Robust near-optimal output feedback control of nonlinear systems

This work proposes a robust near-optimal nonlinear output feedback controller design for a broad class of nonlinear systems with time-varying uncertain variables. Through combination of a high-gain observer with a robust optimal state feedback controller, a dynamic robust output feedback controller is constructed that enforces exponential stability and robust asymptotic output tracking with arbitrary degree of attenuation of the effect of uncertainty on the output of the closed-loop system, for initial conditions and uncertainty in arbitrarily large compact sets, provided that the observer gain is sufficiently large. Utilising the inverse optimal control approach and singular perturbation techniques, the controller is shown to be near-optimal in the sense that its performance can be made arbitrarily close to the optimal performance of the robust optimal state feedback controller on the infinite time-interval by selecting the observer gain to be sufficiently large.