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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Sebatik ComTech: Computer, Mathematics and Engineering Applications Journal of Intelligent Computing and Health Informatics (JICHI) Journal of Fundamental Mathematics and Applications (JFMA)
Mahardika, Dhimas
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Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Dentistry Economics, Econometrics & Finance Electrical & Electronics Engineering Energy Engineering Mathematics Mechanical Engineering Medicine & Pharmacology Physics Public Health Transportation

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Mathematical Modeling on the Control of Hunting Problems Redemtus Heru Tjahjana; Dhimas Mahardika
ComTech: Computer, Mathematics and Engineering Applications Vol. 12 No. 1 (2021): ComTech
Publisher : Bina Nusantara University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21512/comtech.v12i1.6424

Abstract

Modeling a natural phenomenon or the action mechanism of a tool is often done in science and technology. Observations through computer simulations cost less relatively. In the research, a bullet control model moving towards the target was explored. The research aimed to try to simulate the trajectory of the bullet that could be controlled in hunting. To model a controlled bullet, the Dubins model was used. Then, the used approach was control theory. The optimal trajectory and control for bullets were designed using the Pontryagin Maximum Principle. The results show that with this principle and the dynamic system of the bullet, a system of differential equations and adjoining is obtained. The fundamental problem arises because the bullet dynamics model in the form of a differential equation system has initial and final requirements. However, the adjoint matching system has no conditions at all. This problem is solved by using numerical methods. In addition, the research proves the convergence of the calculation results with the required results. The track simulation results are also reported at the end of the research to ensure a successful control design. From the simulation results, the presented method with its convergence has successfully solved the problem of bullet control.
Dynamical Modeling of COVID-19 and Use of Optimal Control to Reduce the Infected Population and Minimize the Cost of Vaccination and Treatment Yohannes Dhimas Mahardika
ComTech: Computer, Mathematics and Engineering Applications Vol. 12 No. 2 (2021): ComTech
Publisher : Bina Nusantara University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21512/comtech.v12i2.6466

Abstract

The research described a model formulation of COVID-19 using a dynamic system of Ordinary Differential Equation (ODE) which involved four population systems (susceptible, exposed, infectious, and recovered). Then, the research analyzed the direction of the equilibrium, Disease Free Equilibrium (DFE), and Endemic Equilibrium (EE). The treatment and vaccination were the control functions applied to the dynamical system modeling of COVID-19. The research was done by determining dimensionless number R0 or Basic Reproduction Number and applying optimal control into the dynamical system using the Pontryagin Minimum Principle. Numerical calculations were also performed to illustrate and compare the graph of the dynamical system with and without a control function. From the results, there is a reduction in the number of susceptible and infected populations. It indicates that giving vaccines to susceptible populations and treating infected populations affect the number of susceptible and infected populations. It also means thatthis control can reduce the spread of the virus.
OPTIMAL CONTROL MODELLING OF COVID-19 OUTBREAK IN SEMARANG CITY INDONESIA Dhimas Mahardika; R. Heru Tjahjana; Sunarsih Sunarsih
Journal of Fundamental Mathematics and Applications (JFMA) Vol 3, No 2 (2020)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (563.399 KB) | DOI: 10.14710/jfma.v3i2.8546

Abstract

Corona virus infection is lethal and life threatening to human life, for prevention it is necessary to carry out quarantined for a portion of susceptible, exposed, and infected population, this kind of quarantine is intended to reduce the spread of the corona virus. The optimal control that will be carried out in this research is conducting quarantine for a portion of susceptible, exposed, and infected individuals. This control function will be applied to the dynamic modelling of Covid-19 spread using Pontryagin Minimum Principle. We will describe the formulation of dynamic system of Covid-19 spread with optimal control, then we use Pontryagin Minimum Principle to find optimal solution of the control. The optimal control will aim to minimize the number of infected population and control measures. Numerical experiments will be performed to illustrate and compare the graph of Covid-19 spread model with and without control.
MEMBUAT DESAIN POLA BATIK MATEMATIKA MENGGUNAKAN RUMUS FUNGSI IMPLISIT TRIGONOMETRI DALAM BIDANG KARTESIUS Dhimas Mahardika
Sebatik Vol. 27 No. 1 (2023): Juni 2023
Publisher : STMIK Widya Cipta Dharma

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46984/sebatik.v27i1.2219

Abstract

Menggambar rumus persamaan fungsi merupakan sesuatu hal yang bisa menghubungkan antara dunia matematika dan seni, tetapi sebelum adanya program kalkulator grafik hal tersebut susah untuk dilakukan, dengan perkembangan teknologi saat ini terdapat suatu software atau program kalkulator grafik online yang bisa membantu dalam memvisualisasikan gambar grafik dari rumus persamaan fungsi dengan cepat dan penggunaannya sangat user friendly. Hal ini sangat berguna untuk memvisualisasikan rumus-rumus persamaan fungsi dengan mudah dan efisien. Suatu rumus persamaan fungsi pada umumnya menghasilkan suatu gambar yang berbentuk kurva atau grafik dalam bidang Kartesius, kurva atau grafik tersebut bisanya bertujuan untuk mendeskripsikan sifat-sifat dari persamaan fungsinya. Rumus-rumus persamaan fungsi yang dibahas dalam artikel ini difokuskan pada rumus persamaan fungsi Implisit Trigonometri. Penulis memilih untuk membahas rumus persamaan fungsi Implisit Trigonometri karena rumus tersebut dapat menghasilkan suatu gambar grafik atau kurva yang mempunyai pola seperti Batik yang dinamakan Batik Matematika. Tujuan penulisan ini adalah untuk mengenalkan kepada masyarakat luas bahwa dengan rumus matematika dapat menghasilkan karya seni yang unik dan menarik lewat penggunaan rumus-rumus persamaan fungsi Implisit Trigonometri. Metode yang digunakan adalah memvisualisasikan grafik dari rumus-rumus persamaan fungsi Implisit Trigonometri tersebut menggunakan program kalkulator grafik online Desmos, dan dari software tersebut maka kemudian dapat ditampilkan gambar grafik atau kurvanya. Adapun hasil yang kami dapatkan yaitu berbagai macam pola yang unik dan menarik dan penulis menamakannya sebagai pola Batik Matematika. Selanjutnya pembelajaran tentang software kalkulator grafik online Desmos ini diperlukan agar semakin optimal dalam memanfaatkan dan mengintegrasikan teknologi untuk mendalami matematika tingkat lanjut.
An Enhanced IS-LM Business Cycle Model for Increasing Income in a Dynamic Economy Diana, Arista Fitri; Rahmasari, Shafira Meiria; Mahardika, Dhimas
Journal of Intelligent Computing & Health Informatics Vol 4, No 2 (2023): September
Publisher : Universitas Muhammadiyah Semarang Press

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26714/jichi.v4i2.13201

Abstract

This paper introduces an enhanced IS-LM business cycle model by integrating control parameters using the Pontiyagin Maximum Principle Method, aiming to maximize income within economic cycles. It develops a dynamic model incorporating import and consumption rates as controls, showcasing their impact on economic variables through simulations and analytical methodologies. The results exhibit a significant increase in income by up to 10% through the reduction of interest rates and capital stock. The efficiency of the proposed controls is visually demonstrated, providing a robust validation of the methodology used, aligning with prior research, and offering substantial insights into dynamic business cycle modelling for economic analysis and policy-making.
DYNAMIC SYSTEM OF TUBERCULOSIS MODEL USING OPTIMAL CONTROL IN SEMARANG CITY INDONESIA Mahardika, Dhimas; Kartika, Sopia
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 1 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss1pp0029-0042

Abstract

Tuberculosis is a disease which is very contagious among human. To prevent this from happening, Semarang city government has enacted vaccination for exposed individuals and treatment for the infected individuals. Vaccination and treatment are forms of control that will be applied to dynamic model systems of Tuberculosis. The present paper will describe epidemic model of Tuberculosis with control using Pontryagin Minimum Principle to find optimal solution of the control with fixed time and free end point. The optimal control will aim to reduce or minimize the number of infected populations. Numerical calculation is carried out with MATLAB software programming to illustrate and compare the graph of the dynamic model with and without optimal control. The results of dynamic modeling of Tuberculosis with control state that vaccination and treatment have succeeded in reducing the population of infected individuals.
Dynamical System Modeling of Dynastic Cycle with Optimal Control Mahardika, Dhimas; Ariyani, Rizki Chika Audita; Kencono, Uvi Dwian; Wanditra, Lucky Cahya; Rahmasari, Shafira Meiria
Sebatik Vol. 29 No. 2 (2025): December 2025
Publisher : STMIK Widya Cipta Dharma

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46984/sebatik.v29i2.2692

Abstract

In ancient China there are three model of society which is farmers, bandits and ruler. When the authority (rulers) is not there, the dynamics system of farmers and bandits become predator-prey interactions system. In here rulers play role on taxing the farmers and catching the bandits and then punish them. Thus, farmers are a sort of renewable resource which is exploited both by bandits and by rulers. In this paper, optimal control is applied to reduce the bandit’s population, by reducing it, the ruler population can also be reduced because the existing bandits can be conquered, so that the cost of running a government is more efficient because it can reduce the need for eradicating bandits from ruler. The type of the optimal control here is fixed time and free end point.
Co-Authors Ariyani, Rizki Chika Audita Diana, Arista Fitri Kartika, Sopia Kencono, Uvi Dwian Rahmasari, Shafira Meiria Redemtus Heru Tjahjana Sunarsih Sunarsih Wanditra, Lucky Cahya