An optimality criterion and an associated iterative method for solving time-optimal problems

Abstract

THE time-optimal problem (of moving a system from one set to another in minimum time under given phase constraints) is discussed for the case of linear controlled systems with elements from a locally convex linear topological space, and with controls from a given linear topological space. The present paper examines an optimality criterion for the linear time-optimal problem in a locally convex linear topological space under constraints on the phase coordinates. A connection is established between this criterion and the problem of moments, and the properties of certain auxiliary functionals are investigated. An iterative method is devised for solving the time-optimal problem in reflexive Banach spaces and its convergence is proved. The method is shown to be applicable to the approximate solution of time-optimal problems involving certain equations of mathematical physics.