Event-triggered robust distributed nonlinear model predictive control using contraction theory

In this paper, we study the cooperation problem over a group of discrete-time nonlinear dynamically decoupled multi-agent systems (MAS). A distributed model predictive control (DMPC) scheme is proposed in the event-triggered context. Agents cooperate through a coupled cost function subject to input constraints. From the practical perspective, the additive disturbances are taken into account in the controller design. Using the contraction theory in the framework of Riemannian manifolds, a novel constraint is constructed in the DMPC optimization problem to provide the capability of disturbance rejection. Moreover, the event-triggered mechanism is introduced for saving computational and communicational resources. The event-triggering condition is developed by checking the Riemannian distance between the actual and optimal state trajectories. The stability of the closed-loop system and recursive feasibility of the DMPC scheme, thereafter, are rigorously analyzed. In particular, the stability analysis is built upon the contraction theory, which distinguishes this work from the existing results using the conventional Lyapunov theory. It is shown that the recursive feasibility is guaranteed if the additive disturbances are bounded and the event-triggering condition is properly designed. The numerical simulation results demonstrate the effectiveness of the proposed algorithm.