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Bounded optimal feedback control of a fractional-order chaotic economic system | ||
| Journal of Mathematical Modeling | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 01 آبان 1405 اصل مقاله (689.31 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2026.34789.3240 | ||
| نویسندگان | ||
| Reza Hejazi* 1؛ Shaban Mohammadi2؛ Mohammad hossein Seifi3؛ Elham Dastranj3 | ||
| 1Department of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran. | ||
| 2Department of Mathematical Sciences, Shahrood University of Technology, shahrood, Semnan, Iran. | ||
| 3Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran. | ||
| چکیده | ||
| We study bounded optimal feedback control of chaos in a fractional-order macroeconomic model. Two equilibria are index-two saddles, so the necessary condition for chaos holds for every commensurate order $\alpha>0.8863$, yet numerically chaos appears only above $\alpha\approx0.96$, after a period-doubling cascade; at $\alpha=0.99$ the $0$--$1$ test gives $K=+0.998$. A normalized quadratic cost about the positive equilibrium is minimized over saturated three-gain feedback laws with $u_{\max}=0.05$, using a genetic algorithm and particle swarm optimization. Both reach $J=244.8213$ and cut the index by $98.7\%\pm1.1\%$ over an ensemble of initial conditions drawn from the attractor. A saturated linear-quadratic regulator comes within $0.03\%$ of this optimum, and under the same bound the design beats active control by only $9\%$ in state cost: equivalence, not superiority. Delay is the binding limitation, about a quarter of a time unit. | ||
| کلیدواژه‌ها | ||
| Fractional-order model؛ Chaotic economic system؛ Optimal control؛ Particle swarm optimization؛ Genetic algorithm | ||
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آمار تعداد مشاهده مقاله: 15 تعداد دریافت فایل اصل مقاله: 15 |
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