Adaptive linearization for nonlinear systems using continuous Neural Networks

The adaptive linearization of dynamic nonlinear systems remains as an open problem due to the complexities associated with the methods required to obtain the linearized sections. This problem is even more difficult if the system is uncertain, it means, if only partial or null information about the mathematical model of the system is available. This paper presents a proposal of an adaptive linearization method for uncertain nonlinear systems affected by additive perturbations by the Aritificial Neural Networks approach. The stability of the indentification error is formally boarded and proved by the second Lyapunov´s method. Such suggested structure preserves some inherited structural properties that allows this method to behave as the original model as is exposed. A comparison of the developed algorithm with a similar structure without adaptable linear term is carried out, considering a genetic regulation mathematical model. The results of the simulation show that this proposal presents a superior performance as is observed in the trajectories of each identifier and by comparing the performance index of each one.