Optimal synchronization control of multiple euler-lagrange systems via event-triggered reinforcement learning

Yuan Xu; Xin Jin; Saiwei Wang; Yang Tang

doi:10.3934/dcdss.2020377

Article Contents

2021, Volume 14, Issue 4: 1495-1518. Doi: 10.3934/dcdss.2020377

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Optimal synchronization control of multiple euler-lagrange systems via event-triggered reinforcement learning

The Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China

^* Corresponding author: Yang Tang
^* Corresponding author: Yang Tang

Received: December 31, 2019

Revised: December 31, 2019

Early access: May 2020

Published: April 2021

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Abstract

In this paper, an event-triggered reinforcement learning-based met-hod is developed for model-based optimal synchronization control of multiple Euler-Lagrange systems (MELSs) under a directed graph. The strategy of event-triggered optimal control is deduced through the establishment of Hamilton-Jacobi-Bellman (HJB) equation and the triggering condition is then proposed. Event-triggered policy iteration (PI) algorithm is then borrowed from reinforcement learning algorithms to find the optimal solution. One neural network is used to represent the value function to find the analytical solution of the event-triggered HJB equation, weights of which are updated aperiodically. It is proved that both the synchronization error and the weight estimation error are uniformly ultimately bounded (UUB). The Zeno behavior is also excluded in this research. Finally, an example of multiple 2-DOF prototype manipulators is shown to validate the effectiveness of our method.

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Mathematics Subject Classification: Primary: 93A16, 49L20; Secondary: 35F21.

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Figure 1. Communication graph of MELSs

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Figure 2. Triggering instants for all agents

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Figure 3. Position trajectories of the first and second component of each EL agent

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Figure 4. Velocity trajectories of the first and second component of each EL agent

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Figure 5. Synchronization errors of the first and second component of each EL agent

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Figure 6. Control policies of the first and second component of each EL agent under event-triggered mechanism

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Figure 7. Norm of estimated weights of the critic neural network

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Figure 8. Validation of Assumption 6 for agent 1

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Table 1. Notations, values and units of the according physical parameters

Notations	Values	Units
$ m_a $	1.2	$ kg $
$ m_b $	1	$ kg $
$ l_{ca} $	0.75	$ m $
$ l_{cb} $	0.75	$ m $
$ l_a $	0.26	$ m $
$ l_b $	0.5	$ m $
$ I_{ca} $	0.125	$ kg\cdot m^2 $
$ I_{cb} $	0.188	$ kg\cdot m^2 $
$ g $	9.81	$ m/s^2 $

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