Distributed Output Formation Optimal Tracking of Heterogeneous Linear Multiagent Systems via Distributed Time-Varying Optimization

This article addresses the problem of distributed output formation optimal tracking for heterogeneous multiagent systems (MASs). Unlike the main approach in most existing formation tracking studies, which relies on prespecified trajectories, this work aims to enable heterogeneous MASs to achieve desired formation while tracking the optimal reference trajectory generated by a distributed optimization algorithm. First, a distributed time-varying optimization algorithm is proposed as the distributed optimal reference trajectory generator, which accounts for inequality constraints and ensures fixed-time convergence in consensus and asymptotic convergence in optimality. Then, a distributed output formation optimal tracking control protocol is developed for heterogeneous MASs, with the integration of the distributed optimal reference trajectory generator. Subsequently, the convergence of the proposed distributed output formation tracking control algorithm-based on time-varying optimization-is rigorously proven using Lyapunov stability analysis. Finally, simulation examples are provided to validate the theoretical results.