Robust Sliding Control of SEIR Epidemic Models

Author:

Ibeas Asier1ORCID,de la Sen Manuel2,Alonso-Quesada Santiago2

Affiliation:

1. Departament de Telecomunicació i Enginyeria de Sistemes, School of Engineering, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

2. Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, P.O.Box 644, 48080 Bilbao, Spain

Abstract

This paper is aimed at designing a robust vaccination strategy capable of eradicating an infectious disease from a population regardless of the potential uncertainty in the parameters defining the disease. For this purpose, a control theoretic approach based on a sliding-mode control law is used. Initially, the controller is designed assuming certain knowledge of an upper-bound of the uncertainty signal. Afterwards, this condition is removed while an adaptive sliding control system is designed. The closed-loop properties are proved mathematically in the nonadaptive and adaptive cases. Furthermore, the usual sign function appearing in the sliding-mode control is substituted by the saturation function in order to prevent chattering. In addition, the properties achieved by the closed-loop system under this variation are also stated and proved analytically. The closed-loop system is able to attain the control objective regardless of the parametric uncertainties of the model and the lack ofa prioriknowledge on the system.

Funder

Spanish Ministry of Economy and Competitiveness

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

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