An approach to polynomial NARX/NARMAX systems identification in a closed-loop with variable structure control

Many physical processes have nonlinear behavior which can be well represented by a polynomial NARX or NARMAX model.The identification of such models has been widely explored in literature.The majority of these approaches are for the open-loop identification.However,for reasons such as safety and production restrictions,open-loop identification cannot always be done.In such cases,closed-loop identification is necessary.This paper presents a two-step approach to closed-loop identification of the polynomial NARX/NARMAX systems with variable structure control(VSC).First,a genetic algorithm(GA) is used to maximize the similarity of VSC signal to white noise by tuning the switching function parameters.Second,the system is simulated again and its parameters are estimated by an algorithm of the least square(LS) family.Finally,simulation examples are given to show the validity of the proposed approach.