On Output Regulation Problems Involving Exogenous Signals

We consider output regulation problems for smooth nonlinear plants driven by exogenous signals. Sample formulations include disturbance signals to be asymptotically rejected, reference signals to be asymptotically tracked, and gain scheduling signals. Using a nonlinear coordinate transformation that depends on the relative degree of the plant linearization, we design nonlinear, static, state feedback control laws that depend also on the exogenous signal and a certain number of its time derivatives. Perturbation results are used to analyze the closed-loop system, and to relate the accuracy of regulation to properties of the exogenous signals.