Distributed Robust Model Predictive Control of Interconnected Polytopic Systems

Alexandra Grancharova (1) , Sorin Olaru (2, 3, 4)

1 University of Chemical Technology and Metallurgy [Sophia]
2 L2S - Laboratoire des signaux et systèmes
3 CentraleSupélec
4 DISCO - Dynamical Interconnected Systems in COmplex Environments

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.

Keywords: Predictive control Distributed control Robust control Distributed optimization Accelerated gradient method Interconnected systems Polytopic systems Constraints

Domains: Engineering Sciences [physics]; Automatic

Alexandra Grancharova, Sorin Olaru. Distributed Robust Model Predictive Control of Interconnected Polytopic Systems. Developments in Model-Based Optimization and Control, 464, pp.73-91, 2015, Lecture Notes in Control and Information Sciences, 978-3-319-26685-5. ⟨10.1007/978-3-319-26687-9_4⟩. ⟨hal-01261636⟩