Approximate Optimal Stabilization Control of Servo Mechanisms based on Reinforcement Learning Scheme

A reinforcement learning (RL) based adaptive dynamic programming (ADP) is developed to learn the approximate optimal stabilization input of the servo mechanisms, where the unknown system dynamics are approximated with a three-layer neural network (NN) identifier. First, the servo mechanism model is constructed and a three-layer NN identifier is used to approximate the unknown servo system. The NN weights of both the hidden layer and output layer are synchronously tuned with an adaptive gradient law. An RL-based critic three-layer NN is then used to learn the optimal cost function, where NN weights of the first layer are set as constants, NN weights of the second layer are updated by minimizing the squared Hamilton-Jacobi-Bellman (HJB) error. The optimal stabilization input of the servomechanism is obtained based on the three-layer NN identifier and RL-based critic NN scheme, which can stabilize the motor speed from its initial value to the given value. Moreover, the convergence analysis of the identifier and RL-based critic NN is proved, the stability of the cost function with the proposed optimal input is analyzed. Finally, a servo mechanism model and a complex system are provided to verify the correctness of the proposed methods.