Nonlinear stabilizers in optimal control problems with infinite time horizon

Tarasyev, A.M. & Usova, A.A. (2013). Nonlinear stabilizers in optimal control problems with infinite time horizon. In: System Modeling and Optimization. Eds. Hoemberg, D & Troeltzsch, F, Berlin: Springer. 10.1007/978-3-642-36062-6_29.

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In optimal control problems with infinite time horizon, arising in models of economic growth, there are essential difficulties in analytical and even in numerical construction of solutions of Hamiltonian systems. The problem is in stiff properties of differential equations of the maximum principle and in non-stable character of equilibrium points connected with corresponding transversality conditions. However, if a steady state exists and meets several conditions of regularity then it is possible to construct a nonlinear stabilizer for the Hamiltonian system. This stabilizer inherits properties of the maximum principle, generates a nonlinear system with excluded adjoint variables and leads its trajectories to the steady state. Basing on the qualitative theory of differential equations, it is possible to prove that trajectories generated by the nonlinear stabilizer are close to solutions of the original Hamiltonian system, at least locally, in a neighborhood of the steady state. This analysis allows to create stable algorithms for construction of optimal solutions.

Item Type: Book Section
Uncontrolled Keywords: Optimal control; Nonlinear control system; Nonlinear stabilizer; Economic systems
Research Programs: Advanced Systems Analysis (ASA)
Bibliographic Reference: In: D Hoemberg, F Troeltzsch (eds); System Modeling and Optimization; Springer, Berlin, Germany pp.286-295
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Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 08:49
Last Modified: 27 Aug 2021 17:39

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