Designing optimal models of nonlinear MIMO systems based on orthogonal polynomial neural networks

Abstract

This paper presents a new method for modelling of dynamic systems by using specially designed orthogonal polynomial neural networks. These networks utilize the feature that the basis made of orthogonal functions can be used for approximation of arbitrary function, while their property of orthogonality enables optimal performances in the sense of both convergence time and approximation error. In this regard, generalized quasi-orthogonal polynomials, specifically tailored for the application in the modelling of complex dynamic systems with time-varying behaviour, are considered. Adaptivity of the designed model is achieved by using variable factors inside the orthogonal basis. The designed orthogonal neural network is applied in modelling of laboratory twin-rotor aero-dynamic system as a representative of nonlinear multiple input-multiple output systems. Detailed comparative analysis is performed for a different number of polynomials in expansion with the purpose of finding the optimal model in the sense of tradeoff between model accuracy and complexity.

Generalized Quasi-Orthogonal Functional Networks Applied in Parameter Sensitivity Analysis of Complex Dynamical Systems

“…It is widely known that every complex industrial system is in some way imperfect [2], [4], [9], [13], [15]. Namely, every real system is made of technical components that can never be realized with a 100 % accuracy of the nominal value.…”

“…The proposed type of network can be used to approximate and model each system with optimal accuracy, adjust the weight of the function w i , and minimize the criterion function. A genetic algorithm will settle optimal weight values [3]- [13].…”

“…In particular, a large number of papers deals with the application of orthogonal systems in electronics [9], circuit theory, digital signal processing [10], and telecommunications. One of the most important applications of orthogonal functions is the design of orthogonal filters that can be successfully applied to design orthogonal signal generators [11], [12], for modelling and identification of dynamical systems, as well as for the practical implementation of optimal and adaptive systems [13], [14].…”

“…In practice, there is also often a need to form filters in which the degree difference in the polynomials of the numerator and denominator of the transfer function is greater than one [5], [12]. Quasiorthogonal polynomials whose Laplace transforms are rational functions with an arbitrary difference in the degree of the polynomials are suitable for the formation of these transfer functions [9], [13]. The terms which are presented as a combination of quasi-orthogonality and almost orthogonality is introduced in [11], [12].…”

Identification of Nonlinear Systems Using the Hammerstein-Wiener Model with Improved Orthogonal Functions

“…In [18]- [21], authors proposed a new class of almost orthogonal polynomials with application in the modelling of dynamical systems. Further, the authors in [22]- [25] present possible applications in orthogonal endocrine adaptive neurofuzzy systems.…”