In this study, we investigate the optimal control of a class of singularly perturbed linear stochastic systems with Markovian jumping parameters. After establishing an asymptotic structure for the stabilizing solution...
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In this study, we investigate the optimal control of a class of singularly perturbed linear stochastic systems with Markovian jumping parameters. After establishing an asymptotic structure for the stabilizing solution of the coupled stochastic algebraic Riccati equations, a parameter-independent composite controller is derived. Furthermore, the cost degradation in a reduced-order controller is discussed. Thus, the exactness of the proposed approximate control is discussed for the first time. As an additional important contribution, a numerical algorithm for solving the coupled stochastic algebraic Riccati equations is proposed, and the feature of the resulting higher-order controller is shown. Finally, a simple example is presented to demonstrate the validity of the proposed method. Copyright (c) 2016 John Wiley & Sons, Ltd.
In this paper we introduce a new method for the simulation of the exit time and exit position of a (delta-dimensional Brownian motion from a domain. The main interest of our method is that it avoids splitting time sch...
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In this paper we introduce a new method for the simulation of the exit time and exit position of a (delta-dimensional Brownian motion from a domain. The main interest of our method is that it avoids splitting time schemes as well as inversion of complicated series. The method, called walk on moving spheres algorithm, was first introduced for hitting times of Bessel processes. In this study this method is adapted and developed for the first time for the Brownian motion hitting times. The idea is to use the connexion between the (delta-dimensional Bessel process and the (delta-dimensional Brownian motion thanks to an explicit Bessel hitting time distribution associated with a particular curved boundary. This allows to build a fast and accurate numerical scheme for approximating the hitting time. We introduce also an overview of existing methods for the simulation of the Brownian hitting time and perform numerical comparisons with existing methods. (C) 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
The dynamic reconstruction of the right-hand side of a second-order differential equation is considered. A solution algorithm is proposed that is robust to information noise and computational errors. The algorithm is ...
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The dynamic reconstruction of the right-hand side of a second-order differential equation is considered. A solution algorithm is proposed that is robust to information noise and computational errors. The algorithm is constructed using dynamic inversion theory.
The article is devoted to multiple circle covering problem for a bounded set in a two-dimensional metric space with a given amount of circles. Such statements arise in the construction of global navigation systems lik...
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The article is devoted to multiple circle covering problem for a bounded set in a two-dimensional metric space with a given amount of circles. Such statements arise in the construction of global navigation systems like GPS and Glonass. A similar problem appears in infrastructure logistics if there is a main servicing system and it is necessary to create a duplicate system to support service in the case of failure of one or more nodes. To solve this problem, we propose a computational algorithm based on a combination of the optical -geometric approach due to Fermat and Huygens principles and Voronoi diagram. A key feature of the algorithm is the ability to deal with non-Euclidean metrics. numerical results and a comparison with known approaches are presented and discussed. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
作者：
Xue, DingyuBai, LuNortheastern Univ
Sch Informat Sci & Engn Shenyang 110006 Liaoning Peoples R China Northeastern Univ
Sch Informat Sci & Engn Shenyang 110006 Liaoning Peoples R China Shenyang Univ
Sch Informat Engn Shenyang 110044 Liaoning Peoples R China
There are many numerical algorithms for solving the fractional-order ordinary differential equations (FODEs). They are usually very different in nature, and it is difficult to compare their performances. To solve this...
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There are many numerical algorithms for solving the fractional-order ordinary differential equations (FODEs). They are usually very different in nature, and it is difficult to compare their performances. To solve this problem, a set of five benchmark problems of different categories of FODEs with known analytical solution are designed and proposed, they can be used as benchmark problems for testing the numerical algorithms. A Simulink block diagram scheme is used for solving these benchmark problems, with computing errors and the running times reported.
In this paper, we complete and improve the study of the simulation of the hitting times of some given boundaries for Bessel processes. These problems are of great interest in many application fields as finance and neu...
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In this paper, we complete and improve the study of the simulation of the hitting times of some given boundaries for Bessel processes. These problems are of great interest in many application fields as finance and neurosciences. In a previous work (Ann. AppL Probab. 23 (2013) 2259-2289), the authors introduced a new method for the simulation of hitting times for Bessel processes with integer dimension. The method, called walk on moving spheres algorithm (WoMS), was based mainly on the explicit formula for the distribution of the hitting time and on the connection between the Bessel process and the Euclidean norm of the Brownian motion. This method does not apply anymore for a non-integer dimension. In this paper we consider the simulation of the hitting time of Bessel processes with non-integer dimension delta >= 1 and provide a new algorithm by using the additivity property of the laws of squared Bessel processes. We split each simulation step of the algorithm in two parts: one is using the integer dimension case and the other one considers hitting time of a Bessel process starting from zero.
We show that a constant-potential time-independent Schrodinger equation with Dirichlet boundary data can be reformulated as a Laplace equation with Dirichlet boundary data. With this reformulation, which we call the D...
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We show that a constant-potential time-independent Schrodinger equation with Dirichlet boundary data can be reformulated as a Laplace equation with Dirichlet boundary data. With this reformulation, which we call the Duffin correspondence, we provide a classical Walk On Spheres (WOS) algorithm for Monte Carlo simulation of the solutions of the boundary value problem. We compare the obtained Duffin WOS algorithm with existing modified WOS algorithms.
The paper is devoted to the Bayesian estimation of finite-state random vector given the indirect non-stationary continuous-time observations corrupted by a Wiener noise. The key feature is that the noise intensity is ...
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The paper is devoted to the Bayesian estimation of finite-state random vector given the indirect non-stationary continuous-time observations corrupted by a Wiener noise. The key feature is that the noise intensity is ...
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The paper is devoted to the Bayesian estimation of finite-state random vector given the indirect non-stationary continuous-time observations corrupted by a Wiener noise. The key feature is that the noise intensity is a function of the estimated vector, hence the traditional optimal filtering framework fails in this case. The estimate is obtained both in the explicit integral form and as the solution to a stochastic differential system with some jump processes in the right hand side. The presence of the multiplicative noise gives a possibility to raise the estimation quality up to the exact value restoration. The numerical procedure for the estimate calculation is accompanied with the accuracy analysis. An example illustrating the performance of the proposed estimate is also presented. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
An efficient numerical method for solution of boundary value problems with additional condition is presented. The approach is based on the shooting method but the procedure of seeking "the proper shot" allow...
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An efficient numerical method for solution of boundary value problems with additional condition is presented. The approach is based on the shooting method but the procedure of seeking "the proper shot" allows one to satisfy "additional" boundary conditions. General considerations are illustrated by a real example. The computational example concerns the "dead zone" regime for the non-linear diffusion-reaction equation in heterogeneous catalysis. Accuracy and efficiency of the presented method confirm results obtained for a wide range of changes of process parameters, including the vicinity of a critical point. Calculations were performed with the use of the Maple (R) program.
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