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An adaptive neuro-fuzzy control approach for nonlinear systems via Lyapunov function derivative estimation

An adaptive neuro-fuzzy controller is proposed in this paper to deal with the problem of tracking nonlinear affine in the control dynamical systems with unknown nonlinearities. The plant is described by means of a Takagi-Sugeno fuzzy model, including dynamic fuzzy rules of generalized form, where the local submodels are realized through nonlinear input-output mappings. Instead of modelling the plant dynamics directly, our approach relies upon the effective approximation of certain terms that involve the derivative of the Lyapunov function and the unknown system nonlinearities on a local basis using linear in the weights neural networks. A resetting scheme is proposed to assure validity of the control input. The uniform ultimate boundedness of the tracking error with respect to an arbitrarily small set of the origin is achieved, along with the boundedness of all other signals in the closed loop. Illustrative simulations highlight the approach