多主体系统分布式动态网络的权值平衡算法

Weight-balancing algorithm for distributed dynamic networks of multi-agent systems

针对加权有向图实现一致均值收敛必须是平衡图的要求,提出了一种分布式权值平衡算法使得任意一种强连通的加权有向图最终能全局渐近收敛到平衡图.该算法对有向图的各个连接权值赋初值,并计算每个节点的输入度和输出度,利用周围邻居节点的输入度和输出度之差等信息对节点的输入权值或输出权值进行权值更新,如此迭代进行直至所有节点都达到输入度和输出度权值平衡.利用特征值圆盘定理证明了保证该分布式算法实现最终一致性收敛的充分条件,给出了算法中调整因子取值的上限值.仿真结果验证了算法的有效性,并对不同调整因子下的系统收敛结果作了分析比较.

Aimed at the problem that a weighted digraph must be balanced graph for global convergence to the average-consensus, a distributed weight-balancing algorithm was proposed, by using which arbitrary strongly connected weighted digraph could globally asymptotically convergence to balanced graph. The initial weight value for each edge in digraph was firstly given, and the in-degree and out-degree of each node were calculated. Then, the weight values were updated based on the difference between the in-degree and out-degree of neighbor nodes. The weight-updating process was iteratively employed for each node until all nodes were weight balanced. The sufficient condition for consensus convergence of the algorithm was proved, and the upper bound on step-size parameter was presented. Simulation showed the effectiveness of the presented algorithm and the validity of the sufficient condition, and the convergence performance of the algorithm with different step-size parameter was also analyzed.