Bézier curve parametrisation and echo state network methods for solving optimal control problems of SIR model.

SIR modelinin optimal kontrol problemlerinin çözümü için Bézier eğrisi parametrizasyonu ve yankı durum ağı yöntemleri.

Clicks: 321
ID: 53972
2019
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Abstract
In this work, we introduce an optimal control problem with two control variables of the SIR (susceptible-infected-recovered) epidemic model to minimise the infective and susceptible individuals. To solve the control problem, we use direct Bernstein-Bézier parametrisation of the control variables and metaheuristic optimisation methods of an objective function, and indirect methods, adaptive critic design (ACD) with echo state networks (ESNs) and Pontryagin's maximum principle. We propose Bernstein-Bézier parametrisation and ESNs based algorithms to solve optimal control problems for systems governed by differential equations. We use ACD with ESNs to approximate co-state equations. Our simulations have shown that the proposed two methods are able to solve optimal control problems.
Bu çalışmada, enfekte ve duyarlı bireyleri en aza indirmek amacıyla SIR (duyarlı-enfekte-iyileşen) salgın modeline ait iki kontrol değişkenli bir optimal kontrol problemi sunmaktayız. Kontrol problemini çözmek için, kontrol değişkenlerinin doğrudan Bernstein-Bézier parametrizasyonunu ve bir amaç fonksiyonunun meta-sezgisel optimizasyon yöntemlerini; dolaylı yöntemler olarak ise yankı durum ağları (ESN'ler) ile uyarlamalı eleştirmen tasarımını (ACD) ve Pontryagin'in maksimum ilkesini kullanmaktayız. Diferansiyel denklemlerle yönetilen sistemlere ait optimal kontrol problemlerini çözmek için Bernstein-Bézier parametrizasyonu ve ESN tabanlı algoritmalar önermekteyiz. Eş-durum denklemlerini yaklaşıklamak için ESN'ler ile ACD yönteminden yararlanmaktayız. Simülasyonlarımız, önerilen iki yöntemin optimal kontrol problemlerini çözebildiğini göstermiştir.
Reference Key
kmet2019bzierbio Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Kmet, Tibor;Kmetova, Maria;
Journal bio systems
Year 2019
DOI
S0303-2647(18)30109-6
URL
Keywords
adaptive critic design bernstein–bézier curve echo state networks invasive weed optimisation numerical examples optimal control problem particle swarm optimisation sir model

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