PnP Operations to Maintain Persistent Feasibility in Linear Constrained Systems

Abstract

Multi-agent systems often have high dimensional state and input spaces that change rapidly as agents join and leave the system. The plug-and-play (PnP) design paradigm provides a framework to design controllers in this context by shifting most computations for individual agents to design-time. Smaller, numerically tractable PnP algorithms are then used to allow the agents to join and leave the network while maintaining persistent feasibility and stability. In constrained systems, persistent feasibility is assured within feasible control invariant (CI) sets. This work develops a PnP framework to compute these sets for a class of distributed, non-cooperative linear systems. The agents are allowed a preview of the cross-disturbance but no other restrictions are placed on the agents’ controllers. At design-time, undisturbed and maximally disturbed CI sets are found for each agent individually. As the network changes, the agents’ current CI sets are computed using linear combinations of these extreme CI sets. With this, on-line constraint adjustments can be accomplished through distributed optimization problems that scale well for large networks. The overall solution is agnostic to the local controller design and accounts for the local states at the time of the PnP operations.