The Experts below are selected from a list of 35472 Experts worldwide ranked by ideXlab platform
C. X. Zhu - One of the best experts on this subject based on the ideXlab platform.
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Control of quasi non-integrable Hamiltonian systems for targeting a specified Stationary Probability density
International Journal of Control, 2017Co-Authors: C. X. Zhu, W. Q. ZhuAbstract:An innovative design procedure for the feedback control of quasi non-integrable Hamiltonian systems to target a specified Stationary Probability density function (SPDF) is proposed based on the ave...
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Control of Stationary Probability density of nonlinear systems subject to Poisson white noise excitation
Journal of Vibration and Control, 2012Co-Authors: C. X. Zhu, Weiqiu ZhuAbstract:An innovative design procedure for controlling a nonlinear system subject to Poisson white noise excitation to target a specified Stationary Probability density function is proposed based on the ap...
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Design of feedback control of a nonlinear stochastic system for targeting a pre-specified Stationary Probability distribution
Probabilistic Engineering Mechanics, 2012Co-Authors: C. X. Zhu, W. Q. Zhu, Yongfeng YangAbstract:Abstract An innovative approach to designing feedback control of a nonlinear stochastic system for targeting a pre-specified Stationary Probability density function (SPDF) is proposed based on the techniques for obtaining the exact Stationary solutions of nonlinear stochastic system. First, the techniques for obtaining the exact Stationary solutions of nonlinear stochastic systems, including the Stationary potential and the generalized Stationary potential, are briefly reviewed. Then, the approach to designing the feedback control of nonlinear stochastic systems for targeting a pre-specified SPDF and the Lyapunov function method for proving that the transient PDF of the controlled systems do converge to the pre-specified SPDF are presented. Finally, two examples are worked out in detail to illustrate the proposed approach and its effectiveness.
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Brief paper: Feedback control of nonlinear stochastic systems for targeting a specified Stationary Probability density
Automatica, 2011Co-Authors: C. X. Zhu, W. Q. ZhuAbstract:In the present paper, an innovative procedure for designing the feedback control of multi-degree-of-freedom (MDOF) nonlinear stochastic systems to target a specified Stationary Probability density function (SPDF) is proposed based on the technique for obtaining the exact Stationary solutions of the dissipated Hamiltonian systems. First, the control problem is formulated as a controlled, dissipated Hamiltonian system together with a target SPDF. Then the controlled forces are split into a conservative part and a dissipative part. The conservative control forces are designed to make the controlled system and the target SPDF have the same Hamiltonian structure (mainly the integrability and resonance). The dissipative control forces are determined so that the target SPDF is the exact Stationary solution of the controlled system. Five cases, i.e., non-integrable Hamiltonian systems, integrable and non-resonant Hamiltonian systems, integrable and resonant Hamiltonian systems, partially integrable and non-resonant Hamiltonian systems, and partially integrable and resonant Hamiltonian systems, are treated respectively. A method for proving that the transient solution of the controlled system approaches the target SPDF as t->~ is introduced. Finally, an example is given to illustrate the efficacy of the proposed design procedure.
Jian-qiao Sun - One of the best experts on this subject based on the ideXlab platform.
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The closed-form Stationary Probability distribution of the stochastically excited vibro-impact oscillators
Journal of Sound and Vibration, 2019Co-Authors: Lincong Chen, Jiamin Qian, Haisheng Zhu, Jian-qiao SunAbstract:Abstract The response of vibro-impact oscillators under random excitations has been studied using various techniques in the last three decades. However, the results available were smooth approximations of the intrinsically non-smooth response of vibroimpact oscillators. This paper proposes a new procedure for the closed-form Stationary Probability density function (PDF) of the response of single-degree-of-freedom (SDOF) vibro-impact system under Gaussian white noise excitation. First, the Zhuravlev-Ivanov transformation is adopted to convert a vibro-impact oscillator with one-side barrier into an oscillator without barrier. The probabilistic description of the system is subsequently defined through the corresponding Fokker-Planck-Kolmogorov (FPK) equation. The closed-form Stationary PDF of the response is obtained by solving the reduced FPK equation using the iterative method of weighted residue together with the concepts of the circulatory Probability flow and the potential Probability flow. Two examples are examined to illustrate the effectiveness of the proposed procedure. Good agreements are found between the analytical solutions and the simulated results of the PDFs and logarithmic PDFs of the examples. The reported studies also show that the proposed procedure can deal with case of small restitution factor. In particular, the closed-form solution for the case of small restitution factor is firstly obtained in literature, and can be used as the benchmark problem to examine the other method in random vibration. Furthermore, the approximate solutions obtained with the proposed procedure are piece-wise form, reflecting the true nature of the intrinsically discontinuous vibro-impact oscillators.
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the closed form solution of the reduced fokker planck kolmogorov equation for nonlinear systems
Communications in Nonlinear Science and Numerical Simulation, 2016Co-Authors: Lincong Chen, Jian-qiao SunAbstract:Abstract In this paper, we propose a new method to obtain the closed-form solution of the reduced Fokker–Planck–Kolmogorov equation for single degree of freedom nonlinear systems under external and parametric Gaussian white noise excitations. The assumed Stationary Probability density function consists of an exponential polynomial with a logarithmic term to account for parametric excitations. The undetermined coefficients in the assumed solution are computed with the help of an iterative method of weighted residue. We have found that the iterative process generates a sequence of solutions that converge to the exact solutions if they exist. Three examples with known exact steady-state Probability density functions are used to demonstrate the convergence of the proposed method.
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covariance control of nonlinear dynamic systems via exact Stationary Probability density function
Journal of Vibration and Acoustics, 2004Co-Authors: O Elbeyli, Jian-qiao SunAbstract:This paper presents a method for designing covariance type controls of nonlinear stochastic systems. The method consists of two steps. The first step is to find a class of nonlinear feedback controls with undetermined gains such that the exact Stationary PDF of the response is obtainable. The second step is to select the control gains in the context of the covariance control method by minimizing a performance index. The exact PDF makes the solution process of optimization very efficient, and the evaluation of expectations of nonlinear functions of the response very accurate. The theoretical results of various orders of response moments by the present method have been compared with Monte Carlo simulations. Special cases are studied when the approximate methods based on the maximum entropy principle or other closure schemes leads less accurate response estimates, while the present method still works fine.
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nonlinear stochastic control via Stationary Probability density functions
American Control Conference, 2002Co-Authors: L G Crespo, Jian-qiao SunAbstract:Presents a control strategy for externally excited stochastic systems with parametric uncertainties. The objective is to drive the system to match a target Probability density function (PDF) in steady state. The control consists of a nonlinear feedback and a switching term for handling parameter uncertainty. The fast rate of convergence to the Stationary PDF is observed in the time evolution of the mean and variance of the closed loop system through Monte Carlo simulations. The dependence of the control performance on the number of terms in the polynomial control series and on the rate of convergence to the steady state distribution are studied numerically. This control design based on the Stationary PDF is also applied to the tracking of a time-varying Probability density function.
Carsten Proppe - One of the best experts on this subject based on the ideXlab platform.
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exact Stationary Probability density functions for non linear systems under poisson white noise excitation
International Journal of Non-linear Mechanics, 2003Co-Authors: Carsten ProppeAbstract:Abstract The paper presents exact Stationary Probability density functions for systems under Poisson white noise excitation. Two different solution methods are outlined. In the first one, a class of non-linear systems is determined whose state vector is a memoryless transformation of the state vector of a linear system. The second method considers the generalized Fokker–Planck (Kolmogorov-forward) equation. Non-linear system functions are identified such that the Stationary solution of the system admits a prescribed Stationary Probability density function. Both methods make use of the stochastic integro-differential equations approach. This approach seems to have some computational advantages for the determination of exact Stationary Probability density functions when compared to the stochastic differential equations approach.
W. Q. Zhu - One of the best experts on this subject based on the ideXlab platform.
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Control of quasi non-integrable Hamiltonian systems for targeting a specified Stationary Probability density
International Journal of Control, 2017Co-Authors: C. X. Zhu, W. Q. ZhuAbstract:An innovative design procedure for the feedback control of quasi non-integrable Hamiltonian systems to target a specified Stationary Probability density function (SPDF) is proposed based on the ave...
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Design of feedback control of a nonlinear stochastic system for targeting a pre-specified Stationary Probability distribution
Probabilistic Engineering Mechanics, 2012Co-Authors: C. X. Zhu, W. Q. Zhu, Yongfeng YangAbstract:Abstract An innovative approach to designing feedback control of a nonlinear stochastic system for targeting a pre-specified Stationary Probability density function (SPDF) is proposed based on the techniques for obtaining the exact Stationary solutions of nonlinear stochastic system. First, the techniques for obtaining the exact Stationary solutions of nonlinear stochastic systems, including the Stationary potential and the generalized Stationary potential, are briefly reviewed. Then, the approach to designing the feedback control of nonlinear stochastic systems for targeting a pre-specified SPDF and the Lyapunov function method for proving that the transient PDF of the controlled systems do converge to the pre-specified SPDF are presented. Finally, two examples are worked out in detail to illustrate the proposed approach and its effectiveness.
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Brief paper: Feedback control of nonlinear stochastic systems for targeting a specified Stationary Probability density
Automatica, 2011Co-Authors: C. X. Zhu, W. Q. ZhuAbstract:In the present paper, an innovative procedure for designing the feedback control of multi-degree-of-freedom (MDOF) nonlinear stochastic systems to target a specified Stationary Probability density function (SPDF) is proposed based on the technique for obtaining the exact Stationary solutions of the dissipated Hamiltonian systems. First, the control problem is formulated as a controlled, dissipated Hamiltonian system together with a target SPDF. Then the controlled forces are split into a conservative part and a dissipative part. The conservative control forces are designed to make the controlled system and the target SPDF have the same Hamiltonian structure (mainly the integrability and resonance). The dissipative control forces are determined so that the target SPDF is the exact Stationary solution of the controlled system. Five cases, i.e., non-integrable Hamiltonian systems, integrable and non-resonant Hamiltonian systems, integrable and resonant Hamiltonian systems, partially integrable and non-resonant Hamiltonian systems, and partially integrable and resonant Hamiltonian systems, are treated respectively. A method for proving that the transient solution of the controlled system approaches the target SPDF as t->~ is introduced. Finally, an example is given to illustrate the efficacy of the proposed design procedure.
Weiqiu Zhu - One of the best experts on this subject based on the ideXlab platform.
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Control of Stationary Probability density of nonlinear systems subject to Poisson white noise excitation
Journal of Vibration and Control, 2012Co-Authors: C. X. Zhu, Weiqiu ZhuAbstract:An innovative design procedure for controlling a nonlinear system subject to Poisson white noise excitation to target a specified Stationary Probability density function is proposed based on the ap...
