Trajectory tracking with input delay in multi-agent system: Double integrator case

Our objective is to design a consensus based control law for a multi-agent system to track a desired trajectory in the presence of a constant input delay. The agents of the multi-agent system are modeled as double integrator. The communication topology is represented by a fixed and weakly connected digraph. The controller works in conjugation with an estimator to help the agents track the desired trajectory. We present the design of two different estimators, each of which compensate for the delayed input. The first estimator model is designed as a double integrator. We find a condition on the estimator gain such that the controller can achieve trajectory tracking in the presence of constant input delay. The second estimator model is designed as a pair of single integrators. Here, we find conditions on the gains of the estimator model so as to achieve trajectory tracking in the presence of delay. The stability of the system is analysed using the frequency response approach. Simulation results illustrate the effectiveness of the proposed controller.