PREDICTIVE CONTROL OF THE VARIABLE-ORDER FRACTIONAL CHAOTIC ECOLOGICAL SYSTEM

Bo Wang, Samaneh Sadat Sajjadi, Hadi Jahanshahi, Yeliz Karaca, Dingkun Hou, Li Pi, Wei-Feng Xia and Ayman A. Aly
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Bo Wang: School of Electronic Information and Automation, Aba Teachers University, Wenchuan 623002, P. R. China†School of Applied Mathematics, University Electronic Science and Technology of China, Chengdu 610054, P. R. China
Samaneh Sadat Sajjadi: ��Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, USA
Hadi Jahanshahi: �Department of Mechanical Engineering, University of Manitoba, Winnipeg, Canada R3T 5V6, Canada
Yeliz Karaca: �University of Massachusetts Medical School, Worcester, MA 01655, USA
Dingkun Hou: ��Changde Branch of Hunan Special Equipment, Inspection and Testing Institute, Changde, Hunan 415000, P. R. China
Li Pi: ��Changde Branch of Hunan Special Equipment, Inspection and Testing Institute, Changde, Hunan 415000, P. R. China
Wei-Feng Xia: *School of Engineering, Huzhou University, Huzhou 313000, P. R. China††Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou 311121, P. R. China
Ayman A. Aly: ��‡Department of Mechanical Engineering, College of Engineering, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-17

Abstract: Since ecological systems are history-dependent, incorporating fractional calculus and especially variable order ones could significantly improve the emulation of these systems. Nonetheless, in the literature, no study considers ecological processes by variable-order fractional (VOF) model. This study is motivated by this issue. At first, we propose to extend a predator–prey mathematical model with VOF derivatives. The underlying assumption in the proposed model lies in considering values of fractional derivatives as time-varying functions instead of constant parameters. Some system’s dynamic features are investigated, and then the control of the proposed system is studied. To this end, a nonlinear model predictive control is offered for the VOF system. The necessary optimality and sufficient conditions for solving the nonlinear optimal control problem in the form of fractional calculus with variable-order derivative are formulated, and the controller’s design procedure is delineated. Finally, numerical simulations are performed to demonstrate the developed control technique’s effectiveness and performance for the VOF predator–prey model.

Keywords: Ecological Systems; Predator–Prey Model; Fractional Calculus; Variable-Order Derivative; Model Predictive Controller; Nonlinear Optimal Control (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0218348X22401788

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