Guaranteed control policy with arbitrary set of correction points for linear-quadratic system with delay

For continuous, uncertain, linear quadratic control system with delayed input, we consider a min-max control policy in which the elements of feedback are present. The feedback is introduced into control optimization by allowing a control to be corrected at a given set of correction points from the control interval. This helps to overcome the feasibility difficulties that arise with standard min-max techniques. We show that construction of the optimal policy involves a sequence of min-max optimizations formulated as dynamic programs that do not yield simple analytical solutions. That is why the paper is mainly focused on construction and justification of suboptimal control policy that can be effectively implemented. Simulated examples demonstrate the proposed approach.