TRANSFORMATION TECHNIQUES AND NUMERICAL SOLUTION OF MINIMAX PROBLEMS OF OPTIMAL CONTROL: PRELIMINARY RESULTS

Abstract

This chapter presents a few preliminary results on transformation techniques and numerical solution of minimax problems of optimal control. Considerable research has been done on the problem of optimizing a trajectory from the standpoint of an integral performance index. This problem can be formulated in two forms that are called minimax problems. The objective is to minimize the maximum value achieved along the interval of integration by some function of the state, the control, and the parameter. These are nonclassical problems of the calculus of variations, in that they are not particular cases of the Bolza problem. They are called Chebyshev problems. Chebyshev-type problems have great importance in various branches of engineering. In aerospace engineering, Chebyshev problems are of interest for the reentry of a variable-geometry ballistic missile and the reentry of the space-shuttle vehicle. The chapter also describes a few transformation techniques, highlighting that by means of transformation techniques the Chebyshev problem can be converted into the Bolza problem.