Cooperative Tube-based Distributed MPC for Linear Uncertain Systems Coupled Via Constraints
This chapter presents a robust form of distributed model predictive control for multiple, dynamically decoupled subsystems subject to bounded, persistent disturbances. Control agents make decisions locally and exchange plans; satisfaction of coupling cons
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Cooperative Tube-based Distributed MPC for Linear Uncertain Systems Coupled Via Constraints P. A. Trodden and A. G. Richards
Abstract This chapter presents a robust form of distributed model predictive control for multiple, dynamically decoupled subsystems subject to bounded, persistent disturbances. Control agents make decisions locally and exchange plans; satisfaction of coupling constraints is ensured by permitting only non-coupled subsystems to update simultaneously. Robustness to disturbances is achieved by use of the tube MPC concept, in which a local control agent designs a tube, rather than a trajectory, for its subsystem to follow. Cooperation between agents is promoted by a local agent, in its optimization, designing hypothetical tubes for other subsystems, and trading local performance for global. Uniquely, robust feasibility and stability are maintained without the need for negotiation or bargaining between agents.
3.1 Introduction This chapter presents a distributed form of MPC for systems defined by the following characteristics: the overall system is composed of, or may be decomposed to, a number of dynamically decoupled subsystems. Each has linear, time-invariant dynamics, and is subject to local constraints and persistent, bounded disturbances. The subsystems are coupled via constraints, and should coordinate decision-making to satisfy these constraints robustly and also to minimize some system-wide cost. In the described approach, the distributed control agents exchange plans to achieve constraint satisfaction. Key features are that (i) coupled subsystems may not update P. A. Trodden (B) Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, UK e-mail: [email protected] A. G. Richards Department of Aerospace Engineering, University of Bristol, Bristol, UK e-mail: [email protected]
J. M. Maestre and R. R. Negenborn (eds.), Distributed Model Predictive Control Made Easy, Intelligent Systems, Control and Automation: Science and Engineering 69, DOI: 10.1007/978-94-007-7006-5_3, © Springer Science+Business Media Dordrecht 2014
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their plans simultaneously; (ii) robust stability is guaranteed for any choice of update sequence; (iii) an agent communicates only when strictly necessary, and (iv) cooperation between agents is promoted by a local agent considering the objectives of, and designing hypothetical plans for, other subsystems. The resulting algorithm offers flexibility in communication and computation, and requires no inter-agent negotiation, iteration or bargaining. The approach, which first appeared in its non-cooperative form [10], uses the concept of tube MPC [6], a form of robust MPC that guarantees feasibility and stability despite the action of an unknown but bounded disturbance. The approach shares similarities with the ‘sequential’ DMPC method of Richards and How [7], in that robust feasibility and stability of the overall system is guaranteed by local agents updating plans one at a time, w
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