Regularized Filtered Basis Functions Approach for Accurate Tracking of Discrete-Time Linear Time Invariant Systems With Bounded Random Uncertainties

This paper proposes a regularized filtered basis functions (RFBF) approach for robust tracking of discrete-time linear time invariant systems with bounded random (unstructured) uncertainties. Identical to the filtered basis functions (FBF) approach, studied in prior work by the authors, the RFBF approach expresses the control trajectory as a linear combination of user-defined basis functions with unknown coefficients. The basis functions are forward filtered using a model of the system and their coefficients are selected to fulfill the tracking control objective. The two approaches differ in the coefficient selection process. The FBF approach selects the coefficients such that the tracking error is minimized in the absence of uncertainties, whereas, the proposed RFBF approach formulates the coefficient selection problem as a constrained game-type problem where the coefficients are selected to minimize the worst case tracking error in the presence of model uncertainty. Illustrative examples are used to demonstrate significantly more accurate tracking of uncertain systems using RFBF compared with FBF.