Distributed Control of Multi-Agent Systems and Management of Networked Battery Units

In this dissertation, distributed control problems of multi-agent systems are studied. The applications of distributed control algorithms to the management of networked battery units are also investigated.

The leader-following almost output consensus problem for both continuous-time and discrete-time linear heterogeneous multi-agent systems is considered, in which the unstable zero dynamics of the follower agents are affected by disturbance. Due to the inapplicability of high gain feedback to the discrete-time setting, different conditions on the way the agents are affected by the disturbance in the two cases have to be identified. Low-and-high gain-based state feedback and output feedback consensus protocols are proposed for continuous-time multi-agent systems. State feedback and output feedback consensus protocols for discrete-time multi-agent systems are constructed based on low gain feedback and a modified discrete-time Riccati equation. The proposed consensus protocols are shown to achieve leader-following output consensus to an arbitrarily high level of accuracy, and attenuate the effect of the disturbance on the consensus errors to an arbitrarily low level.

The almost output consensus problem of nonlinear multi-agent systems is then considered. Conditions on the nonlinear systems are established under which distributed consensus protocols are designed in a recursive manner. The protocols are shown to achieve almost output consensus, that is, output consensus of the system is achieved in the absence of the disturbances, and the L2-gain from the disturbances to the output consensus error of agents when the system is operating in output consensus can be made arbitrarily small.

The suboptimal output consensus problem for discrete-time heterogeneous linear multi-agent systems with unstable zero dynamics is also studied, where each agent possesses its own objective function, and the sum of all these private objective functions, called the overall objective function, is to be minimized. Mild assumptions on the communication topology and the agent dynamics are made under which a parameterized distributed consensus protocol based on low gain feedback is proposed for each agent. The multi-agent system is shown to achieve suboptimal output consensus under the proposed protocols in the sense that the states of all agents remain bounded while their outputs converge to a pre-specified arbitrarily small neighborhood of the optimal point as long as the design parameter is chosen small enough.

Finally, the management problem of networked battery units in DC microgrids is studied. Specifically, the control problem of balancing the state-of-charge (SoC) among the networked battery units while satisfying the total charging/discharging power demand is considered. Power allocation algorithms for the battery units that make use of distributed estimators for the average desired power and the average unit state and the adaptive parameter estimators are proposed. Power allocation algorithms are also proposed based on adaptive parameter estimations for battery units with unknown parameters. Algorithms that make use of SoC observers based on equivalent circuit models of the batteries are also constructed for networked battery systems with unknown SoC. The algorithms are shown to achieve SoC balancing among all battery units while satisfying the power demand.