Multi-Model Method Decentralized Adaptive Control for a Class of Discrete-Time Multi-Agent Systems

This paper studies the decentralized adaptive tracking control problem for a class of discrete-time multi-agent systems with unknown parameters and high-frequency gains using multi-model method. Each agent is strong coupling with its neighbors by the historical outputs. All agents are interacted either directly or indirectly. In the face of uncertainties, the projection algorithm as a normal adaptive method is adopted. In order to improve quality of identification, the multi-model method is taken to identify unknown parameters and high-frequency gains using switching sets of the multiple parameters' and high-frequency gains' estimates, and the index switching functions. Using the certainty equivalence principle, the control law for the hidden leader agent is designed by the desired reference signal; the control law for each follower agent is devised by neighbors' historical outputs. Moreover, the proposed decentralized adaptive control laws can guarantee the following performances of the system: (1) the leader agent tracks the reference trajectory and each follower agent follows the average value of its neighborhood historical outputs; (2) the synchronization of all the follower agents to the leader agent is achieved; (3) all the agents track the reference trajectory, and the closed-loop system eventually achieves strong synchronization. Finally, simulations validate the effectiveness on improving control performance of multi-model adaptive algorithm by comparing with the projection algorithm.