Adaptive stabilization of parameter-affine minimum-phase plants under Lipschitz uncertainty

The maximum capability of feedback control for discrete-time systems under a nonparametric Lipschitz uncertainty was first established in Xie and Guo (2000) for the simplest dynamical control system. It was shown that the necessary and sufficient condition for the adaptive stabilizability is of the form L < 3/2 + root 2, where L is the Lipschitz constant of the uncertainty. This result was extended in Huang and Guo (2012) to a basic class of scalar discrete-time minimum-phase control systems under an additional parametric uncertainty, and the adaptive stabilization was achieved with the use of an impracticable infinite memory feedback based on a brute-force search over a sufficiently fine grid in the prior set of unknown parameters. In the present paper, the adaptive stabilization problem is considered for a subclass of parameter-affine minimum-phase systems. The solution of the problem is based on new recurrent objective inequalities enabling to estimate and validate the closed loop system online and to formulate a simple projection-type parameter estimation algorithm instead of the brute-force search used in Huang and Guo (2012). The computational tractability of the proposed finite-memory stabilizing feedback is illustrated via simulations. (C) 2016 Elsevier Ltd. All rights reserved.