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The qualitative structure of a class of infinite horizon optimal control problems
Author(s) -
CAPUTO MICHAEL R.
Publication year - 1997
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/(sici)1099-1514(199705/06)18:3<195::aid-oca599>3.0.co;2-9
Subject(s) - comparative statics , optimal control , class (philosophy) , stability (learning theory) , mathematical economics , mathematics , qualitative analysis , mathematical optimization , state (computer science) , computer science , qualitative research , economics , algorithm , artificial intelligence , social science , machine learning , sociology , macroeconomics
Many papers in economics have been written using optimal control theory with what appear to be diverse models. The qualitative results developed in the papers have been related only to the specific model at hand. This paper shows that most of the useful qualitative results occur because the same small number of crucial assumptions are being made about the mathematical structure of the integrand and/or state equation. The taxonomy of models is examined and the seemingly diverse results are unified in this research for the class of one‐dimensional, discounted infinite horizon optimal control problems. This is achieved by explicitly linking the local stability of the steady state, the steady state comparative statics and the local comparative dynamics of the optimal control problem. © 1997 John Wiley & Sons, Ltd.