Abstract
This paper is concerned with a free-time optimal control problem for nonconvex-valued differential inclusions with a nonsmooth cost functional in the form of Bolza and general endpoint constraints involving free time. We develop a finite difference method for studying this problem and focus on two major topics: 1) constructions of well-posed discrete approximations ensuring a strong convergence of optimal solutions, and 2) necessary optimality conditions for free-time differential inclusions obtaining by the limiting process from discrete approximations. As a result, we construct a sequence of discrete approximations with the strong convergence of optimal solutions in the W 1, 2 norm. Then using the convergence result and appropriate tools of nonsmooth analysis, we prove necessary optimality conditions for differential inclusions in the refined Euler-Lagrange form with a new relation for an optimal free time.
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