A Fuzzy-Neural Adaptive Terminal Iterative Learning Control for Fed-Batch Fermentation Processes

A fuzzy-neural adaptive terminal iterative learning controller is proposed in this paper for uncertain fed-batch fermentation processes with iteration-varying initial states. In order to derive a terminal output tracking error model, a technique of sampled-data transformation for differentiation is firstly utilized to transform the fed-batch fermentation process into a sampled-data system. An input and output algebraic function is then derived based on the sampled-data formulation of fed-batch fermentation process as well as the differential mean value theorem. According to the derived terminal output tracking error model, a fuzzy neural network is applied to approximate the unknown terminal desired input. In order to overcome a lumped uncertainty from the error induced by fuzzy-neural function approximation and the unknown initial states, an iteration-varying boundary layer is developed to construct an auxiliary terminal output error. This auxiliary terminal output error is then used to derive suitable adaptive laws for the weights of fuzzy neural network and the width of boundary layer. Based on a Lyapunov-like analysis, we show that the boundedness of control parameters, control input, and process output are guaranteed for each iteration. Furthermore, the norm of terminal output error will asymptotically converge to a tunable residual set whose size depends on the width of boundary layer as iteration number goes to infinity.