlarged edition of a book with the same title published in Romanian by the Publishing House of the Romanian Academy in 1989. It grew out of lecture notes for a graduate course given by the author at the University if Ia~i and was initially intended for students and readers primarily interested in applications of optimal control of ordinary differential equations. In this vision the book had to contain an elementary description of the Pontryagin maximum principle and a large number of examples and applications from various fields of science. The evolution of control science in the last decades has shown that its meth­ ods and tools are drawn from a large spectrum of mathematical results which go beyond the classical theory of ordinary differential equations and real analy­ ses. Mathematical areas such as functional analysis, topology, partial differential equations and infinite dimensional dynamical systems, geometry, played and will continue to play an increasing role in the development of the control sciences. On the other hand, control problems is a rich source of deep mathematical problems. Any presentation of control theory which for the sake of accessibility ignores these facts is incomplete and unable to attain its goals. This is the reason we considered necessary to widen the initial perspective of the book and to include a rigorous mathematical treatment of optimal control theory of processes governed by ordi­ nary differential equations and some typical problems from theory of distributed parameter systems.