Archive of Issues
Russia Yekaterinburg
Section  Mathematics 
Title  Asymptotic properties of optimal solutions and value functions in optimal control problems with infinite time horizon 
Author(s)  Usova A.A.^{a} 
Affiliations  Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences^{a} 
Abstract  The research is devoted to the investigation of the behavior of optimal solutions and value functions in optimal control problems on infinite horizon, which arise in the economic growth models when an elasticity parameter of the CobbDouglas production function grows up to its limit value which is equal to unity. The solution is constructed within the framework of the Pontryagin maximum principle for problems on infinite time horizon. In the limit case the problem becomes linear and has a constant optimal control depending on model parameters only. Qualitative analysis of Hamiltonian systems outlines significant changes in solution behavior, namely, the absence of steady states in the limit case. Nevertheless, both the Hamiltonian function and the maximized Hamiltonian function save their properties of smoothness with respect to all variables, and strict concavity with respect to phase variables. Value functions are constructed for both linear and nonlinear optimal control problems. Numerical experiments are implemented for illustrating results of the sensitivity analysis. 
Keywords  optimal control, Hamiltonian systems, value function, Pontryagin maximum principle 
UDC  517.977 
MSC  34H05, 49L20 
DOI  10.20537/vm120108 
Received  3 November 2011 
Language  Russian 
Citation  Usova A.A. Asymptotic properties of optimal solutions and value functions in optimal control problems with infinite time horizon, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 1, pp. 7795. 
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