Tracking Algorithms for Multiagent Systems

This paper is devoted to the consensus tracking issue on multiagent systems. Instead of enabling the networked agents to reach an agreement asymptotically as the time tends to infinity, the consensus tracking between agents is considered to be derived on a finite time interval as accurately as possible. We thus propose a learning algorithm with a gain operator to be determined. If the gain operator is designed in the form of a polynomial expression, a necessary and sufficient condition is obtained for the networked agents to accomplish the consensus tracking objective, regardless of the relative degree of the system model of agents. Moreover, the H_∞ analysis approach is introduced to help establish conditions in terms of linear matrix inequalities (LMIs) such that the resulting processes of the presented learning algorithm can be guaranteed to monotonically converge in an iterative manner. The established LMI conditions can also enable the iterative learning processes to converge with an exponentially fast speed. In addition, we extend the learning algorithm to address the relative formation problem for multiagent systems. Numerical simulations are performed to demonstrate the effectiveness of learning algorithms in achieving both consensus tracking and relative formation objectives for the networked agents.