title: Continuous neural identifier for uncertain nonlinear systems with time delays in the input signal.
abstract: Time-delay systems have been successfully used to represent the complexity of some dynamic systems. Time-delay is often used for modeling many real systems. Among others, biological and chemical plants have been described using time-delay terms with better results than those models that have not consider them. However, getting those models represented a challenge and sometimes the results were not so satisfactory. Non-parametric modeling offered an alternative to obtain suitable and usable models. Continuous neural networks (CNN) have been considered as a real alternative to provide models over uncertain non-parametric systems. This article introduces the design of a specific class of non-parametric model for uncertain time-delay system based on CNN considering the so-called delayed learning laws analysis. The convergence analysis as well as the learning laws were produced by means of a Lyapunov-Krasovskii functional. Three examples were developed to demonstrate the effectiveness of the modeling process forced by the identifier proposed in this study. The first example was a simple nonlinear model used as benchmark example. The second example regarded the human immunodeficiency virus dynamic behavior is used to show the performance of the suggested non-parametric identifier based on CNN for no fictitious neither academic models. Finally, a third example describing the evolution of hepatitis B virus served to test the identifier presented in this study and was also useful to provide evidence of its superior performance against a non-delayed identifier based on CNN.
authors.affiliation: Centro de Investigación en Computación del Instituto Politécnico Nacional. Venus, Nueva Industrial Vallejo, Gustavo A. Madero, P.O. Box 07738, Mexico City, Mexico.
authors.forename: M
authors.initials: M
authors.lastname: Alfaro-Ponce
authors.affiliation: Centro de Investigación en Computación del Instituto Politécnico Nacional. Venus, Nueva Industrial Vallejo, Gustavo A. Madero, P.O. Box 07738, Mexico City, Mexico.
authors.forename: A
authors.initials: A
authors.lastname: Argüelles
authors.affiliation: Bioprocess Department, Unidad Profesional Interdisciplinaria en Biotecnologia del Instituto Politécnico Nacional. Acueducto s/n, La laguna Ticoman, Gustavo A. Madero, P.O. Box 07340, Mexico City, Mexico. Electronic address: jchairez@ctrl.cinvestav.mx.
authors.forename: I
authors.initials: I
authors.lastname: Chairez
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006678:HIV / Q000502:physiology; D006515:Hepatitis B virus / Q000502:physiology; D008954:Models, Biological; D016571:Neural Networks, Computer; D018709:Statistics, Nonparametric; D013997:Time Factors; D035501:Uncertainty
keywords: Continuous neural networks; Lyapunov–Krasovskii functional; Time-delay uncertain systems