Double-Layer Fuzzy Neural Network Based Optimal Control for Wastewater Treatment Process

To obtain the effective purification performance in wastewater treatment process (WWTP), the optimal control is an important method to guarantee the effluent quality reaching the standard and improve the treatment efficiency. The concentrations of dissolved oxygen (DO) and nitrate nitrogen (NO<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{\text{3}}$</tex-math></inline-formula>-N) are primary metrics that impact effluent quality, which is needed to be stably tracking controlled for achieving optimal performance in WWTP. Therefore, the double-layer fuzzy neural network (FNN)-based optimal control method with multivariable is proposed. First, considering the dynamic characteristic of WWTP, the FNN-based actor network is exploited to approximate the unknown dynamic information. Subsequently, the FNN-based critic network is integrated to minimize the cost function of DO and NO<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{\text{3}}$</tex-math></inline-formula>-N concentrations, which is composed of the control error and the control variable. Then, to guarantee the stability of the optimal controller, the Lyapunov function is constructed through backstepping method to analyze the control system performance. Finally, the optimality and effectiveness of the control system with multivariable are verified via the simulation experiments in benchmark simulation model 1.