Abstract: An optimal control problem for a mathematical model of efficiency of antiviral therapy in hepatitis B virus infections is considered. The aim of the study is to control the new viral production, block the new infection cells and maintain the number of uninfected cells in the given range. The optimal controls represent the efficiency of antiviral therapy in inhibiting viral production and preventing new infections. Defining the cost functional, the optimal control problem is converted into the constrained optimization problem and the first order optimality system is derived. For the numerical simulation, we propose the steepest descent algorithm based on the adjoint variable method. A computer program in MATLAB is developed for the numerical simulations.
Abstract: The optimal control problem for the viscoelastic melt
spinning process has not been reported yet in the literature. In this
study, an optimal control problem for a mathematical model of a
viscoelastic melt spinning process is considered. Maxwell-Oldroyd
model is used to describe the rheology of the polymeric material, the
fiber is made of. The extrusion velocity of the polymer at the spinneret
as well as the velocity and the temperature of the quench air and the
fiber length serve as control variables. A constrained optimization
problem is derived and the first–order optimality system is set up
to obtain the adjoint equations. Numerical solutions are carried out
using a steepest descent algorithm. A computer program in MATLAB
is developed for simulations.
Abstract: This paper presents the determination of the proper
quality costs parameters which provide the optimum return. The
system dynamics simulation was applied. The simulation model was
constructed by the real data from a case of the electronic devices
manufacturer in Thailand. The Steepest Descent algorithm was
employed to optimise. The experimental results show that the
company should spend on prevention and appraisal activities for 850
and 10 Baht/day respectively. It provides minimum cumulative total
quality cost, which is 258,000 Baht in twelve months. The effect of
the step size in the stage of improving the variables to the optimum
was also investigated. It can be stated that the smaller step size
provided a better result with more experimental runs. However, the
different yield in this case is not significant in practice. Therefore, the
greater step size is recommended because the region of optima could
be reached more easily and rapidly.