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stochastic optimal control of First-Passage Failure for Rectangular Thin Plate Vibration Model under Gaussian White-Noise Excitations

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Transactions of Tianjin University 2011年第6期17卷 431-434页

作者：葛根王洪礼 School of Civil Engineering Tianjin University School of Mechanical Engineering Tianjin Poly-technic University School of Mechanical Engineering Tianjin University

A rectangular thin plate vibration model subjected to inplane stochastic excitation is simplified to a quasinonintegrable Hamiltonian system with two degrees of freedom. Subsequently a one-dimensional Ito stochastic differential equation for the system is obtained by applying the stochastic averaging method for quasi-nonintegrable Hamiltonian systems. The conditional reliability function and conditional probability density are both gained by solving the backward Kolmogorov equation numerically. Finally, a stochastic optimal control model is proposed and solved. The numerical results show the effectiveness of this method.

关键词： rectangular thin plate first-passage failure stochastic optimal control

stochastic optimal control OF HYSTERETIC SYSTEMS UNDER EXTERNALLY AND PARAMETRICALLY RANDOM EXCITATIONS

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Acta Mechanica Solida Sinica 2003年第1期16卷 61-66页

作者： Ying Zuguang Zhu Weiqiu (Department of Mechanics,Zhejiang University,Hangzhou 310027,China) Department of Mechanics Zhejiang University Hangzhou 310027 China

A stochastic optimal control method for nonlinear hysteretic systems under externally and/or parametrically random excitations is presented and illustrated with an example of hysteretic column system. A hysteretic system subject to random excitation is first replaced by a nonlinear non-hysteretic stochastic system. An It$\hat {\rm o}$ stochastic differential equation for the total energy of the system as a one-dimensional controlled diffusion process is derived by using the stochastic averaging method of energy envelope. A dynamical programming equation is then established based on the stochastic dynamical programming principle and solved to yield the optimal control force. Finally, the responses of uncontrolled and controlled systems are evaluated to determine the control efficacy. It is shown by numerical results that the proposed stochastic optimal control method is more effective and efficient than other optimal control methods.

关键词： stochastic optimal control hysteretic systems random vibration stochastic averaging

Maximum principle for anticipated recursive stochastic optimal control problem with delay and Lvy processes

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Applied Mathematics(A Journal of Chinese Universities) 2014年第1期29卷 67-85页

作者： LI Na WU Zhen School of Mathematics Shandong University Mathematics Department QiLu Normal Institute

In this paper, we study the stochastic maximum principle for optimal control prob- lem of anticipated forward-backward system with delay and Lovy processes as the random dis- turbance. This control system can be described by the anticipated forward-backward stochastic differential equations with delay and L^vy processes （AFBSDEDLs）, we first obtain the existence and uniqueness theorem of adapted solutions for AFBSDEDLs; combining the AFBSDEDLs＇ preliminary result with certain classical convex variational techniques, the corresponding maxi- mum principle is proved.

关键词： maximum principle stochastic optimal control L′evy processes stochastic differential equation with delay anticipated backward differential equation

A NOTE ON stochastic optimal control OF REFLECTED DIFFUSIONS WITH JUMPS

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Applied Mathematics and Mechanics(English Edition) 2000年第9期21卷 1079-1090页

作者：丁灯 Department of Mathematics Zhongshan University Guangzhou 510725 China Faculty of Science and Technology University of Macau Macau P O Box 3001 Macao

stochastic optimal control problems for a class of reflected diffusion with Poisson jumps in a half-space are considered. The nonlinear Nisio' s semigroup for such optimal control problems was constructed. A Hamilton-Jacobi-Bellman equation with the Neumann boundary condition associated with this semigroup was obtained. Then, viscosity solutions of this equation were defined and discussed, and various uniqueness of this equation was also considered. Finally, the value function was such optimal control problems is shown to be a viscosity solution of this equation.

关键词： stochastic optimal control reflected diffusion with jumps Hamilton-Jacobi-Bellman equation viscosity solution

On stochastic optimal control of partially observable nonlinear quasi Hamiltonian systems

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Journal of Zhejiang University Science 2004年第11期5卷 1313-1317页

作者：朱位秋应祖光 DepartmentofMechanics CollegeofMechanicalandEnergyEngineeringZhejiangUniversityHangzhou310027China

A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.

关键词： Nonlinear system Partially observation stochastic optimal control Separation principle stochastic averaging Dynamical programming

Moving least-squares approximations for linearly-solvable stochastic optimal control problems

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控制理论与应用（英文版） 2011年第3期9卷 451-463页

作者： Mingyuan Zhong Emanuel Todorov Department of Applied Mathematics University of Washington Seattle USA Department of Computer Science University of Washington Seattle USA

Nonlinear stochastic optimal control problems are fundamental in control theory.A general class of such problems can be reduced to computing the principal eigenfunction of a linear ***,we describe a new method for finding this eigenfunction using a moving least-squares function *** use efficient iterative solvers that do not require matrix factorization,thereby allowing us to handle large numbers of basis *** bases are evaluated at collocation states that change over iterations of the algorithm,so as to provide higher resolution at the regions of state space that are visited more *** shape of the bases is automatically defined given the collocation states,in a way that avoids gaps in the *** results on test problems are provided.

关键词： stochastic optimal control Bellman equations

A Sample-Wise Data Driven control Solver for the stochastic optimal control Problem with Unknown Model Parameters

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Communications in Computational Physics 2023年第4期33卷 1132-1163页

作者： Richard Archibald Feng Bao Jiongmin Yong Computational Science and Mathematics Division Oak Ridge National LaboratoryOak RidgeTennesseeUSA Department of Mathematics Florida State UniversityTallahasseeFloridaUSA Department of Mathematics University of Central FloridaOrlandoFloridaUSA

In this work,an efficient sample-wise data driven control solver will be developed to solve the stochastic optimal control problem with unknown model parameters.A direct filter method will be applied as an online parameter estimation method that dynamically estimates the target model parameters upon receiving the data,and a sample-wise optimal control solver will be provided to efficiently search for the optimal ***,an effective overarching algorithm will be introduced to combine the parameter estimator and the optimal control *** experiments will be carried out to demonstrate the effectiveness and the efficiency of the sample-wise data driven control method.

关键词： stochastic optimal control parameter estimation optimal filter backward stochastic differential equations stochastic gradient descent

Backward linear quadratic stochastic optimal control problems and nonzero sum differential games

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Backward linear quadratic stochastic optimal control problem...

FORWARD-BACKWARD stochastic DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC stochastic optimal control AND NONZERO SUM DIFFERENTIAL GAMES

第25届中国控制与决策会议

作者： Yanjun Lou Wenqiang Li School of Mathematics and Statistics Shandong University at Weihai

ISBN: (纸本)9781467355339

In R. Buckdahn, Li, Peng [6], the authors obtained mean-field backward stochastic Differential equations （BSDEs） in a natural way as a limit of some highly dimensional system of forward and backward SDEs, corresponding to a great number of particles. In this paper, firstly, we prove that there exists a unique solution of fully coupled MF-FBSDE. Then we use the solutions of mean-field forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic optimal control problem and the open-loop Nash equilibrium point of nonzero sum differential games.

关键词： Mean-field forward-backward stochastic differential equations stochastic optimal control nonzero sum differential games.

来源： cnki会议评论

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Journal of Systems Science & Complexity 2005年第2期18卷 179-192页

作者： WUZhen SchoolofMathematicsandSystemsScience ShandongUniversityJinan250100China

In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.

关键词： stochastic differential equations stochastic optimal control riccatiequation nonzero sum stochastic differential game