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PID control of a chaotic system: An application to an epidemiological model. (English) Zbl 0872.93060
An epidemiological model describing the dynamics of a childhood disease within a given population is considered. After discretization, the nonlinear model has as state variables the number of susceptible individuals, the number of infective individuals and the number of cases reported yearly and as the control variable the vaccination rate. As the model is not known explicitly, the feedback PID control law is used, derived from the number of cases reported yearly. Stability, bifurcation and sensitivity analysis were performed. As the policy is bounded, the control action is aimed at reducing rather than suppressing chaos.

MSC:
93C95Applications of control theory
37D45Strange attractors, chaotic dynamics
93C10Nonlinear control systems
34C23Bifurcation (ODE)
92D30Epidemiology
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References:
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