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A numerical solution of the stochastic discrete algebraic Riccati equation

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Abstract

This article proposes two algorithms for solving a stochastic discrete algebraic Riccati equation which arises in a stochastic optimal control problem for a discrete-time system. Our algorithms are generalized versions of Hewer’s algorithm. Algorithm I has quadratic convergence, but needs to solve a sequence of extended Lyapunov equations. On the other hand, Algorithm II only needs solutions of standard Lyapunov equations which can be solved easily, but it has a linear convergence. By a numerical example, we shall show that Algorithm I is superior to Algorithm II in cases of large dimensions.

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Authors and Affiliations

  1. Faculty of Engineering, University of Miyazaki, 1-1 Gakuenkibanadai Nishi, Miyazaki, 889-2192, Japan

    Nobuya Takahashi, Michio Kono & Osamu Sato

  2. Faculty of Engineering, Gifu University, Gifu, Japan

    Tatsuo Suzuki

Authors
  1. Nobuya Takahashi
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  2. Michio Kono
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  3. Tatsuo Suzuki
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  4. Osamu Sato
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Additional information

This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008

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Takahashi, N., Kono, M., Suzuki, T. et al. A numerical solution of the stochastic discrete algebraic Riccati equation. Artif Life Robotics 13, 451–454 (2009). https://doi.org/10.1007/s10015-008-0562-0

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  • DOI: https://doi.org/10.1007/s10015-008-0562-0

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