Microalgae is one of the energy to be used as biodiesel. Chlorella Vulgaris is one of the most economical algae to produce biodiesel, because these green algae are rich in carbohydrates, require no special care, and easy to grow. Algae oil obtained for biodiesel production is obtained through a fairly long process, one of which is the process of lipid extraction. In the study of lipid extraction process using solid-liquid or leaching extraction is the transfer of dissolved dissolved components from solids into the solvent. In the study used CO2-expended methanol (CXM). Soxhlet Extraction Method is a method for lipid extraction using hexane, in the process of extraction with Soxhlet tool there is a process of lipid mass transfer contained in Chlorella Vulgaris to flow CXM. This process of displacement has created a diferential equation which can be viewed as a system by Sriati Monalisa Siahaan(2016) to be used as a mathematical model to predict extractable lipid results for subsequent use as the main ingredient of biodiesel production. In her research, Sriati refers to a research conducted by Yi-Hung Yang(2015). In this research aims to perform optimal control with Pontryagin Maximum Principle (PMP) method to produce maximum lipid extraction result. This method is used to obtain the best control of the dynamic system from the initial state to the last by maximizing the objective function and more modern than other methods such as Linear Quadratic Regulator (LQR). Using the PMP method to optimal control in this systems, can increase the value of lipid concentration.

Algae are good plants as raw materials for biodiesel. Chlorella Vulgaris is one of the most economical algae to produce biodiesel since it is rich in carbohydrates, require no special care, and easy to grow. Algae oil for biodiesel production is obtained through fairly long processes, one of which is the lipid extraction. Mathematical model can be used to obtain optimal results. The optimal control theory itself is concerned with the analysis of controlled dynamic systems, in which a system is directed from configurations given to some desire target by minimizing or maximizing some criteria. In this study, LQR formulation has the advantages of easy to analyze and implementation. In comparison, optimum control is performed using the PMP method, to obtain the best control of the dynamic system from the initial state to the end, i.e by maximizing the objective function. This method is a better method than the LQR method. Optimal control is performed in order to optimize the yield of lipid concentration in the solvent flow (Cs), in the microalgae particles (Cp), and minimizing the volume of solvent (v). From the simulation, it is found that the PMP method is more optimal in this system compared to the LQR method.

This paper presents a dynamic model of smoking with optimal control. The mathematical model is divided into 5 sub-classes, namely, non-smokers, occasional smokers, active smokers, individuals who have temporarily stopped smoking, and individuals who have stopped smoking permanently. Four optimal controls, i.e., anti-smoking education campaign, anti-smoking gum, anti-nicotine drug, and government prohibition of smoking in public spaces are considered in the model. The existence of the controls is also presented. The Pontryagin maximum principle (PMP) was used to solve the optimal control problem. The fourth-order Runge-Kutta was employed to gain the numerical solutions.

In this study, we used a mathematical model of the smoking epidemic which was divided into three sub-classes. In this model we provide four optimal controls, namely education campaign about cigarettes, vaccines, treatment and rehabilitation. To solve the problem of optimal control, we use the principle of maximum pontryagin, where the objective function is set to increase the population of individuals who quit smoking and reduce the number of smokers. In the solution, we use the numerical method namely Runge Kutta forward-backward sweep order4 and simulated using MATLAB with the values of initial parameters and conditions are given based on the results of a survey that conducted on high school students in several schools in Lamongan. The control provided in this study shows a decrease in the number of individual population of potential smokers and active smokers, as well as an increase in the number of individual ex-smokers. These results also indicate that the system gets the optimal solution according to certain values of the control level.

Indonesia's economy is influenced by many factors, including the tourism sector. Through this tourism sector, it is possible for many foreign tourists to visit Indonesia. There are so many foreign tourists who come to Indonesia, forecasting is needed to find out the estimates of foreign tourists in the following months based on existing data. The method that used is the Seasonal Autoregressive Integrated Moving Average (SARIMA) method. The foreign tourist’s coming to Indonesia through Soekarno Hatta Airport were taken from the center agency on statistics (BPS) Indonesia. Data on the number of foreign tourists who come to Indonesia through Soekarno Hatta Airport is data with a seasonal pattern. The data used is secondary data obtained from Soekarno Hatta Airport for the period January 2010 to June 2015. In this case it is used to predict the value of the data for the next 6 months using the best model is the . Forecasting results show the number of each month increases from the previous year. In July it showed the highest yield of 342536, which was 297878 in the previous year. Forecasting results show the number of each month increases from the previous year. In July, the highest yield was 342536, which was 297878 in the previous year.