Robust Coalitional Distributed Model Predictive Control Algorithm with Stability via Terminal Constraint

This paper proposes a robust coalitional distributed model predictive control algorithm suitable for input coupled sub-systems. The core idea is based on a distributed iterative implementation with minimum information exchange, in which the coupling information is regarded as bounded additive uncertainty. If the disturbance received from the neighbours is too large for the local optimization problem, then a coalitional strategy is adopted. The closed-loop stability is guaranteed via terminal constraint. The performance of the coalitional strategy is compared with an iterative min-max distributed model predictive controller and a centralized model predictive controller.

[1]  Hong Chen,et al.  On min-max feasible cooperation-based distributed model predictive control , 2011, 2011 IEEE International Conference on Computer Science and Automation Engineering.

[2]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[3]  D. Jia,et al.  Min-max feedback model predictive control for distributed control with communication , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[4]  A. Garulli,et al.  Robustness in Identification and Control , 1989 .

[5]  Johan A. K. Suykens,et al.  Min-max feedback MPC using a time-varying terminal constraint set and comments on "Efficient robust constrained model predictive control with a time-varying terminal constraint set" , 2005, Syst. Control. Lett..

[6]  Olaf Stursberg,et al.  Hierarchical Distributed Control for Interconnected Systems , 2013 .

[7]  Eduardo F. Camacho,et al.  Distributed model predictive control based on a cooperative game , 2011 .

[8]  Alberto Bemporad,et al.  Robustness in Identification and Control , 1999 .

[9]  Eduardo F. Camacho,et al.  Coalitional model predictive control of an irrigation canal , 2014 .

[10]  J. H. Leet,et al.  Worst-case formulations of model predictive control for systems with bounded parameters , 1997, Autom..

[11]  B. Rohal’-Ilkiv,et al.  Robust min-max model predictive control of linear systems with constraints , 2003, IEEE International Conference on Industrial Technology, 2003.

[12]  Eduardo F. Camacho,et al.  Coalitional Control: Cooperative Game Theory and Control , 2017, IEEE Control Systems.

[13]  L. Magni,et al.  Decentralized open-loop MPC of nonlinear systems: An Input-to-State Stability Approach , 2007, 2007 European Control Conference (ECC).

[14]  Eduardo F. Camacho,et al.  A coalitional control scheme with applications to cooperative game theory , 2014 .

[15]  Jan M. Maciejowski,et al.  Predictive control : with constraints , 2002 .

[16]  Eduardo F. Camacho,et al.  Distributed model predictive control based on agent negotiation , 2011 .

[17]  Johan Löfberg,et al.  Automatic robust convex programming , 2012, Optim. Methods Softw..

[18]  Hideaki Ishii,et al.  A PageRank based coalitional control scheme , 2017 .

[19]  E. Gilbert,et al.  Theory and computation of disturbance invariant sets for discrete-time linear systems , 1998 .

[20]  Eduardo F. Camacho,et al.  Input to state stability of min-max MPC controllers for nonlinear systems with bounded uncertainties , 2006, Autom..