Article Contents
Article Contents

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

• * Corresponding author: Yang Tang
• 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.

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

 Citation:

• Figure 1.  Communication graph of MELSs

Figure 2.  Triggering instants for all agents

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

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

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

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

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

Figure 8.  Validation of Assumption 6 for agent 1

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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