(A) study on robust gain scheduling in uncertain nonlinear systems with exogenous signals

Abstract

The gain scheduling methodology has been successful used in many application. How-ever, the theoretical tools for the analysis and design are rather poorly investigated. In this dissertation, we present analytical solutions to solve the problem of the robust gain scheduling in uncertain nonlinear systems with exogenous signals and build up the application technique. The various gain scheduling controllers has been developed and applied to the systems with the exactly known exogenous signals. However, there exist many cases where we happen to meet an additional disturbance in the exogenous signals. For the nonlinear systems with uncertain exogenous signals, a matching condition is presented so as to design an additional compensator and a control law is proposed to reduce the output error. Thus, if the disturbance signal is less than the maximum tolerable uncertainty, the control objective is achieved. Most of the previous controllers proposed for the output regulation problems on uncertain nonlinear systems are supposed to keep the state variables along the nominal equilibrium points instead of the perturbed equilibrium points. However, we propose an equilibria estimator which computes the perturbed equilibrium points for an uncertain system, using upper and lower bound functions on the uncertainty. We also propose a dynamic state feedback controller which enables the state variables to asymptotically track the equilibrium points computed by the equilibria estimator. The overall system shows robustness for the bounded uncertainties, and the tighter bound on uncertainty provides better regulation performance. Furthermore, we propose an alternative robust gain scheduled control law in the nonlinear system with structural uncertainties. For the uncertain nonlinear system satisfying the given matching condition, the proposed control law reduces the output error bound to the desired bound. This dissertation develops the $H_∞$ gain scheduled controller for uncertain n...