Optimal Control Strategies for Constrained Linear Time-Delay Systems with Disturbances

We study two optimal control problems for a linear time-delay system subject to input and terminal state constraints and unknown bounded disturbances: The terminal control problem and the total control impulse minimization problem. A solution to the problems under consideration is defined in terms of optimal control strategies that are constructed on base of state measurements at several future time instants when the control loop is closed and a new control input is calculated. An efficient method for constructing optimal control strategies is proposed. The method uses finite-dimensional parametrization of the time-delay system state with respect to constraint and cost parameters and then reduces a multilevel optimization problem that arises from the definition of the control strategy to a number of linear programs. This results in low computational demands for the optimal strategy construction.