Distributed control of higher-order nonlinear multi-agent systems with unknown non-identical control directions under general directed graphs

Abstract

This paper addresses the leaderless consensus control problem for higher-order nonlinear multi-agent systems with completely unknown non-identical control directions. In contrast to the existing consensus results, we propose a distributed consensus algorithm using only local information available to the individual agent under a general directed graph. Nussbaum-type functions are used to deal with the unknown control directions, and novel auxiliary variables including the estimate of the consensus value are defined and employed in designing the control algorithm to avoid the appearance of multiple Nussbaum-type function terms in the stability analysis. The uncertain dynamics of each agent is approximated by the function approximation technique, and the unknown disturbance and the approximation error are suppressed by introducing an adaptive robust term. By leveraging the unique properties of the Laplacian matrix on directed graphs and matrix theory, it is shown that under the proposed distributed algorithm, the boundedness of all the closed-loop signals and asymptotic consensus can be achieved. Simulation results on pendulum plants are given to verify the theoretical analysis.