Optimal synchronized control of nonlinear coupled harmonic oscillators based on actor–critic reinforcement learning

A distributed optimal control algorithm based on adaptive neural network is proposed for the synchronized control problem of a class of second-order nonlinear coupled harmonic oscillators. Firstly, the graph theory is used to establish the coupling relationship between the harmonic oscillator models; secondly, the neural network is used to fit the unknown nonlinearity in the harmonic oscillator model, and the virtual controller and the actual controller are designed based on the backstepping method; then, according to the state error and the controller, the cost function and the HJB function are designed. Since the HJB function cannot be solved directly, the critic neural network approximates its solution. The above two neural networks constitute a simplified reinforcement learning to achieve optimal consistent control of nonlinear coupled harmonic oscillators. Finally, the stability and effectiveness of the scheme are verified by the Lyapunov stability theorem and numerical simulation, respectively.