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The hyperbolic tangent law in optimal control synthesis for a nonlinear model with discounting

The hyperbolic tangent law in optimal control synthesis for a nonlinear model with discounting ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 11, pp. 1562–1578.  c Pleiades Publishing, Inc., 2006. Original Russian Text  c Yu.N. Kiselev, S.N. Avvakumov, M.V. Orlov, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 11, pp. 1490–1506. ORDINARY DIFFERENTIAL EQUATIONS The Hyperbolic Tangent Law in Optimal Control Synthesis for a Nonlinear Model with Discounting Yu.N.Kiselev, S. N.Avvakumov, and M. V. Orlov Moscow State University, Moscow, Russia Received May 19, 2006 DOI: 10.1134/S0012266106110061 1. INTRODUCTION In the present paper, we consider one-dimensional optimization mathematical models that are of interest in applications to hardrock mining. Economically, the functional to be maximized has the meaning of discounted profit. We consider a number of statements of optimization problems with finite and infinite horizons and construct optimal solutions in closed form. The optimal control is found in the form of a function of time (a programmed control) and in the form of a function of the phase coordinate (a feedback control obeying the hyperbolic tangent law). Theoretical consid- erations are based on the Pontryagin maximum principle and the Bellman dynamic programming method. The theoretical results obtained are used in numerical experiments with model and real data. 1.1. Transition from the Original http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

The hyperbolic tangent law in optimal control synthesis for a nonlinear model with discounting

Kiselev, Yu.; Avvakumov, S.; Orlov, M.
Differential Equations , Volume 42 (11) – Jan 3, 2006
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References (3)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Pleiades Publishing, Inc.
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266106110061
Publisher site
See Article on Publisher Site

Abstract

ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 11, pp. 1562–1578.  c Pleiades Publishing, Inc., 2006. Original Russian Text  c Yu.N. Kiselev, S.N. Avvakumov, M.V. Orlov, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 11, pp. 1490–1506. ORDINARY DIFFERENTIAL EQUATIONS The Hyperbolic Tangent Law in Optimal Control Synthesis for a Nonlinear Model with Discounting Yu.N.Kiselev, S. N.Avvakumov, and M. V. Orlov Moscow State University, Moscow, Russia Received May 19, 2006 DOI: 10.1134/S0012266106110061 1. INTRODUCTION In the present paper, we consider one-dimensional optimization mathematical models that are of interest in applications to hardrock mining. Economically, the functional to be maximized has the meaning of discounted profit. We consider a number of statements of optimization problems with finite and infinite horizons and construct optimal solutions in closed form. The optimal control is found in the form of a function of time (a programmed control) and in the form of a function of the phase coordinate (a feedback control obeying the hyperbolic tangent law). Theoretical consid- erations are based on the Pontryagin maximum principle and the Bellman dynamic programming method. The theoretical results obtained are used in numerical experiments with model and real data. 1.1. Transition from the Original

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Differential Equations – Springer Journals

Published: Jan 3, 2006

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