Lyapunov-like functions for attitude control via feedback integrators
For control engineers working on attitude control systems, this work provides a Lyapunov-based method that expands the domain of attraction and ensures robustness, though it is an incremental improvement over existing feedback integrator techniques.
The paper proposes a constructive Lyapunov function for attitude dynamics embedded in Euclidean space, combined with feedback integrators to obtain a feedback law for attitude control. The approach yields a domain of attraction for the closed-loop dynamics, improving upon linearization-based methods, and is robust to numerical errors.
The notion of feedback integrators permits Euclidean integration schemes for dynamical systems evolving on manifolds. Here, a constructive Lyapunov function for the attitude dynamics embedded in an ambient Euclidean space has been proposed. We then combine the notion of feedback integrators with the proposed Lyapunov function to obtain a feedback law for the attitude control system. The combination of the two techniques yields a domain of attraction for the closed loop dynamics, where earlier contributions were based on linearization ideas. Further, the analysis and synthesis of the feedback scheme is carried out entirely in Euclidean space. The proposed scheme is also shown to be robust to numerical errors.