Distributed Cooperative Optimal Load-Sharing Control for Coupled Parallel-Connected Dynamical Systems

In this paper, a distributed load-sharing control is proposed for one class of coupled parallel-connected dynamical systems with non-identical nonlinear dynamics. The communication between subsystems is modeled into a digraph. To construct the relationship between input and output, the input-output linearization technique is adopted to transform the load-sharing control design into a tracking synchronization problem of a general linear multi-agent system. LQR-based method is introduced to design the cooperative load-sharing control law based on the nearest neighbor principle, which makes the coupling strength only depend on the communication topology and the control gain only depend on the sub-system model. The asymptotical stability of the entire closed-loop systems can be decoupled into each sub-system's stability through matrix transformation provided that the directed graph has a spanning tree, which is rigorously proved with the aid of the Lyapunov function. A desired response speed can be obtained by tuning the control parameters based on the LQR method. The proposed approach is successfully applied to address the current-sharing problem of parallel charging systems for energy storage type light rail vehicles.