Robust distributed model predictive control of constrained dynamically decoupled nonlinear systems: A contraction theory perspective

This paper considers the robust distributed model predictive control (MPC) of a group of dynamically decoupled nonlinear systems cooperating via the cost function subject to control constraints. Inspired by the contraction theory, we develop the robust distributed MPC scheme assuming that the dynamics of the cooperating systems satisfy the contraction property (they are contracting in a tube centered around a nominal state trajectory). Compared to conventional robust distributed MPC which uses the Lipschitz continuity property, the proposed method features the following aspects: (1) it can tolerate larger disturbances; and (2) it is feasible for a larger prediction horizon and could enlarge the feasible region accordingly. The paper evaluates the maximum disturbance which the nonlinear system can tolerate when controlled using the proposed method and derives sufficient conditions for the recursive feasibility of the optimization and for the practical stability of the closed-loop system. The effectiveness of the proposed method is illustrated using a simulation example.