Adaptive Control for Distributed Multi-Agent Coordination

Distributed multi-agent coordination has drawn increased attention in past decades. Distributed coordination refers to the behavior that a group of agents reaches a certain group coordination with local sensor information and limited inter-agent communications. Depending on the specific task of the distributed multi-agent coordination, a group of agents may move together in a collective manner, maintain a certain formation configuration, or reach an agreement on certain quantity of interest. These coordination problems are called flocking, formation control and consensus, respectively. A majority of existing research on distributed multi-agent coordination mainly considers agents governed by linear dynamics, while few papers address the coordination with uncertainties. The presence of uncertainties will degenerate the performance, or even destabilize the whole multi-agent system. The main contribution of this dissertation is to develop a control framework for distributed multi-agent coordination with nonlinear uncertainties by integrating cooperative control and L1 adaptive control laws. The L1 adaptive control law is used to handle the mismatched dynamics between the real agent’s and the ideal agent’s dynamics, which mainly stem from unknown nonlinear uncertainties. The cooperative control law is designed for ideal multi-agent systems without uncertainties, where information regarding the ideal states, instead of the real states, is exchanged through a communication network. Additionally, the cooperative control law uses an artificial potential function to capture the coordination of ideal agents, where the minimum corresponds to the equilibrium state of the desired coordination. Hence, by changing the potential function design, the cooperative control law can handle different coordination such as flocking, formation control, and consensus. Some new extensions of the L1 adaptive control for nonlinear Multi-Input Multi-Output (MIMO) systems and Linear Time-Varying (LTV) systems with disturbances are first presented. The effectiveness of using the L1 adaptive control for coordination of a two-agent system with uncertainties is also discussed and demonstrated. Then, details of the control framework for multi-agent coordination are introduced, followed by a study on how to employ the control framework for flocking, consensus, and formation control. For the flocking case, flocking algorithms under a fixed graph and a time-varying graph are discussed. For the consensus case, both normal consensus and consensus with a virtual leader are analyzed. For the formation control case, formation achieved with collision avoidance is considered. For these multi-agent coordination problems, the real multi-agent system stays close to the ideal multi-agent system which achieves the desired coordination by using the presented control framework