Control of Multi-Agent Systems with Applications to Distributed Frequency Control Power Systems

Abstract: Multi-agent systems are interconnected control systems with many application domains. The first part of this thesis considers nonlinear multi-agent systems, where the control input can be decoupled into a product of a nonlinear gain function depending only on the agent's own state, and a nonlinear interaction function depending on the relative states of the agent's neighbors. We prove stability of the overall system, and explicitly characterize the equilibrium state for agents with both single- and double-integrator dynamics.Disturbances may seriously degrade the performance of multi-agent systems. Even constant disturbances will in general cause the agents to diverge, rather than to converge, for many control protocols. In the second part of this thesis we introduce distributed proportional-integral controllers to attenuate constant disturbances in multi-agent systems with first- and second-order dynamics. We derive explicit stability criteria based on the integral gain of the controllers.Lastly, this thesis presents both centralized and distributed frequency controllers for electrical power transmission systems. Based on the theory developed for multi-agent systems, a decentralized controller regulating the system frequencies under load changes is proposed. An optimal distributed frequency controller is also proposed, which in addition to regulating the frequencies to the nominal frequency, minimizes the cost of power generation.