Reduction of dimension of optimal estimation problems for dynamical systems with singular perturbations

Osintsev, Mikhail S.; Sobolev, Vladimir

doi:10.1134/s0965542514010102

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2014

2024

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Cited by 9 publications

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“…The slow integral manifolds for the matrix Riccati equation of linear-quadratic control problem are constructed and it is shown that the method of integral manifolds allows us to reduce the dimension of control problems. This approach was used for the investigation of optimal filtering problems in [28,29].…”

Section: Resultsmentioning

confidence: 99%

Critical Cases in Slow/Fast Control Problems

Sobolev

2016

Collection of Selected Papers of the II International Conference on Information Technology and Nanotechnology

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Abstract. The aim of the paper is to describe the main critical cases in the theory of singularly perturbed optimal control problems and to give examples which are typical for slow/fast systems. The theory has traditionally dealt only with perturbation problems near normally hyperbolic manifold of singularities and this manifold is supposed to isolated. We reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory. We illustrate our approach by several examples of control problems.Keywords: integral manifolds, singular perturbations, optimal control Citation: Sobolev VA. Critical cases in slow/fast control problems.

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Section: Resultsmentioning

confidence: 99%