An iterative direct-backward procedure for construction of optimal trajectories in control problems with infinite horizon

Tarasyev, A.M. & Usova, A.A. (2011). An iterative direct-backward procedure for construction of optimal trajectories in control problems with infinite horizon. DOI:10.3182/20110828-6-IT-1002.01836. In: Proceedings, 18th IFAC World Congress, 28 August - 2 September 2011.

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Abstract

In optimal control problems with infinite time horizon, arising in economic growth models, the analytical solution can be derived in specific cases only. This fact is explained, first of all, by nonlinear character of the Hamiltonian system arising in the Pontryagin maximum principle. Another difficulty is connected with the so-called transversality condition which describes the asymptotic behavior of adjoint variables at the infinite time. In the paper, a numerical algorithm is proposed for constructing the optimal trajectory. The algorithm is based on existence of a steady state for the Hamiltonian system and properties of eigenvalues and eigenvectors of the corresponding Jacobian matrix. An important element of the algorithm is the trajectory generated by a nonlinear stabilizer which leads trajectories of the controlled system to the steady state with similar tangent properties as the optimal trajectory. Such trajectory is used as a "zero" approximation for starting an iterative procedure of searching the optimal trajectory. The algorithm is discussed and tested for a variant of the classical model of economic growth.

Item Type:	Conference or Workshop Item (UNSPECIFIED)
Research Programs:	Advanced Systems Analysis (ASA)
Bibliographic Reference:	In:; Proceedings, 18th IFAC World Congress; 28 August - 2 September 2011, Milan, Italy
Depositing User:	IIASA Import
Date Deposited:	15 Jan 2016 08:46
Last Modified:	27 Aug 2021 17:39
URI:	https://pure.iiasa.ac.at/9777

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