Enhancing optimal controllers via techniques from robust and adaptive control

Optimal control strategies for both non‐linear and linear plants and indices are notoriously sensitive to modelling errors and external noise disturbances. In this paper a general framework to enhance robustness of an optimal control law is presented, with emphasis on the non‐linear case. The framework allows a blending of off‐line non‐linear optimal control, on‐line linear robust feedback control for regulation about the optimal trajectory and on‐line adaptive techniques to enhance performance/robustness. The adaptive‐Q techniques are those developed in previous work based on the Youla‐Kucera parametrization for the class of all stabilizing two‐degree‐of‐freedom controllers. Some general fundamental stability properties are developed which are new, at least for the non‐linear plant and linear robust controller case. Also, performance enhancement results in the presence of unmodelled linear dynamics based on an averaging analysis are reviewed. A convergence analysis based on averaging theory appears possible in principle for any specific non‐linear system but is beyond the scope of the present paper. Certain model reference adaptive control algorithms come out as special cases. A non‐linear 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.