Cooperative Control of Multiple High-Order Agents With Nonidentical Unknown Control Directions Under Fixed and Time-Varying Topologies

Abstract

Existing results for cooperative control of high-order agents mainly employ the Nussbaum-type function to cope with unknown control directions and mostly require an assumption that the control directions are identical and unknown. This paper proposes a class of algorithms with nonlinear PI functions to relax such an assumption and make them suitable for nonidentical unknown control directions. It is proven that if the distributed nonlinear PI functions are suitably selected, the proposed algorithms can achieve consensus for high-order agents under strongly connected topologies and switching topologies with a jointly strongly connected basis (JSCB). Furthermore, we extend the consensus results to the case of time-varying topologies described by δ-connected, continuous graphs. As a special case, the consensus of high-order agents under the directed graph having a spanning tree is also investigated. Finally, illustrative simulations are presented to indicate the efficiency of the proposed algorithms.