Asymptotic Approximations to the Solution of the Singularly Perturbed Linear-Quadratic Optimal Control Problem with Terminal Path Constraints

Abstract

The minimum-energy control problem for a linear singularly perturbed system with linear constraints imposed on the right endpoint of the trajectories is considered. Asymptotic approximations in the form of open loop and feedback controls to the optimal control (solution of this problem) are constructed. The main advantage of the algorithms proposed below consists in the decomposition of the original problem into two unperturbed optimal control problems of smaller dimension.

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Correspondence to A. I. Kalinin or L. I. Lavrinovich.

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This paper was recommended for publication by M.M. Khrustalev, a member of the Editorial Board

Russian Text © The Author(s), 2020, published in Avtomatika i Telemekhanika, 2020, No. 6, pp. 29–46.

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Kalinin, A.I., Lavrinovich, L.I. Asymptotic Approximations to the Solution of the Singularly Perturbed Linear-Quadratic Optimal Control Problem with Terminal Path Constraints. Autom Remote Control 81, 988–1002 (2020). https://doi.org/10.1134/S0005117920060041

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Keywords

  • optimal control
  • linear system
  • quadratic performance criterion
  • singular perturbations
  • asymptotic approximations
  • suboptimal feedback design