Distributed Optimal Coordination of Multiple Dynamical Systems under Practical Constraints and its Applications

The distributed optimal coordination of networked multiple dynamical systems has experienced significant advances in recent years because of its great potential in a wide range of applications. Typical examples include cooperative source-seeking with multi-robot systems, formations of unmanned ground/aerial vehicles, and the coordination of distributed energy resources in power systems. Distributed optimal coordination entails the development of distributed control strategies to drive a team of networked agents toward an optimal solution that minimizes the sum of the local cost functions assigned to individual agents. Distributed control strategies refer to the control laws for individual agents that rely on information only from the agent itself and from its neighbors. Such strategies are preferred because they significantly reduce the communication load while greatly enhancing the robustness and flexibility of networked dynamical systems. Considerable research effort in recent years has been devoted to distributed optimal coordination for networked multiple dynamical systems. Most existing works on the topic assume that communication network topologies among agents are undirected graphs or, at most, balanced digraphs. Moreover, the proposed control strategies rely on certain global information about network connectivity and/or objective functions and are thus not fully distributed. However, in many practical scenarios, these assumptions about communication network topologies and global information are hardly satisfied for various reasons, including complex environments and hardware limitations. Instead, communication network topologies among agents in practical scenarios are often unbalanced digraphs, and the required global information is often not available. This project aims to develop a framework to address the fully distributed optimal coordination problems of multi-agent systems with general agent dynamics over unbalanced digraphs. The main challenges of these problems lie in the imbalance of the communication topologies, the lack of global information, as well as the complexity of general agent dynamics. This project will develop novel fully distributed adaptive output feedback control strategies and establish the optimality and stability of the resulting closed-loop multi-agent systems over unbalanced directed communication topologies. The developed control strategies will be consolidated and validated through their application to source-seeking with multiple mobile robotic vehicles. It is expected that the results from this project will address many theoretical hurdles to meeting the demanding challenges faced by distributed optimal coordination of networked dynamical systems in real-world applications.