Distributed Fixed-Time Optimization-Based Formation Optimal Tracking for Heterogeneous Multi-Agent Systems

This paper investigates the problem of distributed formation optimal tracking of heterogeneous linear multi-agent systems (MASs) where the reference trajectory is generated in a distributed optimal manner, instead of using a pre-specified one. The objective of this paper is to ensure that the MASs form a formation while tracking the optimal reference trajectory. First, a distributed time-varying optimization algorithm is proposed to ensure that the local reference trajectories asymptotically track the optimal reference trajectory and achieve the consensus in a fixed time. Then, a distributed formation tracking control protocol with the compensation term of the local time-varying reference trajectory is designed. The convergence of the distributed time-varying optimization algorithm for the optimal time-varying reference trajectory and the stability of the distributed formation tracking control protocol are proved by the Lyapunov analysis. Finally, an example of simulation verification is provided.