DISTRIBUTED CONTROL AND OPTIMIZATION IN MULTI-AGENT SYSTEMS

In recent years, the collective behaviors in nature have motivated rapidly expanding research efforts in the control of multi-agent systems. A multi-agent system is composed of multiple interacting subsystems (agents). In order to seek approaches that respect the network nature of multi-agent systems, distributed algorithms has recently received a significant amount of research attention, the goal of which is allowing multi-agent systems to accomplish global objectives through only local coordination.

Under this scope, we consider three major problems in this dissertation, namely, distributed computation, distributed optimization, and the resilience of distributed algorithms. First, for distributed computation, we devise distributed algorithms for solving linear equations, which can eliminate the initialization step for agents; converge to the minimum $l_1$ and $l_2$ solutions of under-determined linear equations; achieve ultimate scalability inters of agents' local storage and local states. Second, for distributed optimization, we introduce a new method for algorithm discretization so that the agents no longer have to carefully choose their step-size. We also introduce a new distributed optimization approach that can achieve better convergence rate with lower bandwidth requirement. Finally, for the resilience of distributed algorithms, we propose a new approach that allow normal agents in the multi-agent system to automatically isolate any false information from malicious agents without identification process. Though out the dissertation, all mentioned results are theoretically guaranteed and numerically validated.