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All Journal International Journal of Electrical and Computer Engineering BAREKENG: Jurnal Ilmu Matematika dan Terapan Jurnal Sosial dan Sains
Janson Naiborhu
Industrial Financial Mathematics Group Faculty of Mathematics and Natural Science, ITB.
Astronomy Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Electrical & Electronics Engineering Energy Engineering Environmental Science Law, Crime, Criminology & Criminal Justice Library & Information Science Mathematics Mechanical Engineering Physics Transportation

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NONLINEAR TRACKING CONTROL FOR PREY STABILIZATION IN PREDATOR-PREY MODEL USING BACKSTEPPING Mu`tamar, Khozin; Naiborhu, Janson; Saragih, Roberd; Handayani, Dewi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1825-1840

Abstract

The common method used in population dynamics is optimal control, which employs Pontryagin’s minimum principle. This method minimizes costs, with the constraint function being the model dynamics. Unfortunately, if the main objective of the control function is to modify the population’s behavior to follow a specific pattern, this method is challenging to apply. This article introduces a control function to the predator-prey model for the tracking problem using the backstepping method. The control function drives the population from the initial value towards the given trajectory. The goal is to maintain the balance between predator and prey populations in the habitat, with the chosen trajectory being the equilibrium point. The application of backstepping to the predator-prey model is combined with input-output feedback linearization to obtain a normal form, enabling the implementation of backstepping. Simulation results show that the controller successfully drives the predator-prey populations toward the equilibrium point with a relatively small control function and excellent performance.
Tracking control of uncertain third order jerk equation Genesio-Tesi using adaptive backstepping Mu'tamar, Khozin; Naiborhu, Janson; Saragih, Roberd; Handayani, Dewi
International Journal of Electrical and Computer Engineering (IJECE) Vol 15, No 3: June 2025
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijece.v15i3.pp2758-2768

Abstract

This article presents the uncertain Genesio-Tesi, a third-order Jerk equation in the form of an ordinary differential equation, with the potential to exhibit chaos under certain conditions. The main focus of this article is to design a control function for the uncertain Genesio-Tesi, which has uncertain parameters with unknown values. The adaptive backstepping method designs the control function, demonstrating its ability to stabilize the system output towards a given trajectory using Lyapunov stability. To test the robustness of the proposed control method, simulations were conducted with various scenarios, including disturbances to the steady-state system. Simulation results show that the controller successfully drove the system output along a desired trajectory, whether constant or a function, and maintained system stability even with significant disturbances.
Analisis Kemampuan Pemodelan Matematika Siswa SMA Melalui Konteks Soal Pemilihan Universitas Ardyansyah, Arief; Naiborhu, Janson
Jurnal sosial dan sains Vol. 5 No. 6 (2025): Jurnal Sosial dan Sains
Publisher : Green Publisher Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59188/jurnalsosains.v5i6.32256

Abstract

Mathematical modeling is a bridge between mathematics and real problems that occur in students' lives. The introduction of mathematical modeling is an important agenda that must be given to high school students to optimize mathematical literacy and get used to solving problems with contextual problems. The selection of material contexts and relevant real-world problems is the initial key in teaching modeling. The selection of matrix material in the application of determining university criteria is an important consideration in introducing mathematical modeling in this study. This study used a qualitative approach involving a sample of 31 students of grade 11, MAN 1 Kota Bandung, West Java. Based on Galbraith & Holton's framework, this study evaluated the seven stages of modeling and found that students were able to understand and formulate the problem well, reaching an average score of 77.8%, but had difficulty in the interpretation and evaluation stages of the model with scores decreasing to around 60%. The use of decision-making matrices shows students' good ability to apply mathematical concepts to real-world contexts, although assistance is still needed to improve modeling skills.
DESAIN KONTROL PENGOBATAN PADA MODEL SIRD UNTUK PENYEBARAN VIRUS COVID-19 MENGGUNAKAN BACKSTEPPING Mu'tamar, Khozin; Naiborhu, Janson; Saragih, Roberd
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 15 No 4 (2021): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (665.466 KB) | DOI: 10.30598/barekengvol15iss4pp697-708

Abstract

In this article, we present a control design on a SIRD model with treatment in infected individuals. The SIRD model with treatment is obtained from literature study and the parameter model is obtained from covid-19 daily case in the Riau province using the Particle Swarm Optimization method. The control design is carried out based on the backstepping method combined with feedback linearization based on input and output (IOFL). The SIRD model which is a nonlinear system will be transformed into a normal form using IOFL. Each variable is then stabilized Lyapunov using virtual control which at the same time generates a new state variable. This stage will be carried out iteratively until the last state variable is stabilized using a real control function. This control function is then applied to the SIRD model using the inverse of IOFL transformation. The simulation results compared with the Pontryagin Minimum Principle (PMP) method show that by selecting the appropriate control parameters, backstepping obtains better control performance which is a smaller number of infected populations.
Co-Authors Arief Ardyansyah Dewi Handayani Khozin Mu'tamar Khozin Mu’tamar, Khozin Mu'tamar, Khozin