Application of neural networks with orthogonal activation functions in control of dynamical systems

• Published in: International journal of electronics Vol. 103; no. 4; pp. 667 - 685
• Main Authors: Nikolic, Sasa S, Antic, Dragan S, Milojkovic, Marko T, Milovanovic, Miroslav B, Peric, Stanisa Lj, Mitic, Darko B
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.04.2016; Taylor & Francis LLC
• Subjects: Activation; Automotive engineering; Control systems; Dynamical systems; Electrical engineering; Functions (mathematics); Legendre-type filter; magnetic levitation system; Mathematical analysis; neural network; Neural networks; Nonlinear dynamics; orthogonal filters; orthogonal polynomials
• ISSN: 0020-7217; 1362-3060
• DOI: 10.1080/00207217.2015.1036811

In this article, we present a new method for the synthesis of almost and quasi-orthogonal polynomials of arbitrary order. Filters designed on the bases of these functions are generators of generalised quasi-orthogonal signals for which we derived and presented necessary mathematical background. Based on theoretical results, we designed and practically implemented generalised first-order (k = 1) quasi-orthogonal filter and proved its quasi-orthogonality via performed experiments. Designed filters can be applied in many scientific areas. In this article, generated functions were successfully implemented in Nonlinear Auto Regressive eXogenous (NARX) neural network as activation functions. One practical application of the designed orthogonal neural network is demonstrated through the example of control of the complex technical non-linear system - laboratory magnetic levitation system. Obtained results were compared with neural networks with standard activation functions and orthogonal functions of trigonometric shape. The proposed network demonstrated superiority over existing solutions in the sense of system performances.