Distributed MPC Via Dual Decomposition

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.

[1]  Naum Zuselevich Shor,et al.  Minimization Methods for Non-Differentiable Functions , 1985, Springer Series in Computational Mathematics.

[2]  Stephen P. Boyd,et al.  Notes on Decomposition Methods , 2008 .

[3]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[4]  Stephen P. Boyd,et al.  Distributed estimation via dual decomposition , 2007, 2007 European Control Conference (ECC).

[5]  Jakob Stoustrup,et al.  Congestion management in a smart grid via shadow prices , 2012 .

[6]  Harvey J. Everett.  Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources , 1963 .

[7]  M. D. Doan,et al.  A dual decomposition-based optimization method with guaranteed primal feasibility for hierarchical MPC problems , 2011 .

[8]  Anders Rantzer,et al.  Dynamic dual decomposition for distributed control , 2009, 2009 American Control Conference.

[9]  G. Dantzig,et al.  THE DECOMPOSITION ALGORITHM FOR LINEAR PROGRAMS , 1961 .

[10]  Kai Heussen,et al.  Unified System-Level Modeling of Intermittent Renewable Energy Sources and Energy Storage for Power System Operation , 2012, IEEE Systems Journal.

[11]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[12]  Anders Rantzer,et al.  On Prize Mechanisms in linear quadratic team theory , 2007, 2007 46th IEEE Conference on Decision and Control.

[13]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .