NONLINEAR TRACKING CONTROL FOR PREY STABILIZATION IN PREDATOR-PREY MODEL USING BACKSTEPPING

  • Khozin Mu`tamar System Analysis and Control Design Laboratory, Computational Mathematics Research Group, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Riau, Indonesia https://orcid.org/0000-0002-6363-4241
  • Janson Naiborhu Industrial and Financial Mathematics Research Group, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia https://orcid.org/0000-0003-1789-7187
  • Roberd Saragih Industrial and Financial Mathematics Research Group, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia https://orcid.org/0000-0002-7924-378X
  • Dewi Handayani Industrial and Financial Mathematics Research Group, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia https://orcid.org/0000-0003-1213-1801
DOI: https://doi.org/10.30598/barekengvol19iss3pp1825-1840
Keywords: Backstepping Control, Feedback Linearization, Nonlinear Control, Predator-Prey, Tracking Control

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.

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Published
2025-07-01
How to Cite
[1]
Mu`tamarK., J. Naiborhu, R. Saragih, and D. Handayani, “NONLINEAR TRACKING CONTROL FOR PREY STABILIZATION IN PREDATOR-PREY MODEL USING BACKSTEPPING”, BAREKENG: J. Math. & App., vol. 19, no. 3, pp. 1825-1840, Jul. 2025.
Issue
Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
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Articles

Copyright (c) 2025 Khozin Mu`tamar, Janson Naiborhu, Roberd Saragih, Dewi Handayani

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