Kontrol optimo problema bat Lotka-Volterra ereduarekin: turnpike propietatea eta zenbait ebazpen numeriko

Abstract

Turnpike Teoriaren arabera, kontrol optimizazio problema bat denbora-tarte luze batean ebaztean,hipotesi batzuk betez gero, bai estatu optimoa eta bai kontrol optimoa ibilbide konkretu batetik gertumantenduko dira denbora gehienean zehar.Lan honetan, turnpike fenomenoa populazio dinamikaproblema batean aztertzen dugu, Lotka-Volterra ereduan hain zuzen. Ondoren, turnpike hura jaurtierabakarreko metodo klasikoa hobetzeko nola erabili ahal den erakusten dugu, (Trelat eta Zuazua, 2015)-nproposatzen den ideia jarraituz.The Turnpike Theory establishes that, when an optimal control problem is defined in a large time interval,and under certain conditions, its optimal solution remains exponentially close to a concrete path for mostof the time. Here, we analyse the turnpike phenomenon for a control problem in population dynamics,modelled by the Loka-Volterra system. Based on that, we also show how the turnpike property can beused to improve the classical single shooting method, following the idea proposed in (Trelat eta Zuazua,2015).