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Numerical optimization methods for controlled systems with parameters

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Abstract

First- and second-order numerical methods for optimizing controlled dynamical systems with parameters are discussed. In unconstrained-parameter problems, the control parameters are optimized by applying the conjugate gradient method. A more accurate numerical solution in these problems is produced by Newton’s method based on a second-order functional increment formula. Next, a general optimal control problem with state constraints and parameters involved on the righthand sides of the controlled system and in the initial conditions is considered. This complicated problem is reduced to a mathematical programming one, followed by the search for optimal parameter values and control functions by applying a multimethod algorithm. The performance of the proposed technique is demonstrated by solving application problems.

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Authors and Affiliations

  1. Institute of System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, 664033, Russia

    A. I. Tyatyushkin

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  1. A. I. Tyatyushkin
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Correspondence to A. I. Tyatyushkin.

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Original Russian Text © A.I. Tyatyushkin, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 10, pp. 1615–1630.

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Tyatyushkin, A.I. Numerical optimization methods for controlled systems with parameters. Comput. Math. and Math. Phys. 57, 1592–1606 (2017). https://doi.org/10.1134/S096554251710013X

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  • DOI: https://doi.org/10.1134/S096554251710013X

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