An asymptotic decoupling approach for adaptive control with unmeasurable coupled dynamics

While adaptive control methods have the capability to suppress the effect of system uncertainties without excessive reliance on dynamical system models, their stability can be adversely affected in the presence of coupled dynamics. Motivated by this standpoint, the contribution of this article is a decoupling approach for model reference adaptive control algorithms. The key feature of the proposed framework is that it guarantees asymptotic convergence between the trajectories of an uncertain dynamical system and a given reference model without relying on any measurements from the coupled dynamics under a tight sufficient stability condition. We also provide a generalization to address the uncertainty in the control effectiveness matrix, where the resulting sufficient stability condition in this case relies on linear matrix inequalities. Finally, numerical examples are provided to illustrate the efficacy of the presented theoretical results.