Linear Quadratic Synchronization of Multi-Agent Systems: A Distributed Optimization Approach
It provides a novel distributed optimization framework for optimal synchronization in multi-agent systems, addressing a known bottleneck in distributed control.
This paper solves the distributed optimal synchronization problem for multi-agent systems with linear quadratic cost by formulating it as a distributed optimization problem and designing a new control protocol using ADMM. Numerical examples demonstrate effectiveness for both homogeneous and heterogeneous systems.
The distributed optimal synchronization problem with linear quadratic cost is solved in this paper for multi-agent systems with an undirected communication topology. For the first time, the optimal synchronization problem is formulated as a distributed optimization problem with a linear quadratic cost functional that integrates quadratic synchronization errors and quadratic input signals subject to agent dynamics and synchronization constraints. By introducing auxiliary synchronization state variables and combining the distributed synchronization method with the alternating direction method of multiplier (ADMM), a new distributed control protocol is designed for solving the distributed optimization problem. With this construction, the optimal synchronization control problem is separated into several independent subproblems: a synchronization optimization, an input minimization and a dual optimization. These subproblems are then solved by distributed numerical algorithms based on the Lyapunov method and dynamic programming. Numerical examples for both homogeneous and heterogeneous multi-agent systems are given to demonstrate the effectiveness of the proposed method.