Plug and Play Distributed Model Predictive Control Based on Distributed Invariance and Optimization

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

Plug-and-Play Model Predictive Control based on robust control invariant sets

In this paper we consider a linear system represented by a coupling graph between subsystems and propose a distributed control scheme capable to guarantee asymptotic stability and satisfaction of constraints on system inputs and states. Most importantly, as in Riverso et al., 2012 our design procedure enables plug-and-play (PnP) operations, meaning that (i) the addition or removal of subsystems triggers the design of local controllers associated to successors to the subsystem only and (ii) the synthesis of a local controller for a subsystem requires information only from predecessors of the subsystem and it can be performed using only local computational resources. Our method hinges on local tube MPC controllers based on robust control invariant sets and it advances the PnP design procedure proposed in Riverso et al., 2012 in several directions. Quite notably, using recent results in the computation of robust control invariant sets, we show how critical steps in the design of a local controller can be solved through linear programming. Finally, an application of the proposed control design procedure to frequency control in power networks is presented

A scalable line-independent design algorithm for voltage and frequency control in AC islanded microgrids

We propose a decentralized control synthesis procedure for stabilizing voltage and frequency in AC Islanded microGrids (ImGs) composed of Distributed Generation Units (DGUs) and loads interconnected through power lines. The presented approach enables Plug-and-Play (PnP) operations, meaning that DGUs can be added or removed without compromising the overall ImG stability. The main feature of our approach is that the proposed design algorithm is line-independent. This implies that (i) the synthesis of each local controller requires only the parameters of the corresponding DGU and not the model of power lines connecting neighboring DGUs, and (ii) whenever a new DGU is plugged in, DGUs physically coupled with it do not have to retune their regulators because of the new power line connected to them. Moreover, we formally prove that stabilizing local controllers can be always computed, independently of the electrical parameters. Theoretical results are validated by simulating in PSCAD the behavior of a 10-DGUs ImG

Distributed bounded-error state estimation for partitioned systems based on practical robust positive invariance

We propose a partition-based state estimator for linear discrete-time systems composed by coupled subsystems affected by bounded disturbances. The architecture is distributed in the sense that each subsystem is equipped with a local state estimator that exploits suitable pieces of information from parent subsystems. Moreover, differently from methods based on moving horizon estimation, our approach does not require the on-line solution to optimization problems. Our state-estimation scheme, that is based on the notion of practical robust positive invariance developed in Rakovic 2011, also guarantees satisfaction of constraints on local estimation errors and it can be updated with a limited computational effort when subsystems are added or removed

Voltage stabilization in DC microgrids: an approach based on line-independent plug-and-play controllers

We consider the problem of stabilizing voltages in DC microGrids (mGs) given by the interconnection of Distributed Generation Units (DGUs), power lines and loads. We propose a decentralized control architecture where the primary controller of each DGU can be designed in a Plug-and-Play (PnP) fashion, allowing the seamless addition of new DGUs. Differently from several other approaches to primary control, local design is independent of the parameters of power lines. Moreover, differently from the PnP control scheme in [1], the plug-in of a DGU does not require to update controllers of neighboring DGUs. Local control design is cast into a Linear Matrix Inequality (LMI) problem that, if unfeasible, allows one to deny plug-in requests that might be dangerous for mG stability. The proof of closed-loop stability of voltages exploits structured Lyapunov functions, the LaSalle invariance theorem and properties of graph Laplacians. Theoretical results are backed up by simulations in PSCAD

Plug-and-play distributed state estimation for linear systems

This paper proposes a state estimator for large-scale linear systems described by the interaction of state-coupled subsystems affected by bounded disturbances. We equip each subsystem with a Local State Estimator (LSE) for the reconstruction of the subsystem states using pieces of information from parent subsystems only. Moreover we provide conditions guaranteeing that the estimation errors are confined into prescribed polyhedral sets and converge to zero in absence of disturbances. Quite remarkably, the design of an LSE is recast into an optimization problem that requires data from the corresponding subsystem and its parents only. This allows one to synthesize LSEs in a Plug-and-Play (PnP) fashion, i.e. when a subsystem gets added, the update of the whole estimator requires at most the design of an LSE for the subsystem and its parents. Theoretical results are backed up by numerical experiments on a mechanical system

Robust coalitional model predictive control with plug-and-play capabilities

This article presents a distributed implementation of a model predictive controller with information exchange to manage a distributed networked system of coupled dynamic subsystems. We propose a coalitional control method, where local controllers coalesce into clusters to improve performance, as a tool to solve plug-and-play problems. Our main contribution is a tube-based coalitional approach that employs online optimized invariant sets. These sets are instrumental in guaranteeing recursive feasibility and stability when faced with plug-and-play operations, i.e., subsystems joining or leaving the network. We also explore the inherent robustness properties to absorb disturbances not covered by the tubes without the need to group local controllers. Finally, the simulation results show the benefits of our proposed control method.(c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)