Abstract
This chapter presents dual decomposition as a means to coordinate a number of subsystems coupled by state and input constraints. Each subsystem is equipped with a local model predictive controller while a centralized entity manages the subsystems via prices associated with the coupling constraints. This allows coordination of all the subsystems without the need of sharing local dynamics, objectives and constraints. To illustrate this, an example is included where dual decomposition is used to resolve power grid congestion in a distributed manner among a number of players coupled by distribution grid constraints.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
D.P. Bertsekas, Nonlinear Programming (Athena Scientific, Belmont, 1999)
B. Biegel, P. Andersen, J. Stoustrup, J. Bendtsen, Congestion management in a smart grid via shadow prices, in IFAC Power Plant and Power Systems Control, Toulouse, 2012
S. Boyd, L. Xiao, A. Mutapic, Notes on subgradient, methods (2007)
S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge University Press, New York, 2004)
S. Boyd, L. Xiao, A. Mutapcic, J. Mattingley, Notes on decomposition methods (2008)
G.B. Danzig, P. Wolfe, The decomposition algorithm for linear programming. Econometrica 29, 767–778 (1961)
M.D. Doan, T. Keviczky, B. De Schutter, A dual decomposition-based optimization method with guaranteed primal feasibility for hierarchical MPC problems, in Proceedings of the 18th IFAC World Congress, pp. 392–397, Milan, Italy, August–September (2011)
K. Heussen, S. Koch, A. Ulbig, G. Andersson, Unified system-level modeling of intermittent renewable energy sources and energy storage for power system operation. IEEE Syst. J. 99, 1 (2011)
H Everett III, Generalized Lagrange multiplier method for solving problems of optimum allocation of resources. Oper. Res. 11(3), 399–417 (1962)
F.P. Kelly, A.K. Maulloo, D.K.H. Tan, Rate control in communication networks: shadow prices, proportional fairness and stability. J. Oper. Res. Soc. 49, 237–252 (1998)
A. Rantzer, Dynamic dual decomposition for distributed control. In American Control Conference, 2009. ACC ’09, pp. 884–888, June 2009
Anders Rantzer, On prize mechanisms in linear quadratic team theory, in Proceedings of 46th IEEE Conference on Decision and Control, New Orleans, LA, December 2007
S. Samar, S. Boyd, D. Gorinevsky, Distributed estimation via dual decomposition, in IEEE Multi-Conference on Systems and Control, Denver, CO., USA, Kos, Greece, July 2008
N.Z. Shor, Minimization Methods for Non-Differentiable Functions (Springer, New York, 1979)
Acknowledgments
The work is completed as a part of the project iPower and supported by the Danish government via the DSR-SPIR program 10-095378.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Biegel, B., Stoustrup, J., Andersen, P. (2014). Distributed MPC Via Dual Decomposition. In: Maestre, J., Negenborn, R. (eds) Distributed Model Predictive Control Made Easy. Intelligent Systems, Control and Automation: Science and Engineering, vol 69. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7006-5_11
Download citation
DOI: https://doi.org/10.1007/978-94-007-7006-5_11
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-7005-8
Online ISBN: 978-94-007-7006-5
eBook Packages: EngineeringEngineering (R0)