Trajectory tracking in heterogeneous multi-agent system without and with input delay

In this paper, we propose two different trajectory tracking consensus protocols for heterogeneous multi-agent system which comprises of heterogeneous agents. First, we propose a control law for achieving trajectory tracking in absence of time delay and analyze its stability using Lyapunov theory and Barbalat's lemma. Second, we design a control law based on estimators for achieving trajectory tracking in presence of constant homogeneous input delay. We find conditions on the estimator gains such that the control laws can achieve trajectory tracking in the presence of the delay. The stability of the system is analyzed using the frequency response approach. The position and velocity information are exchanged by the agents over different communication networks. The communication network is heterogeneous. In addition to this, we assume that network sharing position and velocity information of desired trajectory among second-order agents are different and have a rooted directed spanning tree. Simulation results illustrate the performance of the proposed controllers.