Generalized Optimal Control of Linear Systems with Distributed Parameters (Applied Optimization, 69)

The author of this book made an attempt to create the general theory of optimization of linear systems (both distributed and lumped) with a singular control. The book touches upon a wide range of issues such as solvability of boundary values problems for partial differential equations with generalized right-hand sides, the existence of optimal controls, the necessary conditions of optimality, the controllability of systems, numerical methods of approximation of generalized solutions of initial boundary value problems with generalized data, and numerical methods for approximation of optimal controls. In particular, the problems of optimization of linear systems with lumped controls (pulse, point, pointwise, mobile and so on) are investigated in detail. "The author of this book made an attempt to create the general theory of optimization of linear systems (both distributed and lumped) with a singular control. The book touches upon a wide range of issues such as solvability of boundary value problems for partial differential equations with generalized right-hand sides, the existence of optimal controls, the necessary conditions of optimality, the controllability of systems, numerical methods of approximation of generalized solutions of initial boundary value problems with generalized data, and numerical methods for approximation of optimal controls. In particular, the problems of optimization of linear systems with lumped controls (pulse, point, pointwise, mobile and so on) are investigated in detail." "Audience: Scientists and engineers engaged in the theory of optimal control of linear systems and its application in physics, ecology, economy, medicine, and other fields. Also suitable as a textbook for graduate and post-graduate students studying modern methods in optimal control."--BOOK JACKET Consider a system which functioning is described by linear partial differential equation [11, 14-17,19, 30, 65-73] Lu = F + Ah, u D(L) (1) in a tube domain Q = (0,T) , where u(t,x) is an unknown function depended on a spatial variable and a time variable t (0,T), is a bounded domain in Rn with smooth boundary , D(L) is a set of the functions which are sufficiently smooth in and satisfy some conditions (bd) on the boundary of the domain Q. Attempts to create the general theory of optimization of linear systems (both distributed and lumped) with a singular control. This book touches upon a range of issues such as the existence of optimal controls, the necessary conditions of optimality, the controllability of systems, and more.