Optimal control systems. Part I, Analysis : the methods of Pontryagin in the optimal control of second order oscillatory systems with discontinuities in the state variables

摘要

It is the purpose of these two reports to demonstrate withvery simple systems, several applications of the optimization theoryof L. S. Pontryagin (1). An attempt to synthesize the control logicusing a modification of dynamic programming is developed,,Part 1 presents the solution to the minimum time problem andthe minimum fuel problem for a second order system with one zero cThe zero causes discontinuities in the state variables . Control difficultiesare encountered when there are discontinuities in the errorstates, but these are alleviated by a transformation to a system withcontinuous variables. Optimum control of the transformed system isthen accomplished using the methods of Pontryagin „ The controlaction is then related back to the original plant. Although the investigationis concerned entirely with second order systems , themethods are sufficiently general to be extended to higher ordersystems with zeros. In part II an example of the extension is given,,Also Part II presents various schemes for the synthesis of optimumcontrols.