Stability of Agent Based Distributed Model Predictive Control Over a Lossy Network

In this paper, an agent based control formulation of a large-scale cyber-physical system is proposed. Each agent can partially observe a part of the global dynamical process and estimate the associated local states through a combination of traditional Kalman filtering algorithm and consensus. The local estimates are then used for state feedback control. The optimal feedback gain of individual agents is obtained through dynamically solving a moving horizon linear quadratic optimization problem. The agents also exchange information among neighbors to coordinate the agent-wise state-feedback controls. Finally, a control decision incurring the least cost among all agents is applied to the global system. A Lyapunov function-based stability analysis is performed to obtain a bound over the degree of agent negotiation in designing the control decision. Besides, the effect of lossy communication network in control design and henceforth in global system stability is also investigated and the corresponding bound in control consensus is obtained. The theoretical results are verified via simulation of a 10-agent and a 50-agent dynamical process within a radial topology.