Cooperative Adaptive Control of Heterogeneous Multi-agent Systems for Leader Tracking

— Discrete-time Case —

Abstract

In this paper, we study an adaptive leader tracking problem for discrete-time multi-agent systems with uncertain heterogeneous dynamics. The proposed distributed controller consists of two components. One is an adaptive controller which modifies the uncertain heterogeneous dynamics of the agent close to a homogeneous model. The other is an ordinary relative state feedback controller which attains leader tracking if the dynamics are homogeneous. An important feature of our approach is that the states of the agents need not be bounded if some parts of their dynamics are known and homogeneous, which is the case with the velocity-to-position integrator in vehicle formation. By constructing a logarithmic Lyapunov function, we show that state tracking is achieved asymptotically and the error system consisting of state tracking errors and parameter errors is Lyapunov stable. We also present a numerical example to demonstrate the effectiveness of the proposed approach.