Continuous neural identifier for uncertain nonlinear systems with time delays in the input signal

• Published in: Neural networks 2014-12, Vol.60, p.53-66
• Main Authors: Alfaro-Ponce, M., Argüelles, A., Chairez, I.
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; Computer science; control theory; systems; Computer Simulation; Continuous neural networks; Control system analysis; Control theory. Systems; Exact sciences and technology; Hepatitis B virus - physiology; HIV - physiology; Lyapunov–Krasovskii functional; Models, Biological; Neural Networks (Computer); Statistics, Nonparametric; System theory; Time Factors; Time-delay uncertain systems; Uncertainty
• ISSN: 0893-6080; 1879-2782
• DOI: 10.1016/j.neunet.2014.07.002

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.