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The asymptotic ii‐test for singular periodic control problems with an application to the management of a class of ecosystems
Author(s) -
Guardabassi G.,
Scattolini R.
Publication year - 1983
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660040411
Subject(s) - constant (computer programming) , class (philosophy) , control (management) , test (biology) , mathematics , optimal control , control theory (sociology) , computer science , mathematical analysis , mathematical optimization , ecology , artificial intelligence , biology , programming language
A basic problem in optimal control theory is to identify circumstances under which a (non‐constant or proper) periodic control exists which is better than the optimal constant one. Considerable attention has therefore been devoted in the literature to the development of criteria to test for properness, i.e. to test whether the optimal constant operation of a given system can definitely be improved by (proper) cycling in the sense that the average return associated with the latter is greater than the obviously constant one associated with the former. One of the most powerful results in this direction is the so‐called II ‐test. In this paper, a special form of the II ‐test, valid for singular optimal periodic control problems, is presented (asymptotic II ‐test), and an application to the periodic control of a class of multispecies ecosystems is discussed.