DETERMINING THE INFUSION SUPPLY RATE BY STOCHASTIC OPTIMAL CONTROL

• Main Author: HANDAYANI (30112016), DEWI
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/26555
• Institution: Institut Teknologi Bandung

Generally, phenomena in nature can be described as a mathematical model involving a nonlinear system. The analysis of the nonlinear system relates to these solution in order to obtain a mathematical conclusions that can describe the phenomenon accurately. However, to obtain the best solutions required some input, such as the selection of parameters and precise controls with the minimum possible cost. These inputs are given as an effort to change the dynamic of the system as ve the models in the form of nonlinear system. One is the model of transmission and treatment of dengue infection in the <br /> human body known as the with-in host dengue infection model. The endemic rate of with-in host dengue infection model is measured from the basic reproduction ratio. <br /> Some stability and bifurcation of virus dynamics are described as the existence of an endemic equilibrium point. The deterministic optimum control design is performed as a first step to determine the effect of intravenous infusion on immune cells and hematocrit. The optimization process is divided into two problems, i.e. fixed-end point and hematocrit tracking. The deterministic model do not involve the disturbance (internal and external) and parameter uncertainties. The disturbance of system is often simplified, but the existences of disturbance can not be predicted and we only know the frequency distribution. The disturbance is assumed as a stochastic to be described as a Brownian motion. Selection criteria for control inputs involving the stochastic disturbances are introduced based on the upper bounded value for nonlinear systems in the proposed value function (VF). Value function is formed based on the control process and the continuous system in the stochastic system that not enough just Lipschitz. <br /> Stochastic optimal control design involving internal and external disturbances and parameter uncertainties will be approached by two types of state conditions: complete state condition and incomplete state condition. In a complete state condition, the dynamic is known exactly, thus the optimum control is expressed as a function of state. It will involve complicated computational processes for the Hamilton-Jacobi-Bellman (HJB) equation. Therefore, designing of value function is required for control implementation. The optimum stochastic control problem will be solved considered of the HJB equation through the value function in the form of Riccati equation. In the incomplete state condition, there inevitably exists uncertainty in the system model either due to modeling error or parameter drifting of the system. This research discusses the design of a filter that has certain performance robustness againts possible parameter uncertainties. In particular, we are interested in the socalled the robust priori finite estimation from two Riccati equation which counting <br /> the least of upper bound. The robust priori estimation is concerned with the design of a nonlinear system as a linear combination of linear matrices using the Jacobian <br /> concept. This robust approach presents the existence and formulation of controllers in the form of Riccati equation. <br /> The stochastic optimal control is applied to the with-in host dengue infection system to minimize the increasing of hematocrit by increase the production of immune cells <br /> to eliminate the infected cells. When the infusion process, the disturbance factors can occur suddenly so that the excessive of infusion can give the negative effect for hematocrit. The stochastic optimal control will provide the proper time and the optimum infusion supply rate. With the stochastic control system, numerical simulation give a specific result and capture a dengue infection phenomena like the onset of symptom and the saddle-like graph.