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 delaydifferential inclusions with state constraints. We formulate the conditions of optimality for the problems with the secondorder polyhedral delay-discrete (P D d) and the delay-differential (P C d) in terms of the Euler-Lagrange inclusions and the distinctive "transversality" conditions. Moreover, some linear control problem with second-order delay differential inclusions is given to illustrate the effectiveness and usefulness of the main theoretic results.