Robust LQR tracking control for a class of affine nonlinear uncertain systems

A new linear quadratic regulator (LQR) strategy is presented to realize robust tracking control for a class of nonlinear uncertain systems with reference input given by a time-varying exosystem. To avoid the difficulty of solving the nonlinear two-point boundary-value (TPBV) problem, which is induced by LQR for nonlinear systems, the input-output linearization technique is adopted to transform the nonlinear system into an equivalent linear system. Considering the exosystem, the tracking error state equation is established and the LQR is designed based on the error equation by ignoring uncertainties. However, the optimal controller for the nominal system is very sensitive to uncertainties, so the sliding mode control (SMC) is used to robustify the LQR. By constructing an optimal integral sliding surface and selecting an appropriate control law, the system exhibits global robustness to uncertainties and the ideal sliding mode dynamics is the same as that of optimal LQR for the nominal system. So a robust LQR tracking controller (RLQRTC) is realized. Simulation results show that the good tracking performance can be achieved and the uncertainties can be compensated using this proposed controller.