Instant Distributed Model Predictive Control for Constrained Linear Systems

Distributed optimal control has emerged as an exciting possibility; however, existing algorithms tend to require excessive computational time and thus may not be able to stabilize systems with fast dynamics. We develop instant distributed model predictive control (iDMPC) with a realization of the primal-dual algorithm embedded in the controller dynamics. Under assumptions on fast communication, we show that the input and state trajectories of iDMPC are equivalent to a centralized suboptimal MPC scheme. We utilize a dissipativity analysis to show that the closed-loop system trajectories asymptotically converge to a desired reference.