Polyhedral optimization of second-order discrete and differential inclusions with delay

The present paper studies the optimal control theory of second-order polyhedral delay discrete and delay diferential inclusions with state constraints. We formulate the conditions of optimality for the problems with the second-order polyhedral delay discrete (PD_d) and the delay differential (PC_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.