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

This paper provides an exponential stability result for the adaptive anti-unwinding attitude tracking control problem of a rigid body with uncertain but constant inertia parameters, without requiring the satisfaction of persistent excitation (PE) condition. Specifically, a composite immersion and invariance (I&I) adaptive controller is derived by integrating a prediction-error-driven learning law into the dynamically scaled I&I 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 tactful establishment of two crucial algebra properties for exponential stability analysis. The regressor filtering method is adopted in combination with the dynamic regressor extension and mixing (DREM) procedure to acquire the prediction error using only easily obtainable signals. In particular, aiding by a constructive liner time-varying filter, the scalar regressor of DREM is extended to generate a new exciting counterpart. In this way, the derived controller is shown to permit closed-loop exponential stability without PE, in the sense that both output-tracking and parameter estimation errors exponentially converge to zero. Further, the composite learning law is augmented with a power term to achieve synchronized finite/fixed-time parameter convergence. Numerical simulations are performed to verify the theoretical findings.