Optimal Synchronization of Heterogeneous Nonlinear Systems With Unknown Dynamics

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Authors
Modares, Hamidreza
Lewis, Frank L.
Kang, Wei
Davoudi, Ali
Subjects
Distributed observer
Hamilton–Jacobi–Bellman (HJB)
optimal output synchronization
reinforce-ment learning (RL)
Advisors
Date of Issue
2018-01
Date
Publisher
IEEE
Language
Abstract
Optimal output synchronization of multi-agent leader-follower systems with unknown nonlinear dynamics is considered. The agents are assumed heterogeneous so that the dynamics may be nonidentical. A distributed observer is designed to estimate the leader state for each agent. A discounted performance function is defined for each agent, and an augmented Hamilton-Jacobi-Bellman (HJB) equation is derived to find its minimal value. The HJB solution depends on the trajectories of the local state and the distributed observer state. A control protocol based on the HJB solution assures that the synchronization error goes to zero locally asymptotically fast for all agents. The proposed approach has two main advantages compared to standard output synchronization methods. First, it is optimal in the sense that it not only makes the steady-state synchronization error zero, but also minimizes the transient error. Second, it does not require the explicit solution to the output regulator equations, though the HJB solutions implicitly provide optimal solutions to them. Finally, a reinforcement learning technique is used to learn the optimal control protocol for each agent without requiring any knowledge of the agents or the leader dynamics. Simulation studies on a notional multi-agent system validate the proposed approach.
Type
Article
Description
The article of record as published may be found at http://dx.doi.org/10.1109/TAC.2017.2713339
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
National Science Foundation
Office of Naval Research
Army Research Office
Funder
National Science Foundation ECCS-1405173
National Science Foundation IIS-1208623
Office of Naval Research N00014-13-1-0562
Office of Naval Research N000141410718
Army Research Office W911NF-11-D-0001
Format
15 p.
Citation
Modares, Hamidreza, et al. "Optimal synchronization of heterogeneous nonlinear systems with unknown dynamics." IEEE Transactions on Automatic Control 63.1 (2018): 117-131.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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