A neural network controller for systems with unmodeled dynamics with applications to wastewater treatment

This paper considers the use of neural networks (NNs) in controlling a nonlinear, stochastic system with unknown process equations. The approach here is based on using the output error of the system to train the NN controller without the need to assume or construct a separate model (NN or other type) for the unknown process dynamics. To implement such a direct adaptive control approach, it is required that connection weights in the NN be estimated while the system is being controlled. As a result of the feedback of the unknown process dynamics, however, it is not possible to determine the gradient of the loss function for use in standard (backpropagation-type) weight estimation algorithms. Therefore, this paper consider´s the use of a new stochastic approximation algorithm for this weight estimation, which is based on a “simultaneous perturbation” gradient approximation that only requires the system output error. It is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite-difference gradient approximations. The approach is illustrated on a simulated wastewater treatment system with stochastic effects and nonstationary dynamics