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Discrete-Time Indefinite Stochastic Linear Quadratic Optimal Control with Second Moment Constraints

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  • Weihai Zhang
  • Guiling Li

Abstract

This paper studies the discrete-time stochastic linear quadratic (LQ) problem with a second moment constraint on the terminal state, where the weighting matrices in the cost functional are allowed to be indefinite. By means of the matrix Lagrange theorem, a new class of generalized difference Riccati equations (GDREs) is introduced. It is shown that the well-posedness, and the attainability of the LQ problem and the solvability of the GDREs are equivalent to each other.

Suggested Citation

  • Weihai Zhang & Guiling Li, 2014. "Discrete-Time Indefinite Stochastic Linear Quadratic Optimal Control with Second Moment Constraints," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-9, May.
    • Handle: RePEc:hin:jnlmpe:278142
    DOI: 10.1155/2014/278142
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    Cited by:

    1. Haoyu Dong & Changna Lu & Hongwei Yang, 2018. "The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations," Mathematics, MDPI, vol. 6(10), pages 1-17, October.
    2. Liang, Yuling & Zhang, Huaguang & Zhang, Juan & Luo, Yanhong, 2021. "Integral reinforcement learning-based guaranteed cost control for unknown nonlinear systems subject to input constraints and uncertainties," Applied Mathematics and Computation, Elsevier, vol. 408(C).

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