Distributed Iterative Learning Control of Leaderless Heterogeneous Nonlinear Signed Networks

This article is aimed at solving the distributed control problem for a leaderless heterogeneous network with signed digraph topology and locally Lipschitz nonlinear dynamics, where the agents may have nonidentical nodal functions and different state dimensions. To realize the control objectives of the heterogeneous nonlinear signed network, a distributed iterative learning control (ILC) algorithm is developed based on the relative outputs of local neighbors from the previous iteration. Despite the difficulties induced by nodal heterogeneities and nonlinearities, it is shown that the outputs of leaderless heterogeneous signed network under the developed ILC algorithm can exhibit the typical behaviors of conventional signed networks over a finite time period. To be more specific, the heterogeneous nonlinear signed network achieves either bipartite or interval bipartite output consensus (respectively, global output stability) along the iteration axis when the subgraph formed by root nodes is structurally balanced (respectively, unbalanced). Numerical studies are conducted to illustrate the proposed ILC scheme.