Adaptive Cooperative Control with Guaranteed Convergence in Time-Varying Networks of Nonlinear Dynamical Systems

In this paper, we investigate the adaptive cooperative control problem with guaranteed convergence for a class of nonlinear multiagent systems with unknown control directions and time-varying topologies. A key lemma is first derived which involves dynamically changing interaction topologies, and then a new kind of distributed control algorithms with Nussbaum-type functions are proposed based on this lemma. It is proven that if the topologies are time varying with integral weight uniform upper bound and reciprocity, then convergence is guaranteed with the proposed algorithms for nonlinear multiagent systems with nonidentical unknown control directions. An important feature of this paper is that, under time-varying topologies, the designed algorithms can deal with nonidentical unknown control directions by using classical Nussbaum-type functions. Moreover, with the proposed algorithms, we extend the adaptive cooperative control results to the case of \delta -connected graphs. In particular, the adaptive leaderless consensus of high-order nonlinear agents with nonidentical unknown control directions and a directed graph having a spanning tree is also tackled as a special case. Finally, theoretical results are illustrated by a group of Genesio-Tesi systems with distributed control algorithms under time-varying topologies and some special network topologies.