Plug and play distributed model predictive control based on distributed invariance and optimization

Abstract

Abstract-This paper presents a method for plug-and-play distributed MPC of a network of interacting linear systems. The previously introduced idea of plug and play control addresses the challenge of performing network changes in the form of subsystems that are joining or leaving the network during closed-loop operation, while maintaining stability and constraint satisfaction. This work extends these ideas to an iterative distributed MPC scheme for systems with strong coupling by employing a recently proposed method for distributed MPC that takes the coupling dynamics into account in the form of time-varying terminal sets and distributed optimization. A distributed synthesis procedure for the update of the local control laws is proposed together with a transition scheme preparing the system for the upcoming modifications. This enables automatic plug-and-play operation, including rejection if the new network topology is infeasible. Both the synthesis and online control are entirely distributed and are only based on local information on the subsystems and their coupled neighbors. Finally, the proposed scheme is applied to the problem of frequency control in a power network. I. INTRODUCTIONDistributed control is a promising tool to overcome the limiting computational complexity and communication requirements associated with centralized control of large-scale networked systems. This paper presents an approach for distributed linear Model Predictive Control (MPC) with plug and play capabilities, enabling network changes by subsystems joining or leaving the network, while ensuring stability and constraint satisfaction of the global system. The proposed scheme makes plug and play MPC available for networks with strongly coupled subsystems by means of distributed invariance and optimization and allows for an entirely distributed controller synthesis.The control of large complex networks represents one of the key challenges in order to cope with many relevant control problems, examples include electric power, water resources, gas and fuel distribution, transportation or telecommunication networks. In this context, Model Predictive Control offers an attractive tool, being a high performance control scheme for constrained systems that allows

Distributed synthesis and stability of cooperative distributed model predictive control for linear systems

“…This method can be executed in a completely distributed way, a feature which is particularly beneficial in case of changing network topologies, where new controllers have to be synthesized on the fly without central coordination. This case has received considerable attention in the context of plug-and-play MPC (Riverso, Farina & Trecate 2013), (Zeilinger, Pu, Riverso, Ferrari-Trecate & Jones 2013).…”

Decentralized Optimal Demand-Side Management for PHEV Charging in a Smart Grid

“…3) If q(k) = q(k) for some k =k, then q(k) + p(k) = q(k) + p(k). Proof: From (12)- (14), we can infer that q(k 1 )…”

“…The three subsets N 1 , N 2 , and N 3 correspond to (14), (12) and (13), respectively. Then Lemma 1 gives properties of the water-filling solution p(k).…”

Distributed model predictive control for continuous‐time nonlinear systems based on suboptimal ADMM

“…A variety of approaches have recently been developed in DMPC that address aspects such as communication effort and flexible (re)configuration in connection with stability aspects for the network. This includes, for instance, robust tube‐based DMPC, plug‐and‐play DMPC, and most recently, coalitional MPC . In addition, dynamically coupled systems have been in the focus of DMPC research over the last years.…”

“…The majority of the literature on DMPC for dynamically coupled systems considers linear discrete‐time systems, although continuous‐time and nonlinear systems have been in the focus of the recent past as well . In most cases, the subsystems are assumed to be linearly coupled to the state and/or control variables of their neighbors . Alternative formulations concern linear output variables or functions or coupling constraints …”