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

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 intere...

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Bibliographic Details
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
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Summary: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.
ISSN:2325-5870
2325-5870
2372-2533
DOI:10.1109/TCNS.2018.2817918