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stochastic Optimal Control for Uncertain Structural Systems Under Random Excitations Based on Bayes Optimal Estimation

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BUILDINGS 2025年第9期15卷 1579-1579页

作者： Lei, Hua Ying, Zhao-Zhong Ying, Zu-Guang Zhejiang Univ Sch Aeronaut & Astronaut Dept Mech Hangzhou 310027 Peoples R China Hoongjun Micro Elect Technol Co Hangzhou 311202 Peoples R China

stochastic vibration control of uncertain structures under random loading is an important problem and its minimax optimal control strategy remains to be developed. In this paper, a stochastic optimal control strategy for uncertain structural systems under random excitations is proposed, based on the minimax stochastic dynamical programming principle and the Bayes optimal estimation method with the combination of stochastic dynamics and Bayes inference. The general description of the stochastic optimal control problem is presented including optimal parameter estimation and optimal state control. For the estimation, the posterior probability density conditional on observation states is expressed using the likelihood function conditional on system parameters according to Bayes' theorem. The likelihood is replaced by the geometrically averaged likelihood, and the posterior is converted into its logarithmic expression to avoid numerical singularity. The expressions of state statistics are derived based on stochastic dynamics. The statistics are further transformed into those conditional on observation states based on optimal state estimation. Then, the obtained posterior will be more reliable and accurate, and the optimal estimation will greatly reduce uncertain parameter domains. For the control, the minimax strategy is designed by minimizing the performance index for the worst-parameter system, which is obtained by maximizing the performance index based on game theory. The dynamical programming equation for the uncertain system is derived according to the minimax stochastic dynamical programming principle. The worst parameters are determined by the maximization of the equation, and the optimal control is determined by the minimization of the resulting equation. The minimax optimal control by combining the Bayes optimal estimation and minimax stochastic dynamical programming will be more effective and robust. Finally, numerical results for a five-story frame structure u

关键词： stochastic optimal control optimal parameter estimation Bayes inference stochastic dynamical programming uncertain structure system minimax strategy unknown random excitation

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Nonlinear stochastic optimal control of partially observable linear structures

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ENGINEERING STRUCTURES 2002年第3期24卷 333-342页

作者： Zhu, WQ Ying, ZG Zhejiang Univ Dept Mech Hangzhou 310027 Peoples R China

A strategy for nonlinear stochastic optimal control of partially observable linear structures is proposed and illustrated with linear building structures equipped with control devices and sensors under horizontal ground acceleration excitation. The control problem of a partially observable structure is first converted into that of a completely observable structure based on the separation principle. Then, a partially averaged control system of Ito equations is obtained from the completely observable structure by using the stochastic averaging method for quasi-Hamiltonian systems. dynamical programming equations for finite and infinite time-interval controls are established based on the stochastic dynamical programming principle and solved to obtain the optimal control law and value function. Finally, the response of controlled structure is obtained from solving the Fokker-Planck-Kolmogorov equation associated with the fully averaged system of Ito equations. The numerical results for a five-story building structure model are obtained by using the proposed control strategy and compared with those by using linear quadratic Gaussian control strategy to show the effectiveness and efficiency of the proposed strategy. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： active structural control stochastic optimal control partially observable system stochastic averaging stochastic dynamical programming

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stochastic optimal coupling-control of adjacent building structures

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COMPUTERS & STRUCTURES 2003年第30-31期81卷 2775-2787页

作者： Ying, ZG Ni, YQ Ko, JM Zhejiang Univ Dept Mech Hangzhou 310027 Peoples R China Hong Kong Polytech Univ Dept Civil & Struct Engn Kowloon Hong Kong Peoples R China

A stochastic optimal coupling-control method for adjacent building structures is proposed. The coupled structures with control devices under random seismic excitation are condensed to form a reduced-order model for the control analysis. The stochastic averaging method is applied to the reduced model to obtain It (o) over cap stochastic differential equations with respect to structural modal vibration energies. Then the stochastic dynamical programming principle is applied to the energy processes to establish a dynamical programming equation, by which the optimal coupling-control law is determined. The seismic response mitigation is achieved through the structural energy control and the dimension of optimal control problem is reduced. The seismic excitation spectrum is taken into account according to the stochastic dynamical programming principle. The random response of the non-linear controlled structures is predicted by using the stochastic averaging method and is compared with that of the uncontrolled structures to evaluate the control efficacy. A numerical study is conducted to demonstrate the response reduction capacity of the proposed stochastic optimal coupling-control method for adjacent building structures. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： building structure random vibration stochastic optimal control stochastic averaging stochastic dynamical programming

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Nonlinear stochastic optimal control of Preisach hysteretic systems

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PROBABILISTIC ENGINEERING MECHANICS 2009年第3期24卷 255-264页

作者： Wang, Y. Ying, Z. G. Zhu, W. Q. Zhejiang Univ Dept Mech Sch Aeronaut & Astronaut State Key Lab Fluid Power Transmiss & Control Hangzhou 310027 Zhejiang Peoples R China

The nonlinear stochastic optimal control of Preisach hysteretic systems is studied, and the control procedure is illustrated with an example of the single-degree-of-freedom Preisach system. The Preisach hysteretic system subjected to a stochastic excitation is first replaced by an equivalent non-hysteretic nonlinear stochastic system with displacement-amplitude-dependent damping and stiffness, by using the generalized harmonic balance technique. Then, the relationship between the displacement amplitude and total system energy is established, and the equivalent damping and stiffness coefficients are expressed as functions of the system energy. The averaged Ito stochastic differential equation for the system energy as one-dimensional controlled diffusion process, is derived by using the stochastic averaging method of energy envelope. For the semi-infinite time-interval ergodic control, the dynamical programming equation is obtained based on the stochastic dynamical programming principle, and is solved to yield the optimal control force. Finally, the Fokker-Planck-Kolmogorov equation associated with the averaged Ito equation is established, and the stationary probability density of the system energy is obtained, from which the variances of the controlled system response and the optimal control force are predicted and the control efficacy is evaluated. Numerical results show that the proposed control strategy for Preisach hysteretic systems is very effective and efficient. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Preisach hysteretic system Nonlinear stochastic optimal control Generalized harmonic balance stochastic averaging of energy envelope stochastic dynamical programming

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Nonlinear stochastic optimal control of tall buildings under wind loading

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ENGINEERING STRUCTURES 2004年第11期26卷 1561-1572页

作者： Zhu, WQ Luo, M Ying, ZG Zhejiang Univ Dept Mech Hangzhou 310027 Peoples R China

A nonlinear stochastic optimal (NSO) control strategy for wind-excited tall buildings is proposed. The power spectral density (PSD) matrix of the fluctuating part of wind velocity vector is diagonalized in eigenvector space. Each element of the diagonalized PSD matrix is modeled as a set of second-order linear filters driven by white noise. A stochastic optimal control problem of partially observable system is formulated and converted into a stochastic optimal control problem of completely observable system based on the separation principle. The latter problem is solved by using the NSC strategy based on the stochastic averaging method for quasi-Hamiltonian systems and the dynamic programming principle. The response statistics of both uncontrolled and controlled structures is predicted analytically. A numerical example is given to show better control effectiveness and efficiency of the proposed NSO controller than those of linear quadratic Gaussian (LQG) controller. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： tall building wind excitation stochastic optimal control partially observable system stochastic averaging stochastic dynamical programming

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A stochastic optimal control strategy for viscoelastic systems with actuator saturation

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PROBABILISTIC ENGINEERING MECHANICS 2016年 45卷 44-51页

作者： Xiong, H. Zhu, W. Q. Zhejiang Univ Dept Mech State Key Lab Fluid Power & Mechatron Syst Key Lab Soft Machines & Smart Devices Zhejiang Pr Hangzhou 310027 Zhejiang Peoples R China

A nonlinear stochastic optimal control strategy for single degree-of-freedom viscoelastic system with actuator saturation is proposed based on the stochastic averaging method and stochastic dynamical programing principle. First, the viscoelastic system is converted into an equivalent nonlinear non-viscoelastic system by replacing the viscoelastic force with amplitude-dependent stiffness and damping. Second, the partially averaged Ito stochastic differential equation for total system energy as one-dimensional controlled diffusion process is derived by using the stochastic averaging method of energy envelope. For the semi-infinite time-interval ergodic control, the dynamical programming equation is established by applying the stochastic dynamical programming principle to the partially averaged Ito equation with a performance index. The optimal saturated control consisting of unbounded optimal control and bang-bang control is determined by solving the dynamical programming equation. Both the analytical and simulation results verify the higher efficiency and chattering attenuation of the proposed control strategy compared with the corresponding bang-bang control. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Viscoelastic systems Nonlinear stochastic optimal control Actuator saturation stochastic averaging Energy envelope stochastic dynamical programming

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Nonlinear stochastic optimal control of viscoelastic systems

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JOURNAL OF VIBRATION AND CONTROL 2015年第5期21卷 1029-1040页

作者： Xiong, Hao Zhu, Weiqiu Zhejiang Univ Dept Mech State Key Lab Fluid Power Transmiss & Control Hangzhou 310027 Peoples R China

A nonlinear stochastic optimal control strategy for single degree-of-freedom viscoelastic systems with strongly nonlinear stiffness under Gaussian white noise excitation is proposed. First, the viscoelastic system is converted into an equivalent nonlinear non-viscoelastic system by replacing the viscoelastic force with amplitude-dependent stiffness and damping. Second, the partially averaged Ito stochastic differential equation for total system energy as one-dimensional controlled diffusion process is derived by using the stochastic averaging method of energy envelope. For the semi-infinite time-interval ergodic control, the dynamical programming equation is established based on the dynamical programming principle and is solved to yield the optimal control force. Finally, the variances of the responses of controlled and uncontrolled systems and that of the optimal control force are predicted analytically. Numerical results show that the proposed control strategy is very effective and efficient.

关键词： Energy envelope nonlinear stochastic optimal control viscoelastic systems stochastic averaging stochastic dynamical programming

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Optimal bounded control for nonlinear stochastic smart structure systems based on extended Kalman filter

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NONLINEAR DYNAMICS 2017年第1期90卷 105-114页

作者： Ying, Z. G. Zhu, W. Q. Zhejiang Univ Sch Aeronaut & Astronaut Dept Mech Hangzhou 310027 Zhejiang Peoples R China

An optimal bounded control strategy for smart structure systems as controlled Hamiltonian systems with random excitations and noised observations is proposed. The basic dynamic equations for a smart structure system with smart sensors and actuators are firstly given. The nonlinear stochastic control system with noised observations is then obtained from the simplified smart structure system, and the system is expressed by generalized Hamiltonian equations with control, random excitation and dissipative forces. The optimal control problem for nonlinear stochastic systems with noised observations includes two parts: optimal state estimation and optimal response control based on estimated states, which are coupled each other. The probability density of optimally estimated systems has generally infinite dimensions based on the separation theorem. The proposed optimal control strategy gives an approximate separate solution. First, the optimally estimated system state is determined by the observations based on the extended Kalman filter, and the estimated nonlinear system with controls and stochastic excitations is obtained which has finite-dimensional probability density. Second, the dynamical programming equation for the estimated system is determined based on the stochastic dynamical programming principle. The control boundedness due to actuator saturation is considered, and the optimal bounded control law is obtained by the programming equation with the bounded control constraint. The optimal control depends on the estimated system state which is determined by noised observations. The proposed optimal bounded control strategy is finally applied to a single-degree-of-freedom nonlinear stochastic system with control and noised observation. The remarkable vibration control effectiveness is illustrated with numerical results. Thus the proposed optimal bounded control strategy is promising for application to nonlinear stochastic smart structure systems with noised observati

关键词： stochastic vibration Nonlinear quasi-Hamiltonian system stochastic optimal bounded control Extended Kalman filter stochastic dynamical programming Smart structure system

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stochastic optimal control of coupled structures

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STRUCTURAL ENGINEERING AND MECHANICS 2003年第6期15卷 669-683页

作者： Ying, ZG Ni, YQ Ko, JM Zhejiang Univ Dept Mech Hangzhou 310027 Peoples R China Hong Kong Polytech Univ Dept Civil & Struct Engn Kowloon Hong Kong Peoples R China

The stochastic optimal nonlinear control of coupled adjacent building structures is studied based on the stochastic dynamical programming principle and the stochastic averaging method. The coupled structures with control devices under random seismic excitation are first condensed to form a reduced-order structural model for the control analysis. The stochastic averaging method is applied to the reduced model to yield Ito stochastic differential equations for structural modal energies as controlled diffusion processes. Then a dynamical programming equation for the energy processes is established based on the stochastic dynamical programming principle, and solved to determine the optimal nonlinear control law. The seismic response mitigation of the coupled structures is achieved through the structural energy control and the dimension of the optimal control problem is reduced. The seismic excitation spectrum is taken into account according to the stochastic dynamical programming principle. Finally, the nonlinear controlled structural response is predicted by using the stochastic averaging method and compared with the uncontrolled structural response to evaluate the control efficacy. Numerical results are given to demonstrate the response mitigation capabilities of the proposed stochastic optimal control method for coupled adjacent building structures.

关键词： building structure random vibration optimal control stochastic averaging stochastic dynamical programming

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A semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers

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SMART STRUCTURES AND SYSTEMS 2009年第1期5卷 69-79页

作者： Ying, Z. G. Ni, Y. Q. Ko, J. M. Zhejiang Univ Dept Mech Hangzhou 310027 Peoples R China Hong Kong Polytech Univ Dept Civil & Struct Engn Kowloon Hong Kong Peoples R China

A non-clipped semi-active stochastic optimal control strategy for nonlinear structural systems with MR dampers is developed based on the stochastic averaging method and stochastic dynamical programming principle. A nonlinear stochastic control structure is first modeled as a semi-actively controlled, stochastically excited and dissipated Hamiltonian system. The control force of an MR damper is separated into passive and semi-active parts. The passive control force components, coupled in structural mode space, are incorporated in the drill coefficients by directly using the stochastic averaging method. Then the stochastic dynamical programming principle is applied to establish a dynamical programming equation, from which the semi-active optimal control law is determined and implementable by MR dampers without clipping in terms of the Bingham model. Under the condition on the control performance function given in section 3, the expressions of nonlinear and linear non-clipped semi-active optimal control force components are obtained as well as the non-clipped semi-active LQG control force, and thus the value function and semi-active nonlinear optimal control force are actually existent according to the developed strategy. An example of the controlled stochastic hysteretic column is given to illustrate the application and effectiveness of the developed semi-active optimal control strategy

关键词： nonlinear stochastic optimal control semi-active optimal control law MR damper stochastic averaging stochastic dynamical programming

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