Optimal control and minimax synthesis of constrained parabolic systems under uncertain perturbations

An efficient design procedure to solve minimax control problems for hard-constrained parabolic systems, which takes into account monotonicity properties of the parabolic dynamics, was developed. Both first-order and second-order approximations were involved to justify an appropriate structure and compute optimal parameters of suboptimal controls to the original state-constrained parabolic problem. An energy-type cost functional in the case of maximal perturbations was minimized and the desired state performance within the required constraints for all admissible disturbances was ensured. Some results of numerical simulation which compare suboptimal solutions obtained via first-order and second-order approximation procedures are discussed.