Distributed time-varying formation optimal tracking for multi-agent systems with optimal formation reference

This paper considers the time-varying formation optimal tracking problems of multi-agent systems. The desirable formation shape can be realized while the achieved common formation reference can optimize the team performance. Each agent is assigned with a local cost function that is only known to itself. Using the neighboring interaction, the sum of local cost functions is expected to be minimized with the macroscopic motion for the formation. Since the desired formation is time-varying, the optimal solution will be a time-varying trajectory. Based on the robust integral of the sign of the error (RISE) strategy, we extend proportion integral (PI) optimization algorithms to resolve time-varying optimization problems, and a continuous distributed formation optimal tracking controller is proposed. The stability of formation tracking error and the optimality of the common formation reference are proved according to Lyapunov theory. Finally, a simulation example for multi-robot system demonstrates the effectiveness of this approach.