Applied Optimal Control Theory of Distributed Systems

Earlier investigations of optimal control problems utilized procedures that did not reveal important features of optimization problems for distributed parameter systems. This monograph explores the modern approach to optimization of distributed systems and reviews its applications, addressing selected issues of the optimal control of systems described by elliptic, hyperbolic, and parabolic equations.
This volume is a substantially revised and updated version of K. A. Lurie's earlier work, Optimal Control in Problems of Mathematical Physics, published in Russian in 1975. The new text features discussions on the existence of optimal controls in the context of Pontryagin's maximum principle and examines the latest results obtained in the problem of the optimal design of nonhomogeneous bodies. Lurie utilizes the idea of composites in the problem of optimal conductivity distribution in an MHD-generator channel flow and details the application of Bellman's method of dynamic programming to optimization problems for systems described by partial differential equations. Other topics include regularization of optimization problems for systems containing the scalar control U in the operator, problems in the optimal design of thin elastic plates, Legendre's necessary condition for the problem of optimizing the shape of a body in supersonic flow, problems of optimal heating of bodies, and optimization problems with moving boundaries.
Applied Optimal Control Theory of Distributed Systems will be a valuable reference source for scientists in the field of optimal control and optimal design of distributed systems, which include elements of constructions, heated bodies, and systems developing in time.