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.
Keywords
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
A. Alessio, D. Barcelli, A. Bemporad, Decentralized model predictive control of dynamically coupled linear systems. J. Process Control 21, 705–714 (2011)
W. Al-Gherwi, H. Budman, A. Elkamel, A robust distributed model predictive control algorithm. J. Process Control 21, 1127–1137 (2011)
P.D. Christofides, R. Scattolini, D. Muñoz de la Peña, J. Liu, Distributed model predictive control: A tutorial review and future research directions. Comput. Chem. Eng. 51, 21–41 (2013)
G. Cohen, B. Miara, Optimization with an auxiliary constraint and decomposition. SIAM J. Control Optim. 28, 137–157 (1990)
G.A. Constantinides, Parallel architectures for model predictive control, in Proceedings of the European Control Conference (Budapest, Hungary, 2009)
G.B. Dantzig, P. Wolfe, The decomposition algorithm for linear programs. Econometrica 29, 767–778 (1961)
W.B. Dunbar, Distributed receding horizon control of dynamically coupled nonlinear systems. IEEE Trans. Autom. Control 52, 1249–1263 (2007)
P. Giselsson, A. Rantzer, Distributed model predictive control with suboptimality and stability guarantees, in Proceedings of the Conference on Decision and Control (Atlanta, GA, 2010)
P. Giselsson, A. Rantzer, On feasibility, stability and performance in distributed model predictive control. IEEE Trans. Autom. Control 59, 1031–1036 (2014)
P. Giselsson, M.D. Doan, T. Keviczky, B. De Schutter, A. Rantzer, Accelerated gradient methods and dual decomposition in distributed model predictive control. Automatica 49, 829–833 (2013)
A. Grancharova, T.A. Johansen, Distributed model predictive control of interconnected nonlinear systems by dynamic dual decomposition, in Maestre JM, ed. by R.R. Negenborn (Springer, Distributed Model Predictive Control Made Easy, 2014)
A. Grancharova, S. Olaru, An approach to distributed robust model predictive control of discrete-time polytopic systems, in Proceedings of the 19th IFAC World Congress, (Cape Town, South Africa, 2014)
L. Grüne, A. Rantzer, On the infinite horizon performance of receding horizon controllers. IEEE Trans. Autom. Control 53, 2100–2111 (2008)
M. Heidarinejad, J. Liu, D. Muñoz de la Peña, J.F. Davis, P.D. Christofides, Multirate Lyapunov-based distributed model predictive control of nonlinear uncertain systems. J. Process Control 21, 1231–1242 (2011)
J.P. Hespanha, P. Naghshtabrizi, Y. Xu, A survey of recent results in networked control systems. Proc. IEEE Spec. Issue Technol. Netw. Control Syst. 95, 138–162 (2007)
J.M. Maestre, R.R. Negenborn, Distributed model predictive control made easy, in Series: Intelligent Systems, Control and Automation: Science and Engineering, vol. 69 (Springer, Hidelberg, 2014)
D.M. Raimondo, L. Magni, R. Scattolini, Decentralized MPC of nonlinear systems: An input-to-state stability approach. Int. J. Robust Nonlinear Control 17, 1651–1667 (2007)
R. Scattolini, Architectures for distributed and hierarchical model predictive control—A review. J. Process Control 19, 723–731 (2009)
A.N. Venkat, I.A. Hiskens, J.B. Rawlings, S.J. Wright, Distributed MPC strategies with application to power system automatic generation control. IEEE Trans. Control Syst. Technol. 16, 1192–1206 (2008)
Y. Zhang, S. Li, Networked model predictive control based on neighbourhood optimization for serially connected large-scale processes. J. Process Control 17, 37–50 (2007)
L. Zhang, H. Gao, O. Kaynak, Network-induced constraints in networked control system—A survey. IEEE Trans. Ind. Inf. 9, 403–416 (2013)
L. Zhang, J. Wang, C. Li, Distributed model predictive control for polytopic uncertain systems subject to actuator saturation. J. Process Control 23, 1075–1089 (2013)
Acknowledgments
This work was financed by the National Science Fund of the Ministry of Education and Science of Republic of Bulgaria, contract No. DRila 01/12 and the Partenariats Hubert Curien (PHC) Programme Rila of the French Government, contract No. 29401YJ “Robust distributed predictive control of complex systems.”
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Grancharova, A., Olaru, S. (2015). Distributed Robust Model Predictive Control of Interconnected Polytopic Systems. In: Olaru, S., Grancharova, A., Lobo Pereira, F. (eds) Developments in Model-Based Optimization and Control. Lecture Notes in Control and Information Sciences, vol 464. Springer, Cham. https://doi.org/10.1007/978-3-319-26687-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-26687-9_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26685-5
Online ISBN: 978-3-319-26687-9
eBook Packages: EngineeringEngineering (R0)