Data-Driven Immersion and Invariance Adaptive Attitude Control for Rigid Bodies With Double-Level State Constraints

Abstract

This article investigates the attitude control problem of a rigid body subject to attitude and angular rate constraints (double-level state constraints), and inertia uncertainties. A data-driven immersion and invariance (I&I) adaptive control scheme is proposed to tackle this technically challenging problem. As a stepping stone, a novel dynamically scaled I&I adaptive controller is designed to bypass the realizability condition that may not hold in the Lyapunov sense when considering angular rate constraints. Lyapunov stability analysis shows that this controller can enable the attitude errors and angular rates to converge asymptotically to zero for most initial conditions in the accessible space, while strictly obeying double-level state constraints with the help of two judiciously constructed potential functions. After that, to further relax the dependence of parameter convergence on the persistent excitation (PE) condition, the I&I adaptive law is extended to a data-driven counterpart through adding a learning term that is acquired by adopting the regressor filtering in conjunction with the dynamic regressor extension and mixing (DREM) procedure. The extended adaptive controller can not only preserve all the results obtained by the earlier proposed I&I adaptive controller, but also ensure asymptotic parameter convergence under a finite excitation condition much weaker than PE. In addition, benefiting from the DREM method and some special designs, the parameter convergence rates across all the parameter vector components can be flexibly tuned in an explicit way, and moreover, they are independent of the excitation level. Finally, simulation results are given to show the effectiveness of the proposed method.