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

TL;DR

This paper introduces a distributed, plug-and-play model predictive control scheme for linear systems that guarantees stability and constraints satisfaction, utilizing robust control invariant sets and local computations, with an application to power network frequency control.

Contribution

It advances PnP control design by integrating robust control invariant sets and linear programming, enabling local controller synthesis with minimal information and computational resources.

Findings

Ensures asymptotic stability and constraint satisfaction in distributed systems.

Enables local controller design via linear programming.

Demonstrates effectiveness in power network frequency control.

Abstract

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.