DESIGN OF ROBUST CONTROL USING ADAPTIVE SLIDING MODE ON THE SPREAD OF CHOLERA

• Main Author: Assegaf, Fatimah
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/42204
• Institution: Institut Teknologi Bandung

Cholera is an acute diarrhoeal infection caused by bacteria Vibrio cholerae. The SIQRB (Susceptible-Infected-Quarantined-Recovered-Bacteria) epidemic model with a control function is studied to analyze the dynamics of cholera. The con- trol function is representing the fraction of infected individuals that are submit- ted to treatment in quarantine until complete recovery. The optimal control strategy is applied to minimize the number of infected individuals, the con- centration of bacteria, and quarantine-related intervention costs. The optimal control problem is solved using Pontryagin's minimum principle and numerica- lly simulated using a forward-backward sweep method. One of the drawbacks of mathematical modeling is the presence of parametric uncertainties. Designing a control strategy used in accommodating these uncertainty factors drives the development of robust control. In this case, the sliding mode control is applied to handle parametric uncertainties. The sliding mode control objective is re- ducing the number of infected individuals to zero through the desired tracking scheme of a reference function. The Lyapunov stability theorem and Barbalat's lemma are used to examine the success of the tracking scheme. Lack of apriori knowledge related to the boundedness of the parametric uncertainties is settled using an adaptive method by updating the switching gain of sliding mode con- trol so that the strategy is called the adaptive sliding mode control. Chattering problem that often appears in the application of sliding mode control can be reduced. Numerical simulation shows that using quarantine as optimal control signicantly reducing the spread of cholera at a minimal cost. Furthermore, the adaptive sliding mode control satises the controller objectives and able to handle parametric uncertainties.