Passivity based distributed control: Optimality, stability and robustness

Abstract

Past decade has witnessed the explosive growth of data network, processing power, sensor miniaturization, and controllable devices. Drawing on the ready availability of such technologies, feedback control is now increasingly applied to highly complex interconnected systems. Applications include data network, robot swarm, and heating, cooling and lighting systems in large buildings. These systems, called distributed control systems, involve a large number of interacting subsystems with individual decision making criteria and sensing capabilities (considered as agents). Key issues for such systems involve the relationship between local optimization objectives and global systems-wide constraints, communication structure between agents, systems stability and robustness, and overall systems architecture to support heterogeneous sensors and actuators. In this paper, we consider distributed control algorithms for each agent in the system that steer the overall system towards collective goal based on the suitable feedback, but without explicit knowledge of the system interconnection and other agents' decision. The key to such robust behavior lies in convexity (for optimization) and passivity (for stability). If appropriate passive outputs, based on the interconnection constraints, are used for feedback, together with gradient type of update, then robust convergence towards the global constrained optimum is assured.