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

• Published in: IEEE transactions on control of network systems 2019-03, Vol.6 (1), p.324-337
• Main Authors: Radenkovic, Miloje S., Krstic, Miroslav
• Format: Article
• Language: English
• Subjects: Adaptive systems; Aerodynamics; Algorithms; Convergence; Coupling; Delays; Directed graph; Discrete time systems; distributed adaptive leader following; Dynamical systems; Explicit knowledge; Graph theory; Heuristic algorithms; Information flow; internal model; Multiagent systems; Parameter estimation; Synchronism; Synchronization; Time setting; Time synchronization; Topology; Tracking errors; Trajectories; Trajectory; unknown control direction
• ISSN: 2325-5870; 2325-5870; 2372-2533
• DOI: 10.1109/TCNS.2018.2817918

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.