Enhancing optimal controllers via techniques from robust and adaptive control

A general framework to enhance the robustness of an optimal control law is presented, with emphasis on the nonlinear case. The framework allows a blending of offline nonlinear optimal control, online linear robust feedback control for regulation about the optimal trajectory, and online adaptive techniques to enhance performance/robustness. Some general fundamental stability properties are developed for the nonlinear plant and linear robust controller case. Performance enhancement results in the presence of unmodeled linear dynamics based on an averaging analysis. A convergence analysis based on averaging theory appears possible in principle for any specific nonlinear system. Certain model-reference adaptive control algorithms come out as special cases. A nonlinear optimal control problem is studied to illustrate the efficacy of the techniques, and the possibility of further performance enhancement based on functional learning is noted