Realization of robust optimal control by dynamic neural-programming

This study solves a finite horizon optimal problem for linear systems with parametric uncertainties and bounded perturbations. The control solution considers the uncertain part of the system in the sub-optimal control solution by proposing a min-max problem solved by a dynamic neural programming approximate solution. The structure of the neural network was proposed to satisfy the charcateristics of the value function including possitiveness and continuity. The impact of the presence of bounded perturbation over the Hamiltonian maximization was analyzed in detail. The explicit learning law used to adjust the weights was obtained directly from the Hamilton-Jacobi-Bellman (HJB) approximate solution. The weights adjustment to the proposed algorithm is based on an on-line state dependent Riccati-like equation. A numerical simulation is presented to illustrate the results of the sub-optimal algorithm including its comparison against the classical linear regulator solved considering the non-perturbed system.