A novel parameter projection mechanism for smooth and stable adaptive control

Abstract

A novel parameter projection technique for handling uncertain parameters with a priori available upper and lower bounds is the subject of this paper. It is a wellknown fact that the conventional parameter projection method employed in certainty equivalence adaptive control is able to guarantee global asymptotic stability only after compromising control smoothness. In contrast, the technique presented in this paper preserves both stability and smoothness guarantees for the closed-loop adaptive system. The novelty of the proposed adaptive control formulation comes through our deliberate introduction of a nonlinear re-parameterization of uncertainty, thereby amounting to a significant shift from the classical certainty equivalence methodology. The proposed controller is non-overparameterized and has the potential to significantly improve transient performance because of full and proper utilization of all the available prior information on the unknown parameters. The technical descriptions are further elaborated via the Duffing nonlinear oscillator example to highlight the advantages of this new approach.