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All Journal International Journal of Electrical and Computer Engineering Journal of the Indonesian Mathematical Society BAREKENG: Jurnal Ilmu Matematika dan Terapan InPrime: Indonesian Journal Of Pure And Applied Mathematics 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.
Multi-Depot Vehicle Routing with Heterogeneous Vehicles using Nearest Neighbor Combined with Simulated Annealing Agustine, Debby; Naiborhu, Janson; Magdalena, Ikha
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 7 No. 2 (2025)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/ggqnkf48

Abstract

The Vehicle Routing Problem (VRP) is an essential component of contemporary logistics, which becomes more complex as the Multi-Depot Vehicle Routing Problem (MDVRP) and the Multi-Depot Vehicle Routing Problem with a Heterogeneous Fleet (MDVRPHF). The main objective of MDVRPHF is to meet all customer demands while minimizing total distribution costs by using vehicles with varying capacities. This paper proposes a metaheuristic framework that first uses the Nearest Neighbor (NN) algorithm to build initial routes and then employs the Simulated Annealing (SA) algorithm to optimize the arrangement of goods within each vehicle, ensuring capacity limits are met. Computational experiments using real-world inspired data, representing 20 items distributed from a Bandung depot to multiple customers with three heterogeneous vehicle types, showed that the proposed hybrid NN–SA method achieved an 18.4% reduction in total distribution cost compared to the NN method alone. These results indicate that this integrated approach offers a practical, computationally efficient solution to the complexities of MDVRPHF, establishing it as a useful tool for logistics planning. Keywords: Multi-Depot Vehicle Routing Problem; Heterogeneous Fleet; Nearest Neighbor; Simulated Annealing; Metaheuristics.   Abstrak Vehicle Routing Problem (VRP) merupakan bagian penting dari logistik kontemporer, yang kompleksitasnya meningkat menjadi Multi-Depot Vehicle Routing Problem (MDVRP) dan Multi-Depot Vehicle Routing Problem with a Heterogeneous Fleet (MDVRPHF). Untuk MDVRPHF, tujuan utamanya adalah memenuhi seluruh permintaan pelanggan sambil meminimalkan biaya distribusi total dengan memanfaatkan kendaraan berkapasitas berbeda. Makalah ini mengusulkan kerangka kerja metaheuristik yang pertama-tama menggunakan algoritma Nearest Neighbor (NN) untuk membentuk rute awal, kemudian algoritma Simulated Annealing (SA) digunakan untuk mengoptimalkan penataan barang di setiap kendaraan agar batas kapasitas terpenuhi. Eksperimen komputasi menggunakan data uji berbasis kondisi nyata yang merepresentasikan distribusi 20 item dari satu depot di Bandung ke beberapa pelanggan dengan tiga jenis kendaraan heterogen. Hasil penelitian menunjukkan bahwa metode hibrida NN–SA ini menghasilkan penurunan biaya distribusi total sebesar 18,4% dibandingkan metode NN murni, yang menunjukkan bahwa pendekatan terpadu ini memberikan solusi praktis dan efisien secara komputasi untuk kompleksitas MDVRPHF. Kata Kunci: Multi-Depot Vehicle Routing Problem; Armada Heterogen; Nearest Neighbor; Simulated Annealing; Metaheuristik. 2020MSC: 90B06, 90C59.
Stochastic Influence on Levenberg-Marquardt Method for Nonlinear Least Squares Problems Christopher, Gerend; Naiborhu, Janson
Journal of the Indonesian Mathematical Society Vol. 32 No. 2 (2026): JUNE
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i2.1960

Abstract

In this digital era, a lot of data can be collected to be extracted and used for decision making through mathematical models in solving cases in certain domains. This paper will focus on solving nonlinear least squares problems in building an optimal model, namely one that has good accuracy and is efficient. In practice, the model is built using numerical methods. The main objective of this study is to investigate the effect of stochasticity in numerical methods that utilize gradients, namely Levenberg-Marquardt, on accuracy and computational efficiency. In addition, several numerical results from several variants of Stochastic Levenberg-Marquardt sampling and data taken in clusters with K-Means will be compared. The results of this paper are Stochastic Levenberg-Marquardt with 100, 200, 300, 400, and 500 data sample sizes outperformed classical Levenberg-Marquardt since they have very low relative errors to Levenberg-Marquardt and are faster in computational time than Levenberg-Marquardt. Therefore, when solving nonlinear least squares problems with large data sets, the Levenberg-Marquardt method requires only a small number of samples, which suggests that using the Stochastic Levenberg-Marquardt approach is advantageous.
Co-Authors Agustine, Debby Arief Ardyansyah Christopher, Gerend Dewi Handayani Khozin Mu'tamar Khozin Mu’tamar, Khozin Magdalena, Ikha