A computational intelligence technique for the identification of non-linear non-stationary systems

Abstract

This paper addresses nonlinear nonstationary system identification from stimulus-response data, a problem concerning a large variety of applications, in dynamic control as well as in signal processing, communications, physiological system modelling and so on. Among the different methods suggested in the vast literature for nonlinear system modelling, the ones based on the Volterra series and the Neural Networks are the most commonly used. However, a strong limitation for the applicability of these methods lies in the necessary property of stationarity, an assumption that cannot be considered as valid in general and strongly affecting the validity of results. Another weakness of the approaches currently used is that they refer to differential systems, thus being unsuitable to model systems described by integral equations. A computational intelligence technique that exploits the potentialities of both the Karhunen-Loève Transform (KLT) and Neural Networks (NNs) representation and without any of the limitations of the previous approaches is suggested in this paper. The technique is suitable for modelling the wide class of systems described by nonlinear nonstationary functionals, thus including both differential and integral systems. It takes advantage of the KLT separable kernel representation that is able to separate the dynamic and static behaviours of the system as two distinct components, and the approximation property of NNs for the identification of the nonlinear no-memory component. To validate the suggested technique comparisons with experimental results on both nonlinear nonstationary differential and integral systems are reported.

Artificial Neural Networks Models Based on ARX and State Space Forms and Adaptive Control PID/LQR of Systems Based on Peltier Cells

“…Then, the ARX (Auto-Regressive eXogenous inputs) model is the one that stands out most in this work, where it develops methods of identification and models based on computational intelligence to represent nonlinear systems. Many examples prove the importance of the use of computational intelligence in identification as in [4] that a radial base network is used to identify a nonlinear system with time variable learning, [5] that uses Computational intelligence to identify a nonlinear stationary system and in [6] that used a high order recurrent network for identification in a manipulator robot. In this context, the optimization methods serve as a tool in the determination of these models, such as least squares (LS), recursive least squares (RLS) and gradient methods.…”

Sensor Network-Based Nonlinear System Identification

“…In order to derive the identification algorithm [2], it is necessary to relate the stochastic properties of the system (that allowed the development of the general theory) to the available ensemble of realizations. Let us then refer to these N realizations of x as x (i) ∈ R Mx×1 , with i = 1, .…”