Linear-convex guarantee optimization problems with control delay

A control problem under condition of disturbances is considered for a linear dynamical system with control delay. Optimized quality index is nonterminal and contains the evaluation of the system motion by a set of deviations at given instants of time from given targets. Depending on the structure of the quality index the existence of optimal control strategies in appropriate classes of feedback strategies is established. For calculating the value of the optimal guaranteed result and finding the optimal control laws a procedure of backward construction of upper convex hulls of auxiliary functions is proposed. In the case of the positional quality index a reduction of this procedure is performed. This reduction significantly reduces the dimension of the domains of covexified functions. Results of numerical simulations are given.