Exponentially stable adaptive optimal control of uncertain LTI systems

Abstract

SummaryA novel method of an adaptive linear quadratic (LQ) regulation of uncertain continuous linear time‐invariant systems is proposed. Such an approach is based on the direct self‐tuning regulators design framework and the exponentially stable adaptive control technique developed earlier by the authors. Unlike the known solutions, a procedure is proposed to obtain a non‐overparametrized regression equation (RE) with respect to the unknown controller parameters from an initial RE of the LQ‐based reference tracking control system. On the basis of such result, an adaptive law is proposed, which under mild regressor finite excitation condition provides monotonous convergence of the LQ‐controller parameters to an adjustable set of their true values, which bound is defined only by the machine precision. Using the Lyapunov‐based analysis, it is proved that the mentioned law guarantees the exponential stability of the closed‐loop adaptive optimal control system. The simulation examples are provided to validate the theoretical contributions.