Composite Adaptive Control for Anti-Unwinding Attitude Maneuvers: An Exponential Stability Result Without Persistent Excitation

Abstract

This paper provides an exponential stability result for the adaptive anti-unwinding attitude tracking problem of a rigid body with uncertain inertia parameters, without the need for a persistent excitation (PE) condition. Specifically, a composite adaptive control scheme with guaranteed parameter convergence is proposed by integrating the dynamic regressor extension and mixing (DREM) technique into the dynamically scaled immersion and invariance adaptive control framework, wherein we modify the scaling factor so that the algorithm design does not involve any dynamic gains. To avoid the unwinding problem, a barrier function is introduced as the attitude error function, along with the establishment of two key algebraic properties for exponential stability analysis. Aiding by an linear time-varying filter, the scalar regressor of DREM is extended to generate an exciting counterpart. In this manner, the derived controller is shown to permit closed-loop exponential stability under a strictly weaker interval excitation condition than PE, in the sense that both the output-tracking and parameter estimation errors exponentially converge to zero. Furthermore, the composite adaptive law is also augmented to achieve finite/fixed-time parameter convergence in a time-synchronized manner. Simulation results are presented to verify our theoretical findings.