Robust Control of Nonlinear Systems: Compensating for Uncertainty

The importance of robust contml has been recognized by control scientists for decades. Various approaches have been used, including the HI, approach, te parametric approach, and others (see references). In this paper we propose an indirect approach to the robust control problem ofstabilizing a nlinoear system, which works in the special case that the uncertainty in the system can be directly compensated for by the control. We first translate the robust control problem into an optimal control problem and then solve the optimal control problem. We show tiat, by properly choosing a cost function that depends on the uncertainty, regulation and control, the solution to the optimal control problem will be a solution to the robust control problem. Our motivation is twofold: (i) to solve a broad class ofnonlinear robust control problems; and (ii) to investigate relations between robust control and optimal control. Consider the nonlinear system