Application of mathematical programming in the design of optimal control systems†

Abstract

Abstract The problem of applying the various computational methods of mathematical programming in the design of an optimal control system is discussed. A general case of non-linear, non-autonomous, state equations, subject to inequality constraints on both state and control variables, is considered. Both continuous and discrete time systems are investigated. In case of discrete time systems, the sampling intervals are assumed generally unequal and aperiodic, with inequality constraints imposed upon them. Systems like these impose considerable computational difficulties when treated by the maximum principle or dynamie programming. Using mathematical programming, one may simplify a wide class of those computational problems. Several examples of applying mathematical programming to particular control problems are presented. Notes † Communicated by the Authors. The paper constitutes a part of a Ph.D Thesis completed by D. Tabak in 1967, under supervision of B. C. Kuo at the Department of Electrical Engineering, University of Illinois, Urbana, Illinois.