Bilinear neuro-fuzzy modeling for adaptive approximation and indirect control of nonlinear systems

To cope with the indirect regulation of unknown affine in the control nonlinear systems, this paper proposes a method which is based on a recurrent Neuro-Fuzzy modeling. Initially, the components of the nonlinear plant are approximated by Fuzzy subsystems. Using appropriately defined “indicating functions”, it is shown that the initial dynamical fuzzy system can be converted to a dynamical neuro-fuzzy model, where the “indicating functions” are replaced by High Order Neural Networks (HONNS), trained by sampled system data. Assuming only parametric uncertainty, the parameters to be estimated are the weights of the HONNs and the centers of the output partitions, both arranged in matrices of appropriate dimensions and leading to a bilinear parametric model. Adaptive laws are derived based on this model and using a Lyapunov stability analysis of the error dynamic equations. The a-priori experts information required by the identification scheme is extremely low, limited to the knowledge of the signs of the center of the fuzzy output partitions. Once the system is identified around an operation point, it is regulated to zero adaptively using an appropriate controller that is built according to the neuro-fuzzy model. The weight updating laws guarantee that both the identification error and the system states reach zero exponentially fast, while keeping all signals in the closed loop bounded. Simulation on a well known benchmark illustrates the potency of the method.