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IUTAM Symposium on Nonlinear Stochastic Dynamics and Control pp 107–116Cite as

Finite Dimensional Markov Process Approximation for Time-Delayed Stochastic Dynamical Systems

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Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 29))

Abstract

This paper presents a method of finite dimensional Markov process (FDMP) approximation for stochastic dynamical systems with time delay. The FDMP method preserves the standard state space format of the system, and allows us to apply all the existing methods and theories for analysis and control of stochastic dynamical systems. The paper presents the theoretical framework for stochastic dynamical systems with time delay based on the FDMP method, including the FPK equation, backward Kolmogorov equation, and reliability formulation. The work of this paper opens a door to various studies of stochastic dynamical systems with time delay.

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Author information

Authors and Affiliations

  1. School of Engineering, University of California, Merced, CA, 95343, USA

    Jian-Qiao Sun

Authors
  1. Jian-Qiao Sun
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Editor information

Editors and Affiliations

  1. Zhejiang University, Zhe Da Road 38, 310027, Hangzhou, People’s Republic of China

    W. Q. Zhu

  2. College of Engineering and Computer Science, Florida Atlantic University , 33431, Boca Raton, Florida, USA

    Y. K. Lin

  3. College of Engineering and Computer Science , Florida Atlantic University, 33431, Boca Raton, Florida, USA

    G. Q. Cai

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Sun, JQ. (2011). Finite Dimensional Markov Process Approximation for Time-Delayed Stochastic Dynamical Systems. In: Zhu, W.Q., Lin, Y.K., Cai, G.Q. (eds) IUTAM Symposium on Nonlinear Stochastic Dynamics and Control. IUTAM Bookseries, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0732-0_11

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  • DOI: https://doi.org/10.1007/978-94-007-0732-0_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-0731-3

  • Online ISBN: 978-94-007-0732-0

  • eBook Packages: EngineeringEngineering (R0)

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