# American Institute of Mathematical Sciences

April  2021, 14(4): 1495-1518. doi: 10.3934/dcdss.2020377

## 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

Received  January 2020 Revised  January 2020 Published  April 2021 Early access  May 2020

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.

Citation: Yuan Xu, Xin Jin, Saiwei Wang, Yang Tang. Optimal synchronization control of multiple euler-lagrange systems via event-triggered reinforcement learning. Discrete & Continuous Dynamical Systems - S, 2021, 14 (4) : 1495-1518. doi: 10.3934/dcdss.2020377
##### References:

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##### References:
Communication graph of MELSs
Triggering instants for all agents
Position trajectories of the first and second component of each EL agent
Velocity trajectories of the first and second component of each EL agent
Synchronization errors of the first and second component of each EL agent
Control policies of the first and second component of each EL agent under event-triggered mechanism
Norm of estimated weights of the critic neural network
Validation of Assumption 6 for agent 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 $m/s^2$
 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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