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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 control.Then,an effective overarching algorithm will be introduced to combine the parameter estimator and the optimal control solver.Numerical 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

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

stochastic optimal control based on variable-period sampling model for Networked control Systems with random delays

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Stochastic optimal control based on variable-period sampling...

Meshfree Approximation for stochastic optimal control Problems

2009中国控制与决策会议

作者： Xinlan Guo~1,Hong Wang~(1,2) 1.Institute of Automation,Chinese Academy of Sciences,Beijing,100080 P.R.China 2.control Systems Center,School of Electrical and Electronics Engineering,the University of Manchester,Manchester M60 1QD,UK

＜正＞This paper presents a stochastic optimal controller using the variable-period sampling Networked control Systems （NCSs） model,where it has been assumed that the random network-induced delay only exists between sensor and controller and the time delay occuring at current sampling step is taken as the sampling period between current sampling step and next sampling step.It is assumed that the random delay is subjected to a uniform distribution in the interval between 0 and the maximal random delay.The proposed stochastic optimal controller is shown to produce a closed loop system which exhibits exponentially mean square stability.In the end,the simulations on an inverted pendulum process and DC motor are studied,which show that the proposed algorithm can produce desired control effect.

关键词： Networked control Systems Variable-period Sampling Model stochastic optimal control Exponentially Mean Square Stable

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Communications in Mathematical Research 2021年第3期37卷 386-418页

作者： Hui Sun Feng Bao Department of Mathematics Florida State UniversityTallahasseeFloridaUSA

In this work,we study the gradient projection method for solving a class of stochastic control problems by using a mesh free approximation ap-proach to implement spatial dimension approximation.Our main contribu-tion is to extend the existing gradient projection method to moderate high-dimensional space.The moving least square method and the general radial basis function interpolation method are introduced as showcase methods to demonstrate our computational framework,and rigorous numerical analysis is provided to prove the convergence of our meshfree approximation approach.We also present several numerical experiments to validate the theoretical re-sults of our approach and demonstrate the performance meshfree approxima-tion in solving stochastic optimal control problems.

关键词： stochastic optimal control maximum principle backward stochastic differ-ential equations meshfree approximation

stochastic optimal control of First Firing Neuron

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Stochastic Optimal Control of First Firing Neuron

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

第八届全国动力学与控制学术会议

作者：吴勇军彭建华罗明华东理工大学信息科学与工程学院复杂系统动力学与控制研究室

First-firing statistics of stochastic optimally controlled integrate-and-fire neuron under stimulation of colored noise is investigated.The stochastic averaging principle is utilized and the model equation is approximated by diffusion process and represented by It? stochastic differential equation.The control problems for maximizing the resting probability and maximizing mean first firing time are constructed and the dynamical programming equations associated with the corresponding optimization problem are established.The optimal control law is obtained and the finally controlled Ito stochastic differential equation is yielded.The corresponding backward Kolmogorov equation and Pontryagin equation are established and solved to yield the resting probability and mean first firing time.The analytical results are verified by Monte Carlo simulation.

关键词： stochastic optimal control stochastic Averaging First-Spiking Colored Noise Integrate-and-Fire Monte Carlo Simulation

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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 operator.Here,we describe a new method for finding this eigenfunction using a moving least-squares function approximation.We use efficient iterative solvers that do not require matrix factorization,thereby allowing us to handle large numbers of basis functions.The 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 often.The shape of the bases is automatically defined given the collocation states,in a way that avoids gaps in the coverage.Numerical results on test problems are provided.

关键词： stochastic optimal control Bellman equations

Turnpike Properties for stochastic Linear-Quadratic optimal control Problems

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Chinese Annals of Mathematics,Series B 2022年第6期43卷 999-1022页

作者： Jingrui SUN Hanxiao WANG Jiongmin YONG Department of Mathematics Southern University of Science and TechnologyShenzhen 518055China Corresponding author.College of Mathematics and Statistics Shenzhen UniversityShenzhen 518060China Department of Mathematics University of Central FloridaOrlandoFL 32816USA

This paper analyzes the limiting behavior of stochastic linear-quadratic optimal control problems in finite time-horizon[0,T]as T→∞.The so-called turnpike properties are established for such problems,under stabilizability condition which is weaker than the controllability,normally imposed in the similar problem for ordinary differential systems.In dealing with the turnpike problem,a crucial issue is to determine the corresponding static optimization problem.Intuitively mimicking the deterministic situations,it seems to be natural to include both the drift and the diffusion expressions of the state equation to be zero as constraints in the static optimization problem.However,this would lead us to a wrong direction.It is found that the correct static problem should contain the diffusion as a part of the objective function,which reveals a deep feature of the stochastic turnpike problem.

关键词： Turnpike property stochastic optimal control Static optimization Linear-quadratic Stabilizability Riccati equation

stochastic maximum principle for optimal control problems involving delayed systems

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Science China(Information Sciences) 2021年第1期64卷 269-271页

作者： Feng ZHANG School of Mathematics and Quantitative Economics Shandong University of Finance and Economics

Dear editor,The main objective of this study is to investigate one type of stochastic optimal control problem for a delayed system using the maximum principle method.The existing research can be categorized into two categories.In the first category,the adjoint equation comprises two backward stochastic differential equations (BSDEs) and one backward ordinary differential equation (BODE),which is assumed to have a zero solution;see e.g.,[1-3].However,there is still scope for improvement in this research direction.Here,a special setting is considered for the system parameters;see e.g.,(3.9)and (3.12) in 21.The BODE is assumed to result in a zero solution when the necessary maximum principle is strictly applied;see e.g.,Theorem 5.1 in 31.In the second category,a typee of anticipated/time-advanced BSDE is introduced as the adjoint equation;see e.g.,[1,4-7].

关键词： stochastic optimal control maximum principle delayed system anticipated BSDE linear quadratic problem

An Introductory Review of Time-Inconsistent stochastic optimal control

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An Introductory Review of Time-Inconsistent Stochastic Optim...