Optimal bounded control of steady-state random vibrations

Dimentberg, M. F.; Iourtchenko, D. V.; Bratus, Alexander S.

doi:10.1016/s0266-8920(00)00008-4

Cited by 50 publications

(37 citation statements)

References 3 publications

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“…Bellman's principle of optimality as stated in Equation (8) suggests that one can obtain a local solution of the optimal control problem over a short time interval τ to form the global solution provided that certain continuity conditions on the solution are satisfied. In this paper, we shall impose such conditions in the probability sense.…”

Section: Bellman's Principle Of Optimalitymentioning

confidence: 99%

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Stochastic optimal control via Bellman's principle

Crespo

Sun

2003

Automatica

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Section: Bellman's Principle Of Optimalitymentioning

confidence: 99%

“…Very few closed form solutions to this problem have been found so far. Dimentberg et al found the analytical solutions of the optimal control of a linear spring mass oscillator with Lagrange and Mayer cost functionals in a region of the phase space [2,8].…”

Section: Introductionmentioning

confidence: 99%

Stochastic optimal control via Bellman's principle

Crespo

Sun

2003

Automatica

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“…29 The stochastic optimal controls for linear and nonlinear systems have been studied and many control strategies have been presented. [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] However, the stochastic optimal control for a nonlinear system with a noised observation was only considered in several studies. 43 Under a specified condition, the separation theorem was applied to convert the nonlinear stochastic system with a noised observation into a completely observable linear system for determining optimal control, but the application is strongly limited.…”

Section: Introductionmentioning

confidence: 99%

Optimal Vibration Control for Structural Quasi-Hamiltonian Systems with Noised Observations

Ying¹,

Hu²,

Huan³

2017

IJAV

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A structural control system with smart sensors and actuators is considered and its basic dynamic equations are given. The controlled, stochastically excited, and dissipative Hamiltonian system with a noised observation is obtained by discretizing the nonlinear stochastic smart structure system. The estimated nonlinear stochastic system with control is obtained, in which the optimally estimated state is determined by the observation based on the extended Kalman filter. Then the dynamical programming equation for the estimated system is obtained based on the stochastic dynamical programming principle. From this, the optimal control law dependent on the estimated state is determined. The proposed optimal control strategy is applied to two nonlinear stochastic systems with controls and noised observations. The control efficacy for stochastic vibration response reductions of the systems is illustrated with numerical results. The proposed optimal control strategy is applicable to general nonlinear stochastic structural systems with smart sensors, smart actuators and noised observations.

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“…The stochastic optimal control is an important research subject in structural engineering [1]. The mathematics theory of stochastic optimal control has been developed [2][3][4]. However, the linear-quadratic-Gauss (LQG) control method has mostly used for structural vibration control [5].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Optimal Control of Structural Systems

Ying¹

2008

TOAUTOCJ

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Abstract:The stochastic optimal control is an important research subject in structural engineering. Recently, a stochastic optimal nonlinear control method has been proposed based on the stochastic dynamical programming principle and stochastic averaging method. The active and semi-active stochastic optimal control methods have been further developed for structural systems. The control saturation or bound, partial state observation, etc. have been taken into account by the stochastic optimal control. The present paper surveys these research developments.

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Optimal bounded control of steady-state random vibrations

Cited by 50 publications

References 3 publications

Stochastic optimal control via Bellman's principle

Stochastic optimal control via Bellman's principle

Optimal Vibration Control for Structural Quasi-Hamiltonian Systems with Noised Observations

Stochastic Optimal Control of Structural Systems

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