Distributed robust model predictive control of interconnected polytopic systems

Abstract

A suboptimal approach to distributed robust MPC for uncertain systems consisting of polytopic subsystems with coupled dynamics subject to both state and input constraints is proposed. The robustness is defined in terms of the optimization of a cost function accumulated over the uncertainty and satisfying state constraints for a finite subset of uncertainties. The approach reformulates the original centralized robust MPC problem into a quadratic programming problem, which is solved by distributed iterations of the dual accelerated gradient method. A stopping condition is used that allows the iterations to stop when the desired performance, stability, and feasibility can be guaranteed. This allows for the approach to be used in an embedded robust MPC implementation. The developed method is illustrated on a simulation example of an uncertain system consisting of two interconnected polytopic subsystems.