Adaptive control for optimal tracking of uncertain dynamical systems

In this paper, we propose a model reference adaptive control scheme for optimal tracking in the presence of uncertainties. A new reference model selection is introduced by using linear quadratic regulator theory. That is, we employ an optimal tracking control law for the nominal system and derive an adaptive tracking control law for the uncertain system with a performance guarantee related to the nominal optimality. Then the adaptive control law achieves the desired behaviour such that the output of the uncertain dynamical system asymptotically tracks a given reference signal in the presence of the system uncertainty. Numerical examples show that the proposed control algorithm is able to adaptively track the optimal response of the reference model and to suppress the influence of the uncertainties.