Robust optimal control of nonlinear systems

Focuses on robust optimal control of a broad class of nonlinear systems with time-varying uncertain variables. Under the assumption of input-to-state stable (ISS) inverse dynamics and vanishing uncertain variables, we synthesize via Lyapunov´s direct method nonlinear controllers that enforce asymptotic stability and output tracking with attenuation of the effect of the uncertain variables on the output of the closed-loop system. The controllers are continuous and require the existence of bounds that capture the magnitude of the uncertain variables. Utilizing the inverse optimal approach, the controllers are shown to be optimal with respect to a meaningful cost that includes penalty on the control effort and the worst-case uncertainty