Robust control in uncertain nonlinear systems with exogenous signals

Gain scheduling control laws have been developed by many researchers (Huang and Rugh 1990, Rugh 1991). Using the extended linearization, Lawrence and Rugh (1990) and Khalil and Kokotovic (1991) proposed the stability results that deal with the response of a nonlinear system to slowly varying exogenous signals. The most recent work on the output regulation for a nonlinear system driven by an exogenous signal was done by Sureshbabu and Rugh (1995) and Lee and Lim (1997b). They proposed a control law with derivative information on the exogenous signal and included nonlinear examples in order to illustrate enhanced regulation performance over existing controller design. Moreover, the gain scheduling in nonlinear systems with bounded uncertain time varying input was also proposed (Lee and Lim 1997a). Those controllers were designed and destined only for the systems with the exactly known plant dynamics. In practice, however, nonlinear plants are not exactly modelled owing to the unknown dynamics. Using those without any modi® cation causes undesirable performance or destabilizes the overall control system. The kth-order approximate equilibrium point was computed in uncertain systems with exogenous signals generated by the known exogenous system (HuangandRugh, 1992, Huang1995). Using the internal model principle, theyproposedakth-order robust control law. However, in most cases, it is di cult to obtain the exogenous system which generates the exogenous signals injected to the plant dynamics. Thus, this paper proposed a compensated state feedback controller to solve the regulation problems for the unknown exogenous system. Using the proposed control law, the system which satis® es a given matching condition can be controlled to provide the desired output error bound.