of stochastic optimal control problems. 系列原名,Applications of Mathematics:Stochastic Modelling and Applied Probability 1 Fleming/Rishel, Deterministic and Stochastic Optimal Control (1975) 2 Marchuk, Methods of Numerical Mathematics (1975, 2nd ed. A general method for obtaining a useful … Stochastic systems theory, numerical methods for stochastic control, stochastic approximation YONG Jiongmin, University of Central Florida (USA). (Tao Zhou), 2009-2020 (C) Copyright Global Science Press, All right reserved, Highly Accurate Numerical Schemes for Stochastic Optimal Control via FBSDEs, @Article{NMTMA-13-296, Markus Klein, Andreas Prohl, Optimal control for the thin-film equation: Convergence of a multi-parameter approach to track state constraints avoiding degeneracies, October 2014. Google Scholar, Khalifa A. K. A., Eilbeck J. C. (1981) Collocation with quadratic and cubic Splines. (Weidong Zhao), [email protected] Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. Please note that this page is old. Comput Econ 39, 429–446 (2012). The cost function and the inequality constraints are functions of the probability distribution of the state variable at the final time. title = {Highly Accurate Numerical Schemes for Stochastic Optimal Control via FBSDEs}, This is a preview of subscription content, log in to check access. Journal of Numerical Analysis 2: 111–121, Kushner H. J., Dupuis P. (2001) Numerical Methods for Stochastic Control Problems in Continuous Time. Chuchu Chen, Jialin Hong, Andreas Prohl, Convergence of a θ-scheme to solve the stochastic nonlinear Schrodinger equation with Stratonovich noise, October 2014. google We introduce a numerical method to solve stochastic optimal control problems which are linear in the control. © 2021 Springer Nature Switzerland AG. In this paper, a computational approach is proposed for solving the discrete-time nonlinear optimal control problem, which is disturbed by a sequence of random noises. The computation's difficulty is due to the nature of the HJB equation being a second-order partial differential equation which is coupled with an optimization. Correspondence to 22, Issue. A non-linear stochastic optimal control method for the system is presented. & Tao Zhou. Therefore, it is worth studying the near‐optimal control problems for such systems. Published online: We study these problems within the game theoretic framework, and look for open-loop Nash equilibrium controls. (1967) Spline function approximations for solutions of ordinary differential equations. In order to achieve the minimization of the infected population and the minimum cost of the control, we propose a related objective function to study the near‐optimal control problem for a stochastic SIRS epidemic model with imprecise parameters. For the solution of SPDEs there has recently been an increasing effort in the development of efficient numerical … INTRODUCTION The optimal control of stochastic systems is a difficult problem, particularly when the system is strongly nonlinear and constraints are present. - 172.104.46.201. Stochastics, 2005, 77: 381--399. Our numerical results show that our schemes are stable, accurate, and effective for solving stochastic optimal control problems. SN - 13 In this work, we introduce a stochastic gradient descent approach to solve the stochastic optimal control problem through stochastic maximum principle. L Control problems for nonlocal set evolutions with state constraints 9 H. M Sensitivity analysis and real-time control of bang-bang and singular control problems 5 J.A. SP - 296 scholar of numerical optimal control has to acquire basic numerical knowledge within both fields, i.e. number = {2}, Stochastic control is a very active area of research and new problem formulations and sometimes surprising applications appear regu­ larly. For other Departments. We discuss the use of stochastic collocation for the solution of optimal control problems which are constrained by stochastic partial differential equations (SPDE). author = {Fu , Yu and Zhao , Weidong and Zhou , Tao }, Markus Klein, Andreas Prohl, Optimal control for the thin-film equation: Convergence of a multi-parameter approach to track state constraints avoiding degeneracies, October 2014. Numerical examples illustrating the solution of stochastic inverse problems are given in Section 7, and conclusions are drawn in Section 8. Meth. This paper addresses a version of the linear quadratic control problem for mean-field stochastic differential equations with deterministic coefficients on time scales, which includes the discrete time and continuous time as special cases. Tax calculation will be finalised during checkout. (1983) Quadratic Spline and Two-Point Boundary Value Problem. We then show how to effectively reduce the dimension in the proposed algorithm, which improves computational time and memory constraints. Algebraic Topology II. Secondly, numerical methods only warrant the approximation accuracy of the value function over a bounded domain, which is … This paper is devoted to exposition of some results that are related to numerical synthesis of stochastic optimal control systems and also to numerical analysis of different approximate analytical synthesis methods. Thereby the constraining, SPDE depends on data which is not deterministic but random. 55, Issue. Chuchu Chen, Jialin Hong, Andreas Prohl, Convergence of a θ-scheme to solve the stochastic nonlinear Schrodinger equation with Stratonovich noise, October 2014. Discrete and Continuous Dynamical Systems - Series B, Vol. 2. RIMS, Kyoto Univ. Here, it is assumed that the output can be measured from the real plant process. Immediate online access to all issues from 2019. Numerical methods for stochastic optimal stopping problems with delays. An example, motivated as an invest problem with uncertain cost, is provided, and the effectiveness of our method demonstrated. 1Modelling and Scienti c Computing, CMCS, Mathematics … Sufficient and necessary conditions for the near optimality of the model are established using Ekeland's principle and a nearly maximum … We first convert the stochastic optimal control problem into an equivalent stochastic optimality system of FBSDEs. The auxiliary value function wis in general not smooth. This multi-modality leads to surprising behavior is stochastic optimal control. 2013 Numer. An optimal control strategy for nonlinear stochastic vibration using a piezoelectric stack inertial actuator has been proposed in this paper. In this paper, we investigate a class of time-inconsistent stochastic control problems for stochastic differential equations with deterministic coefficients. volume 39, pages429–446(2012)Cite this article. DA - 2020/03 19: 7–13, School of Economics and Finance, University of St. Andrews, St. Andrews, Fife, KY16 9AL, UK, School of Mathematics and Statistics, University of Sydney, Camperdown, Australia, Center for Dynamic Macro Economic Analysis, University of St. Andrews, St. Andrews, Fife, UK, You can also search for this author in In this paper, we investigate a class of time-inconsistent stochastic control problems for stochastic differential equations with deterministic coefficients. journal = {Numerical Mathematics: Theory, Methods and Applications}, CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In [4] we presented a numerical algorithm for the computation of the optimal feedback law in an ergodic stochastic optimal control problem. Numerische Mathematik I. Numerical methods for stochastic optimal stopping problems with delays. In general, these can be formulated as: Yu Fu, Some stochastic optimal control models, coming from finance and economy, are solved by the schemes. 1. This book is concerned with numerical methods for stochastic control and optimal stochastic control problems. 2 A control problem with stochastic PDE constraints We consider optimal control problems constrained by partial di erential equations with stochastic coe cients. In this paper, we develop a stochastic SIRS model that includes imprecise parameters and white noise, formulate and analyze the near‐optimal control problem for the stochastic model. Computational Economics Probabilistic Method in Combinatorics. JO - Numerical Mathematics: Theory, Methods and Applications We assume that the readers have basic knowledge of real analysis, functional analysis, elementary probability, ordinary differential equations and partial differential equations. The state variable at the final time ( 1975 ) a collocation method two-point... 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