Control of a Linear Time Varying System With a Forward Riccati Formulation in Wavelet Domain

Abstract

A wavelet domain forward differential Ricatti formulation is proposed in this paper for control of linear timevarying (LTV) systems. The control feedback gains derived are timefrequency dependent, and they can be appropriately tuned for each wavelet scale or frequency band. The gains in the proposed forward formulation are functions of the present and past states and hence lead to a nonlinear controller. This nonlinear controller does not require information or approximation about future system matrices. The proposed controller is suitable for systems with timevarying (TV) system matrices and also for controlling transient dynamics. The performance of the proposed controller is compared with two other control strategies, namely, a TV linear quadratic regulator (LQR) based on a backward formulation of the differential Ricatti equation (DRE) and a multiscale waveletLQR controller based on asymptotic assumptions. Two numerical examples demonstrate promising results on the performance of the controller.