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

This paper is concerned with the global relative controllability of linear and nonlinear fractional stochastic dynamical systems with distributed delays in control for finite dimensional spaces. Sufficient conditions for controllability results are obtained using the Banach fixed point theorem and the controllability Grammian matrix which is dened by the Mittag-Leffler matrix function. An example is provided to illustrate the theory.

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Estimating Stochastic Dynamical Systems Driven by a Continuous-Time Jump Markov Process

Methodology And Computing In Applied Probability ◽

10.1007/s11009-006-0423-z ◽

2006 ◽

Vol 8 (4) ◽

pp. 431-447 ◽

Cited By ~ 9

Author(s):

Julien Chiquet ◽

Nikolaos Limnios

Keyword(s):

Dynamical Systems ◽

Markov Process ◽

Continuous Time ◽

Stochastic Dynamical Systems ◽

Jump Markov Process

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Coherent phenomena in stochastic dynamical systems

Uspekhi Fizicheskih Nauk ◽

10.3367/ufnr.0169.199902c.0171 ◽

1999 ◽

Vol 169 (2) ◽

pp. 171 ◽

Cited By ~ 27

Author(s):

Valerii I. Klyatskin ◽

D. Gurarie

Keyword(s):

Dynamical Systems ◽

Stochastic Dynamical Systems

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SURROGATE MODELING FOR STOCHASTIC DYNAMICAL SYSTEMS BY COMBINING NONLINEAR AUTOREGRESSIVE WITH EXOGENOUS INPUT MODELS AND POLYNOMIAL CHAOS EXPANSIONS

International Journal for Uncertainty Quantification ◽

10.1615/int.j.uncertaintyquantification.2016016603 ◽

2016 ◽

Vol 6 (4) ◽

pp. 313-339 ◽

Cited By ~ 20

Author(s):

Chu V. Mai ◽

Minas D. Spiridonakos ◽

Eleni N. Chatzi ◽

Bruno Sudret

Keyword(s):

Dynamical Systems ◽

Polynomial Chaos ◽

Surrogate Modeling ◽

Stochastic Dynamical Systems ◽

Polynomial Chaos Expansions ◽

Nonlinear Autoregressive

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Integrable two-dimensional dynamical systems and the characteristic Lie algebras

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2007.1.023 ◽

2007 ◽

Vol 5 ◽

pp. 195-200

Author(s):

A.V. Zhiber ◽

O.S. Kostrigina

Keyword(s):

Dynamical System ◽

Dynamical Systems ◽

Lie Algebra ◽

Lie Algebras ◽

Second Order ◽

System Of Equations ◽

Two Dimensional ◽

Finite Dimensional ◽

Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

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