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 pric
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Distributed MPC Via Dual Decomposition B. Biegel, J. Stoustrup and P. Andersen
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.
11.1 Short Introduction In this chapter we consider a number of dynamical subsystems; each subsystem has local inputs and states, a local objective function, and local state and input constraints. Moreover, global state and input constraints make the subsystems mutually dependent. The subsystems are not able (or willing) to share the local information; hence optimization of the operation of the subsystems cannot be performed centrally and a distributed approach is necessary. We consider two small figurative examples to illustrate such global constraints causing coupling of the subsystems. As a first example, consider a number of subsystems that are dependent on the same shared limited resource: this could correspond B. Biegel (B) · J. Stoustrup · P. Andersen Department of Electronic Systems, Automation and Control Aalborg University, Aalborg, Denmark e-mail: [email protected] J. Stoustrup e-mail: [email protected] P. Andersen e-mail: [email protected] J. M. Maestre and R. R. Negenborn (eds.), Distributed Model Predictive Control 179 Made Easy, Intelligent Systems, Control and Automation: Science and Engineering 69, DOI: 10.1007/978-94-007-7006-5_11, © Springer Science+Business Media Dordrecht 2014
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to coupling input inequality constraints. In the second example, consider a number of producing and consuming subsystems in a setup where balance must exist: this could correspond to coupling state equality constraints. In both cases the optimization problem is to minimize the total objective while honoring both local and global constraints—without sharing local information. This chapter presents an approach to solve this problem via dual decomposition: by associating each coupling constraint with a price, the subsystems can be managed by a central entity to reach the solution. This allows coordination of the individual subsystems without sharing local dynamics, constraints or objectives. Further, the final prices of the coupling constraints, the so-called shadow prices, will reveal the marginal cost that each agent is willing to pay for the shared resources. This allows the shadow prices to be used for economical settlement purposes between the subsystems. Dual decomposition is a huge area of research and there exists a large amount of literature on the topic. Dual decomposition appeared already in 1960s where
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