PID control of a chaotic system: An application to an epidemiological model

Authors:
Luca L. Ghezzi;Carlo Piccardi
Affiliations:
Istituto di Metodi Quantitativi, Università `Carlo Cattaneo, corso Matteotti 22, 21053 Castellanza (Varese), Italy;Dipartimento di Elettronica e Informazione, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milano, Italy
Venue:
Automatica (Journal of IFAC)
Year:
1997

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Abstract

This paper is devoted to the control of a nonlinear sampled system that can exhibit chaotic behaviour. The system is derived from a classical epidemiological model in which the vaccination rate is the control variable. It is shown that chaos can be removed by using a constant and suitably large vaccination rate. Nonetheless, reducing rather than suppressing chaos seems to be a more appropriate goal owing to both general and case-specific reasons. PID control laws, for the first time applied to this purpose, prove effective as well as robust, since they make the control system fairly insensitive to parameter misspecification. Bifurcation analysis and simulation play a chief role in the work.