Fully Distributed Adaptive Practical Fixed-Time Optimal Consensus for Multi-Agent Systems

This paper addresses the distributed optimal consensus problem in multi-agent systems (MASs) subject to bounded disturbances. We propose a novel fully distributed adaptive practical fixed-time optimal consensus protocol by integrating sliding mode control with adaptive techniques. The design features a dual sliding-mode structure: i) A gradient compensation sliding mode drives the agent to satisfy the zero-gradient-sum condition within a fixed time; ii) A disturbance rejection sliding mode actively suppresses the bounded disturbances. Lyapunov-based stability analysis rigorously proves that the developed method achieves the neighborhood of the optimal solution within a fixed time. Crucially, the upper bound on settling time is independent of global network information. Additionally, the control parameter and the residual set are all influenced by the topology and the upper bound of the noise disturbance. Simulations on a six-agent system validate the method’s effectiveness.