Adaptive Leader Following in Networks of Discrete-Time Dynamical Systems: Algorithms and Global Convergence Analysis

摘要

Most of the results on adaptive leader following in multiagent systems pertain to continuous-time agent dynamics. It is implicitly presumed that the information flow among agents is continuous and infinitely fast. Since in the discrete-time setting, there no need for this assumption, it is of interest to develop adaptive methods for leader-follower synchronization in networks of discrete-time dynamical systems. There main challenges are as follows: 1) in general, the sample values of the leader's trajectory arrive at each agent with different delays; 2) since the received leader's trajectory samples do not carry the imprint of a leader, and are immersed in the state values of respective neighbors, agents do not have explicit knowledge of the leader's samples; and 3) the uncertainty in the agent dynamics calls for an appropriate adaptive rule for generating interagent coupling gains. This paper considers unknown linear agent dynamics of general order and arbitrary leader's trajectory, on a directed graph topology. Two novel distributed algorithms are proposed for both cases of known and unknown control directions. It is proven that all agents synchronize to the leader's trajectory, the tracking error is an l(2) sequence, the input signals remain bounded, and the parameter estimates are convergent sequences.