Polyhedral Optimization of Second-Order Discrete and Differential Inclusions with Delay

Abstract

The present paper studies the optimal control theory of second-order polyhedral delay discrete and delay-differential inclusions with state constraints. We formulate the conditions of optimality for the problems with the second-order polyhedral delay-discrete (PDd) and the delay-differential (PCd) in terms of the Euler-Lagrange inclusions andthe distinctive \transversality" conditions. Moreover, some linear control problem with second-order delay differentialinclusions is given to illustrate the effectiveness and usefulness of the main theoretic results.