Distributed Adaptive Time-Varying Mean Square Formation Tracking Control for Linear Multi-Agent Systems With External Random Noise Disturbance Based on Joint Connectivity Topology

This work investigates the issue of controlling formation tracking in linear multi-agent systems with time variations under external stochastic disturbances. In addition to accomplishing the intended time-varying formation, the followers must follow the leader's state trajectory, as they are also impacted by outside disruptions. First, the external disturbance of the leader and followers is described using Brownian motion, and the formation problem of the system is a global optimization problem. Furthermore, for both fixed and jointly connected topologies of the multi-agent system, a fully distributed time-varying formation tracking controller is designed using the Riccati inequality. An adaptive coupling weight suppression term is introduced to ensure the convergence of the system's adaptive coupling weights under random noise interference. This is achieved without requiring global topology information, relying solely on the relative error between adjacent agents to adaptively adjust and update the weights. Using Lyapunov's stability theory, the stability of the time-varying formation system of multi-agents with external random disturbances is studied under both fixed and jointly connected topologies. It is proven that under external random disturbances, the system is able to achieve time-varying formation, and the time-varying formation tracking error asymptotically converges to zero. Lastly, the strategy works of the approach is demonstrated through digital simulations.