Robust linear quadratic optimal control for systems with linear uncertainties

This paper presents two simple but effective algorithms for selecting the weighting matrices needed in designing linear quadratic optimal control for systems with linear uncertainties. By utilizing the Lyapunov stability criterion, it is shown that the optimal state feedback control law designed for the nominal system can stabilize the uncertain system, provided the uncertainties satisfy the so-called matching conditions and are within a given bounding set. The methods are tested for three examples, and the results show that the current methods have wider application ranges than some approaches treating similar problems in the literature. Furthermore, this paper considers the case in which matching conditions are not exactly satisfied. A measure of mismatch is adopted from the literature, and a threshold on the mismatch is found to guarantee that the optimal controller designed for the system without the mismatching uncertainties is effective when the mismatching part is added. Finally, a method for adjusting the weighting matrix of the state variables in the cost function is suggested to facilitate the computation of the threshold value Communicated by Professor H. Kimura