Guaranteed cost equilibrium strategies for the control of networked multi-agent systems

Abstract

The study of multi-agent systems (MAS) and related control architectures is becoming increasingly popular in emerging engineering systems such as power grids, multi-robot systems, IoT (Internet of Things) systems, and sensor networks. These systems are large-scale and characterized by multiple interdependent decision-making entities, or agents, that are networked and heterogeneous.

This work focuses on the distributed control of networked MAS with linear time-invariant dynamics and quadratic performance measures. Since the MAS is networked, each agent has access only to the state information of its neighbors, also referred to as the local or output feedback information structure. Consequently, full-state feedback controllers are not implementable.

Using a game-theoretic framework, we model the distributed control problem as a networked differential game. We illustrate that verifying the existence of an output feedback Nash equilibrium is challenging due to structural constraints imposed by the network topology. To address this, we develop the notion of an output feedback guaranteed cost equilibrium. These equilibrium controllers ensure an upper bound on individual agent costs while maintaining an equilibrium property.

We derive several properties of these equilibrium strategies and provide linear matrix inequality-based conditions for their existence, along with an algorithm for synthesizing them. Finally, we demonstrate the performance of the proposed equilibrium strategies through numerical experiments.

(joint work with Aniruddha Roy).