Abstract
This paper studies optimal control of nonlinear systems. An inverse optimal approach to associated Hamilton-Jacobi-Isaacs (HJI) partial differential equations is developed form the viewpoint of robust stabilization. Since there are no practical direct ways to solve HJI equations non-locally for general nonlinear systems, the inverse optimality is an attractive avenue to optimal control. Although inverse optimal controllers are known to exhibit some stability margins with respect to limited types of input uncertainties, the robustness usually does not agree with actual structures and sets of uncertainties. This paper clarifies a new class of cost functionals whose optimal controllers guarantee robustness with respect to a priori specified structures and sets of dynamic and static uncertainties. The cost functional includes free functions which are not chosen a prior by the designer. The freedom allowed by the state-dependent scaling factors provides us with nice flexibilities to solve solutions of HJI equations for a broad class of nonlinear systems easily.
