DESIGN OF OPTIMAL AND SWITCHED STATE-FEEDBACK CONTROLS USING POLYTOPIC LPV APPROACH FOR TUBERCULOSIS MODEL - Ar Rizka, Sailah
Controlling tuberculosis (TB) epidemic is carried out through an optimal and a switched state-feedback control strategies, applied to a tuberculosis model that considers reinfection and post-exposure interventions. The purpose of the im- plementation of control strategies is to reduce the number of active TB infe- ctious individuals and the number of persistent latent individuals. The given controls represent the eort that prevents the failure of treatment for active TB infectious individuals and the provision of treatment for identied persis- tent latent individuals. Optimal control strategy is obtained by using Pontrya- gin Minimum Principle to minimize the given objective functional. Numerical results show that the obtained optimal control strategy can reduce the number of active TB infectious individuals and the number of persistent latent indivi- duals with minimum implementation cost. Since the tuberculosis model being considered contains several parameters whose values are still exploratory at an interval, the robust control strategy is needed such that the tuberculosis epi- demic remains controlled for all possible parameter values. However, there is no general method to design robust controller for nonlinear model. The LPV (Linear Parameter Varying) system is used to approach the nonlinearity of the tuberculosis model. The nonlinear tuberculosis model which contains para- meter uncertainty is transformed into polytopic LPV form. The synthesis of the switched state-feedback control was performed based on the polytopic LPV description of tuberculosis model which contains parameter uncertainty. The switched state-feedback control consisting of the set of state-feedback gains and switching rule is then applied to the nonlinear tuberculosis model. Numerical results show that the implementation of the switched state-feedback control stra- tegy can reduce the number of active TB infectious individuals and the number of persistent latent individuals in the presence of parameter uncertainties of the tuberculosis model being considered.