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.

Asymptotic tracking control for state‐constrained strict‐feedback systems with non‐vanishing uncertainties

“…With θ1 (0) ≥ 0, it is obvious that z 1 𝜂 1 g 1 𝛼 1 ≤ 0. Substitute (19) and ( 20) into ( 18), we have…”

“…Thereby, when system has non-vanishing uncertainties, most existing studies seem to only obtain uniformly ultimately bounded (UUB) results. 19,20 There have been some other efforts to be made to derive the zero-error convergence precision. The signum function 21 or soft signum function 22,23 based methods have been used to derive asymptotic stability results, however, the discontinuous control input may result in the undesirable chattering phenomenon 24 and their control schemes cannot be applied to the systems with non-vanishing uncertainties.…”

Adaptive control of unactuated dynamical systems through interconnections: Stability and performance guarantees

“…To see this, we similarly augment the dynamics in and yielding From , the challenge of this “augment the dynamics” approach is that the uncertainty in the term “” is unmatched, meaning that there is no access to the control channel to suppress this uncertainty with standard model reference adaptive control architectures. While there are some approaches to handle unmatched uncertainties in the context of model reference adaptive control, they involve additional complexity; hence, they are not adopted in the context of this article.…”