基于LQR的耦合动态互联系统分布式协作 负载均衡优化控制

针对一类非等同非线性耦合互联系统,提出分布式协作负载均衡优化控制方法.将子系统间的通信联系建模成有向图,借助输入输出反馈线性化技术,将耦合互联系统的分布式负载均衡控制设计问题转化为广义线性多智能体系统的同步跟踪问题;基于最近邻原则和LQR方法,设计增益可调的分布式协作负载均衡优化控制律,耦合强度依赖于通信拓扑,控制增益依赖于子系统模型;借助矩阵变换方法,整个闭环系统的渐近稳定性可以解耦成每个子系统的稳定性,在假定通信拓扑只含有生成树的条件下,借助李亚谱诺夫函数,可证明整个闭环系统是稳定的,且通过调节控制增益,可以得到期望的响应速度.仿真结果验证了所提出控制方法的有效性及可行性.

LQR-based distributed cooperative load-sharing optimal control for coupled inter-connected dynamical systems

A distributed cooperative optimal load-sharing control is proposed for one class coupled parallel-connected dynamical systems with non-identical nonlinear dynamics. The communication among subsystems is modeled as a digraph. 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 optimal load-sharing control law with tunable gains 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 asymptotically stability of the entire closed-loop systems can be decoupled into each sub-system''s stability through matrix transformation. Assuming that the directed graph has a spanning tree, the stability of the whole system can be proved with the aid of the Lyapunov function. A desired response speed can be obtained by tuning the control parameters with the proposed method. Simulation results verify the effectiveness and feasibility of the proposed approach.