Penerapan Kontrol Optimal Pada Model Matematika Persebaran Dukungan Pemilih Terhadap Tokoh Politk Menggunakan Prinsip Minimum Ponrtyagin

Valeva, Daniel Lozes (2026) Penerapan Kontrol Optimal Pada Model Matematika Persebaran Dukungan Pemilih Terhadap Tokoh Politk Menggunakan Prinsip Minimum Ponrtyagin. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Pemilihan umum presiden adalah sarana dalam menjalankan sistem demokrasi dengan kedaulatan rakyat yang menjadi prinsip utama sistem demokrasi. Pemilihan umum presiden di Indonesia dihadapkan pada tantangan tingginya populasi golongan putih yang mencerminkan rendahnya partisipasi politik masyarakat dalam penyelenggaraan pemilihan umum. Analisis dan modifikasi model matematika SI1I2I3R dengan diberi kontrol optimal berupa edukasi dan kampanye kreatif dilakukan untuk menurunkan tingginya populasi golongan putih, dan mengetahui dinamika persebaran suara sebelum dan setelah kontrol diberikan. Kedua kontrol dioptimalkan menggunakan Prinsip Minimum Pontryagin dan disimulasikan secara numerik menggunakan metode Runge Kutta Orde Empat untuk mengetahui keefektifan pemberian kontrol. Berdasarkan hasil penelitian, model matematika yang telah diberi kontrol dapat menurunkan populasi golongan putih dengan nilai akhir proporsi populasi sebesar 0.0232 atau 2.32% dari total populasi. Secara signifikan lebih efektif dibandingkan model tanpa kontrol, sehingga penambahan kedua kontrol pada model SI1I2I3R terbukti efektif dan efisien dalam meminimalkan populasi golongan putih.
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Presidential elections are a means of implementing a democratic system with popular sovereignty as the main principle of democracy. Presidential elections in Indonesia face the challenge of a high number of non-voting populations, reflecting low political participation among the public in the election process. Analysis and modification of the mathematical model SI1I2I3R with optimal control in the form of education and creative campaigns were carried out to reduce the high number of non-voting populations and to determine the dynamics of vote distribution before and after the control was applied. Both controls were optimized using Pontryagin's Minimum Principle and simulated numerically using the Fourth Order Runge Kutta method to determine the effectiveness of the controls. Based on the research results, the mathematical model that has been given control can reduce the non-voting populations with a final population proportion value of 0.0232 or 2.32% of the total population, which is significantly more effective than the model without control. Thus, the addition of both controls to the SI1I2I3R model is proven to be effective and efficient in minimizing the non-voting populations.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Golongan Putih, Kontrol Optimal, Model SI1I2I3R, Metode Runge-Kutta Orde 4, Pemilihan Umum, Prinsip Minimum Pontryagin, Non-Voting Population, Optimal Control, SI1I2I3R Model, Fourth-Order Runge-Kutta Method, General Election, Pontryagin’s Minimum Principle.
Subjects:	Q Science > QA Mathematics > QA371 Differential equations--Numerical solutions Q Science > QA Mathematics > QA401 Mathematical models. Q Science > QA Mathematics > QA614.8 Differentiable dynamical systems
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Daniel Lozes Valeva
Date Deposited:	27 Jan 2026 06:30
Last Modified:	27 Jan 2026 06:30
URI:	http://repository.its.ac.id/id/eprint/130471

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