On the Existence of a Lipschitz Feedback Control in a Control Problem with State Constraints

We consider a nonlinear control system with state constraints given as a solution set for a finite system of nonlinear inequalities. The problem of constructing a feedback control that ensures the viability of trajectories of the closed system in a small neighborhood of the boundary of the state constraints is studied. Under some assumptions, the existence of a feedback control in the form of a Lipschitz function of the state of the system is proved.     

The Numerical Solution of a Variational Problem in Automatic Control

In this paper we examine the numerical solution of a two-pointboundary value problem whose boundary condition depends on thevalue of the solution at interior points.     

Numerical Solution for the Non-linear Dirichlet Problem of a Branching Process

We give a probabilistic numerical approach for the nonlinear Dirichlet problem associated with a branching process. Main tools are the probabilistic representation of the solution with the measure-valued branching process, as well as specific techniques for the numerical solution of linear partial differential equations, introduced and developed by Milstein and Tretyakov, and Monte Carlo methods.     

梁振动边界反馈的最优反馈增益的数值解

本用Legendre谱方法估计一端固定,一端加弯矩耗散线性反馈的梁振动的闭环系统使能量最快衰减的最优反馈增益,我们给出了数值产生的图形结果,通过比较发现另一种非耗散的线性反馈在最优反馈增益下比相应的耗散线性反馈有更好的衰减率。     

Numerical Solution to a Control Problem for Integro-Differential Equations

Computational Mathematics and Mathematical Physics - A control problem for an integro-differential equation is approximated by a problem with parameter for a loaded differential equation. A mutual...     

Solution of the Feedback Control Problem in the Mathematical Model of Leukaemia Therapy

A mathematical model of leukaemia therapy based on the Gompertzian law of cell growth is investigated. The effect of the medicine on the leukaemia and normal cells is described in terms of therapy functions. A feedback control problem with the purpose of minimizing the number of the leukaemia cells while retaining as much as possible the number of normal cells is considered. This problem is reduced to solving the nonlinear Hamilton–Jacobi–Bellman partial differential equation. The feedback control synthesis is obtained by constructing an exact analytical solution to the corresponding Hamilton–Jacobi–Bellman equation.     

The Numerical Solution of the Linear Regulator Problem with Positive Control

The standard linear regulator problem with positive controlis solved using a minimum principle, a maximum principle, andthe hypersphere inequality method. Comparisons are made betweenthe numerical results produced, to examine the theoretical superiorityof the hypersphere method.     

Optimal Solution of a Bottleneck Problem with State Delay

Two computational procedures for solving a class of bottleneck problems with state delay are presented. The first one uses a direct computation scheme for the solution of the continuous-time problem, while the second one is obtained by discretizing the continuous-time problem using piecewise constant controls on small intervals. Examples show that these two approaches agree.     

Numerical Solution of a Singular Two-point Boundary Value Problem

A singular two-point boundary value problem of the fourth orderis restated in a form amenable to difference methods. The resultsof a former paper are then applied with slight modifications.The abbreviations BVP and IVP, for boundary value problem andinitial value problem are used throughout the paper.     

Existence of a Weak Solution for the Phase Change Problem with Joule's Heating

A phase change problem with Joule's heat ing describes tbe processes of electric heating in a conducting material. It is modeled as a coupled system of nonlinear partial differential equations with quadratic growth in the gradient. We establish the existence of a weak solution for the problem in two dimensions.     

A Stability Estimate for a Solution of the Problem of Determining the Dielectric Permittivity

We consider the problem of determining the dielectric permittivity for a nonconducting and nonmagnetic medium. As information we take the traces of the tangential components of the electromagnetic field on the lateral surface of a cylindrical domain. These traces correspond to a solution to some direct problem for the Maxwell system. The impulse source of the current flux lies outside the domain in which the coefficient is sought. The main result of the article is a stability estimate for a solution to the inverse problem in question.     

Numerical Solution of the Cauchy Problem for a Second-Order Integro-Differential Equation

Differential Equations - In a finite-dimensional Hilbert space, we consider the Cauchy problem for a second-order integro-differential evolution equation with memory where the integrand is the...     

奇摄动非线性状态调节器问题的渐近解*

我们将寻求最优控制和奇摄动非线性状态调节器问题的相应轨道.在适当的假设下将有可能去完成当ε→0时一致有效的渐近解.     

Feedback in a Control Problem for a System with Discontinuous Right-Hand Side

Differential Equations - On a finite time horizon, we consider a control system described by a vector differential equation with right-hand side that changes its structure at some times spaced by a...     

弹性振动点观测反馈控制古典解的存在性

本文运用有界线性算子的积分半群理论证明弹性振动点观测反馈控制方程古典解的存在性     

Determining the Source Term in an Abstract Parabolic Problem From a Time Integral of the Solution

We consider the problem of reconstruction of the source term in an abstract parabolic system. The supplementary information, which is necessary to determine the solution of the system together with the unknown part of the source term, is given by the knowledge of a time integral of the solution with respect to a general Borel measure in the time interval. A theorem of existence and uniqueness of a solution, which is also of maximal regularity type, is proved. Certain particular cases are treated, together with the fact that, in some circumstances, the problem enjoys a sort of Fredholm property.