The SILP-Relaxation Method in Optimal Control I: General Boundary Conditions

Abstract

The paper deals with the relaxation method,a measure-theoretical approach for the treatment of classical control problems. After establishing a linear program over measure spaces as a substitute for a control problem, it is possible to use methods of semi-infinite linear programming (SILP), especially the semi-infinite simplex method (SISM), in order to estimate the solution of the linear program. In this way, approximations for the global optimal solution of the control problem can be obtained; a lower bound for the corresponding optimal value can also be found, by means of duality theory.