An adaptive neurofuzzy H-infinity control method for bioreactors and biofuels production

A novel adaptive neurofuzzy H-infinity control approach to feedback control and stabilization of the nonlinear dynamical model of bioreactors used in biofuels production is developed. The form and the parameters of the differential equations that constitute the dynamic model of the bioreactor are considered to be unknown, while there is only knowledge about the order of the system. The model of the controlled system undergoes approximate linearization round a temporary equilibrium which is recomputed at each iteration of the control algorithm. The linearization procedure makes use of Taylor series expansion and the computation of Jacobian matrices. For the approximately linearized model of the bioreactor it is possible to design a stabilizing H-infinity feedback controller, provided that knowledge about the matrices of the linearized state-space description is available. Neurofuzy networks are used to estimate the unknown dynamics of the system and its Jacobians. The computation of the feedback controller's gain comes from the solution of an algebraic Riccati equation taking place at each iteration of the control method, and this allows the implementation of the H-infinity feedback controller. The learning rate of the neurofuzzy approximators is chosen from the requirement the first derivative of the system's Lyapunov function to be always a negative one, thus assuring the stability of the control loop. The global asymptotic stability and the robustness properties of the control method are proven through Lyapunov stability analysis.