Direct Methods in Control Problems

Peter Falb is Professor Emeritus of Applied Mathematics: Applied Mathematics at the Brown University in Providence, RI, USA. His research interests are in the areas of systems science and engineering, particularly algebraic and geometric methods, parametric dependence, numerical methods, multivariable linear systems, and infinite dimensional stochastic systems, as well as control and stability theory and mathematics of investment.

“This is clearly a book aimed at specialists in control theory. It is more a monograph … .” (Bill Satzer, MAA Reviews, November 28, 2021)“This book offers a useful reading and provides interesting classroom material on the theory of finite-element indirect methods for optimal control problems.” (Fernando Lobo Pereira, Mathematical Reviews, July, 2021)“The book will become a valuable reference for researchers, engineers and students in the field of mathematics, management science, operations research, optimal control science and economics.” (Savin Treanta, zbMATH 1444.93002, 2020)

• Part I. Introduction.- Introductory Remarks.- Historical Perspective.- Outline of Contents.- Part II. Problem Statement.- Deterministic Systems.- Stochastic Systems.- General Problem.- Part III. The Direct Method Approach: Generalities.- General Approach.- Gradient and Integration Methods.- Representation Methods.- Part IV. Gradient and Integration Methods in Control Problems.- Computation of Gradients for ODE Problems.- Computation of Gradients for PDE Problems.- Integration Methods.- Part V. Representation Methods.- Ritz–Galerkin Expansion.- Karhunen–Loeve Expansion.- Lévy Processes.- Bibliography.- Index