Uniform ultimate boundedness of a Model Reference Adaptive Controller in the presence of unmatched parametric uncertainties

Abstract

In this paper, a novel Linear Matrix Inequality (LMI) condition for Uniform Ultimate Boundedness (UUB) of Model Reference Adaptive Control with σ-Modification in the presence of unmatched parametric uncertainties is presented. Due to the presence of unmatched uncertainties and due to the usage of the σ-Modification, the control objective of tracking a reference model may only be achieved approximately. A formulation of the UUB condition within the LMI framework provides less conservative bounds on the tracking error. This feature also enables the extension of the UUB condition towards a gain synthesis procedure, which allows the explicit specification of tracking error requirements. For a low-order system, it is demonstrated that the theoretically guaranteed bound on the tracking error of the synthesized adaptive controller is not overly conservative.