Robust inverse optimal control laws for nonlinear systems

This work proposes a robust inverse optimal controller design for a class of nonlinear systems with bounded, time-varying uncertain variables. The basic idea is that of re-shaping the scalar nonlinear gain of an LgV controller, based on Sontag’s formula, so as to guarantee certain uncertainty attenuation properties in the closed-loop system. The proposed gain re-shaping is shown to yield a control law that enforces global boundedness of the closed-loop trajectories, robust asymptotic output tracking with an arbitrary degree of attenuation of the effect of uncertainty on the output, and inverse optimality with respect to a meaningful cost that penalizes the tracking error and the control action. The performance of the control law is illustrated through a simulation example and compared with other controller designs. Copyright # 2003 John Wiley & Sons, Ltd.