Performance improvement of discrete-time linear-quadratic regulators applied to uncertain linear systems using the Tikhonov regularization method

Abstract

The linear-quadratic regulator (LQR) problem of optimal control of an uncertain discrete-time linear system (DTLS) is revisited in this paper from the perspective of Tikhonov regularization. We show that an optimally chosen regularization parameter reduces, compared to the classical LQR, the values of a scalar error function, as well as the cost function. The scalar regularization parameter can be calculated using a standard parameter choice method. Simulations confirm performance improvement when this regularized control signal is applied to a DTLS subject to a varying sampling rate