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.

💡 Research Summary

The paper addresses the problem of controlling a networked linear system whose subsystems are linked by a directed coupling graph. It proposes a distributed Model Predictive Control (MPC) architecture that guarantees asymptotic stability and strict adherence to input and state constraints while supporting true plug‑and‑play (PnP) operations. Building on the framework introduced by Riverso et al. (2012), the authors replace the original robust invariant set computation with a modern linear‑programming (LP) based method for constructing robust control invariant (RCI) sets. By representing each local invariant set as a polyhedron obtained via LP, the design of each local tube‑MPC controller becomes computationally lightweight and can be performed using only information from the subsystem’s predecessors.

The synthesis procedure consists of four steps: (1) extraction of the interconnection matrices from the graph, (2) LP‑based computation of a local RCI set, (3) selection of tube‑MPC parameters (cost matrices, constraint tightening, terminal set), and (4) solving a local quadratic program at each sampling instant. Because the RCI set is guaranteed to contain all admissible disturbances, the local controller can enforce tightened constraints that ensure the true system respects the original limits.

PnP capability is achieved in two ways. When a new subsystem is added, only its direct successors need to redesign their controllers; the existing controllers of all other subsystems remain unchanged. Conversely, when a subsystem is removed, only its successors must recompute their local tubes. This localized redesign dramatically reduces the communication and computational burden in large‑scale networks such as power grids, traffic systems, or modular robotics.

The authors provide a rigorous stability proof: the existence of local RCI sets allows the construction of a global Lyapunov function composed of the local terminal costs, establishing global asymptotic stability of the closed‑loop system. Constraint satisfaction follows directly from the tube construction.

To demonstrate practicality, the methodology is applied to frequency regulation in a benchmark power network. Simulation results show faster frequency recovery, reduced overshoot, and strict compliance with generation and line flow limits compared with the original PnP‑MPC scheme. Moreover, the LP‑based invariant set computation cuts the offline design time by an order of magnitude, confirming the feasibility of real‑time deployment.

In summary, the paper delivers a scalable, computationally efficient, and theoretically sound PnP‑MPC solution that leverages recent advances in robust invariant set computation, making it highly suitable for modern large‑scale cyber‑physical systems.