A multi-rate hierarchical fault-tolerant adaptive model predictive control framework: Theory and design for quadrotors

This paper presents the design and stability analysis of a dual-loop hierarchical controller for the trajectory tracking of quadrotors subject to unexpected actuator faults. The hierarchical controller, developed based on a dual-time-scale model decomposition, consists of two loops of control: the outer-loop translation control and the inner-loop rotation control. For translation control, we propose a novel fault-tolerant Lyapunov-based model predictive control strategy with the integration of an adaptive parameter estimator. For rotation control, feedback linearization and adaptive estimation are employed and a fault-tolerant control law is designed. The two loops of the developed hierarchical control system are both implemented in a sample-and-hold scheme with dual sampling rates — the outer-loop is sampled several times slower than the inner-loop. With the inter-sample behavior and the interconnection between the translational and rotational dynamics taken into account, the closed-loop stability of the dual-loop and dual-rate control system is rigorously proven using singular perturbation theory. Sufficient stability conditions are established, based on which control parameters and sampling periods can be tuned jointly such that a trade-off between computation efficiency and control accuracy can be attained. Results of numerical simulations are provided to demonstrate the effectiveness of the proposed control design in trajectory tracking and fault tolerance.