Necessary conditions for mini-max optimal control problems

Abstract

Mini-max optimal control problems are optimal control problems, the data for which depends on a vector /spl alpha/ of unknown parameters. 'Optimality' is defined on a worst case basis, as /spl alpha/ ranges over the parameter set A. This paper deals with optimality conditions for such problems. The key result is a general mini-max maximum principle which improves on earlier, related optimality conditions in the literature, by allowing A to be an arbitrary compact set (not merely a finite set). The general mini-max maximum principle captures as special cases necessary conditions for optimal control problems with mini-max costs and problems involving 'semi-infinite' end-point constraints.