Distributed Consensus Tracking Control of a Second-Order Nonlinear Multiagent System via Immersion and Invariance Method

Abstract

In this article, a consensus tracking control problem is investigated for a second-order nonlinear multiagent system (MAS). Based on the immersion and invariance (I&I) theory, a distributed I&I consensus tracking control strategy is proposed with known dynamics first. On the basis of graph theory, an error system is established. The tracking problem of an MAS is transformed into a stabilizing issue. An implicit manifold is constructed, and an improved form of the off-the-manifold coordinate, with a regulating factor, is introduced. Further, a consensus tracking control problem for an MAS with unknown dynamics is studied. A distributed I&I consensus tracking control strategy is designed in combination with an adaptive I&I estimator. The error between the real value and its estimation is selected as an I&I implicit manifold, and an off-the-manifold coordinate is then defined. An adaptive update law is designed for guaranteeing the invariance and attractiveness of this manifold. Finally, two illustrative examples corroborate the effectiveness of the obtained theoretical results.