A Kalman Filter Based PID Controller for Stochastic Systems

This paper proposes a neural network PID controller for stochastic systems with unknown parameters. The controller minimizes the innovation dual control objective function, which combines the estimation objective and control objective to a mixed problem. The system parameters and the covariance matrix needed to update the neural network are estimated by the standard Kalman filter. The gradient descent algorithm is used to train the weights of the neural network. Simulation results show the neural network PID controller has dual property that can achieve preferable estimation performance and satisfactory control performance