Feedback control optimization of nonlinear systems under random excitations

Elbeyli, O.; Sun, Jian‐Qiao

doi:10.1016/j.cnsns.2002.03.001

Cited by 6 publications

(4 citation statements)

References 16 publications

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“…In this case, the averaged FPK equation is of the form of Eq. (11) with the following drift and diffusion coefficients…”

Section: Examplementioning

confidence: 99%

“…In the last few years, a nonlinear stochastic optimal control strategy has been proposed for the control of mechanical and structural systems under random excitations [5][6][7] based on the stochastic averaging method for quasi Hamiltonian systems [8][9][10] and the stochastic dynamical programming principle. The feedback control optimization of nonlinear systems under random excitations was studied by Elbeyli et al [11] and the feedback minimization of first-passage failure of quasi integrable Hamiltonian systems was studied by Deng et al [12]. In the implementation of control, time delay is usually unavoidable due to the time spent in measuring and estimating the system state, calculating and executing the control forces, etc.…”

mentioning

confidence: 99%

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Time-delayed feedback control optimization for quasi linear systems under random excitations

De-min

Zhu

2009

Acta Mech Sin

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A strategy for time-delayed feedback control optimization of quasi linear systems with random excitation is proposed. First, the stochastic averaging method is used to reduce the dimension of the state space and to derive the stationary response of the system. Secondly, the control law is assumed to be velocity feedback control with time delay and the unknown control gains are determined by the performance indices. The response of the controlled system is predicted through solving the Fokker-Plank-Kolmogorov equation associated with the averaged Itô equation. Finally, numerical examples are used to illustrate the proposed control method, and the numerical results are confirmed by Monte Carlo simulation.

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“…In this case, the averaged FPK equation is of the form of Eq. (11) with the following drift and diffusion coefficients…”

Section: Examplementioning

confidence: 99%

mentioning

confidence: 99%

Time-delayed feedback control optimization for quasi linear systems under random excitations

De-min

Zhu

2009

Acta Mech Sin

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“…In engineering field, however, only the linear quadratic Gaussian control strategy has been widely used. In the last few years, a nonlinear stochastic optimal control strategy has been proposed for the control of structural systems under random excitations [3][4][5][6]. Generally, the random excitation of the building structures is a non-stationary process and unpredictable.…”

Section: Introductionmentioning

confidence: 99%

Instantaneous Stochastic Optimal Control of Seismically Excited Structures Based on Time Domain Explicit Method

Zhang³

et al. 2013

AMR

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A new instantaneous stochastic optimal control (ISO) for the linear building structures subjected to non-stationary random excitations is proposed. A plane shear structure is taken as the example to illustrate the proposed method. The main advantage of the method is that the control force is easy to be calculated because the expression of the control force is independent of the state of the system.

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“…Westman and Hanson (1999) investigated a dynamic programming control strategy to find optimal control for a nonlinear stochastic system. Elbeyli and Sun (2006) studied feedback control optimization of nonlinear systems under random excitations. Ying (2010) proposed a minimax stochastic optimal control for bounded-uncertain systems.…”

Section: Introductionmentioning

confidence: 99%

Stochastic stabilization of quasi-generalized Hamiltonian systems

Ling

Jin

Wang

et al. 2013

Journal of Vibration and Control

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A procedure for designing a feedback control to asymptotically stabilize, with probability one, quasi-generalized Hamiltonian systems subject to stochastically parametric excitations is proposed. First, the motion equations of controlled systems are reduced to lower-dimensional averaged Itô stochastic differential equations by using the stochastic averaging method. Second, a dynamic programming equation for the averaged system with an appropriate performance index (with undetermined parameters in cost function) is established based on the dynamic programming principle, and the optimal control law is derived from a minimization condition with respect to control. Third, the Lyapunov function method is adopted to evaluate the stability boundary of asymptotic stability with probability one for the uncontrolled/ controlled systems. Finally, the parameters in cost function are selected to guarantee the sufficient stability of the controlled systems. Numerical results for a nine-dimensional mathematical system and a three-dimensional practical system, which describes a structure including viscoelastic element, illustrate the effectiveness of the feedback control strategy, and stability domains can be obviously enlarged when imposing the feedback controls on the original systems.

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Feedback control optimization of nonlinear systems under random excitations

Cited by 6 publications

References 16 publications

Time-delayed feedback control optimization for quasi linear systems under random excitations

Time-delayed feedback control optimization for quasi linear systems under random excitations

Instantaneous Stochastic Optimal Control of Seismically Excited Structures Based on Time Domain Explicit Method

Stochastic stabilization of quasi-generalized Hamiltonian systems

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