共查询到20条相似文献,搜索用时 31 毫秒
1.
P. G. Surkov 《Russian Mathematics (Iz VUZ)》2016,60(10):44-54
We consider a control problem for a parabolic equation with memory. It consists in constructing an algorithm for finding a feedback control which enables one to track a solution of the given equation with an unknown right-hand side. For this problem we propose two noise-resistant solution algorithms based on the method of extremal shift. The first algorithm is applicable in the case of continuous measurements of phase states, whereas the second one presumes discrete measurements. 相似文献
2.
We consider the general continuous time finite-dimensional deterministic system under a finite horizon cost functional. Our
aim is to calculate approximate solutions to the optimal feedback control. First we apply the dynamic programming principle
to obtain the evolutive Hamilton–Jacobi–Bellman (HJB) equation satisfied by the value function of the optimal control problem.
We then propose two schemes to solve the equation numerically. One is in terms of the time difference approximation and the
other the time-space approximation. For each scheme, we prove that (a) the algorithm is convergent, that is, the solution
of the discrete scheme converges to the viscosity solution of the HJB equation, and (b) the optimal control of the discrete
system determined by the corresponding dynamic programming is a minimizing sequence of the optimal feedback control of the
continuous counterpart. An example is presented for the time-space algorithm; the results illustrate that the scheme is effective. 相似文献
3.
In this paper, the problem of the numerical computation of the stabilizing solution of the game theoretic algebraic Riccati
equation is investigated. The Riccati equation under consideration occurs in connection with the solution of the H
∞ control problem for a class of stochastic systems affected by state dependent and control dependent white noise. The stabilizing
solution of the considered game theoretic Riccati equation is obtained as a limit of a sequence of approximations constructed
based on stabilizing solutions of a sequence of algebraic Riccati equations of stochastic control with definite sign of the
quadratic part. The efficiency of the proposed algorithm is demonstrated by several numerical experiments. 相似文献
4.
The main goal of this paper is to apply the so-called policy iteration algorithm (PIA) for the long run average continuous
control problem of piecewise deterministic Markov processes (PDMP’s) taking values in a general Borel space and with compact
action space depending on the state variable. In order to do that we first derive some important properties for a pseudo-Poisson
equation associated to the problem. In the sequence it is shown that the convergence of the PIA to a solution satisfying the
optimality equation holds under some classical hypotheses and that this optimal solution yields to an optimal control strategy
for the average control problem for the continuous-time PDMP in a feedback form. 相似文献
5.
E. V. Tarasova 《Ukrainian Mathematical Journal》2007,59(11):1776-1782
We prove a uniqueness theorem for the inverse scattering problem for a wave equation with absorption and develop an algorithm
for the solution of this problem on the basis of a given scattering operator.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 11, pp. 1580–1584, November, 2007. 相似文献
6.
V. L. Rozenberg 《Proceedings of the Steklov Institute of Mathematics》2011,275(1):149-160
Based on the approach of the theory of dynamic inversion, the problem of continuous estimation of an unknown deterministic disturbance in an Ito stochastic differential equation is investigated with the use of inaccurate measurements of the current phase state. An auxiliary model equation with a control approximating the unknown input is derived. The suggested solution algorithm is constructive; an estimate for its convergence rate is written explicitly. 相似文献
7.
We propose an algorithm for the construction of an asymptotic solution of the Cauchy problem for the singularly perturbed
Korteweg-de Vries equation with variable coefficients and prove a theorem on the estimation of its precision.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 1, pp. 122–132, January, 2007. 相似文献
8.
We consider the problem on the infinite-duration tracking of a prescribed trajectory of an inaccurately observed control system
subjected to an unobservable dynamic disturbance. We construct a solution algorithm that is resource-saving in the sense that
the control resources used for solving the problem for small noise values in the state observation channel are little different
from the corresponding resources in the “ideal case” where the current values of the dynamic disturbance are available to
direct observation. 相似文献
9.
The solution of an elliptic equation in an unbounded region is approximated by the solution of an ordinary differential equation.
To obtain a new inverse problem we prove a uniqueness theorem and exhibit a solution algorithm. Bibliography: 14 titles.
Translated fromProblemy Matematicheskoi Fiziki, 1998, pp. 132–140. 相似文献
10.
V. M. Shul’ga 《Journal of Mathematical Sciences》1998,90(1):1899-1902
The wave problem of electroelastic waves in a cylinder is reduced to a spectral problem for a system of eight ordinary differential
equations. We give an algorithm for numerical solution based on reducing the original boundary-value problem to four Cauchy
problems and determining the roots of the dispersion equation by the method of bisection. One figure. Bibliogrpahy: 4 titles.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 27, 1997, pp. 149–153. 相似文献
11.
D. S. Filippychev 《Computational Mathematics and Modeling》2007,18(1):19-28
The asymptotic solution of the integro-differential plasma-sheath equation is considered. This equation is singularly perturbed
because of the small coefficient multiplying the highest order (second) derivative. The asymptotic solution is obtained by
the boundary function method. Equations are derived for the first two coefficients in the form of both a regular series expansion
and an expansion in boundary functions. The equation for the first coefficient of the regular series has only a trivial solution.
A numerical algorithm is considered for the solution of the second-order differential equation describing the behavior of
the zeroth-order boundary function. The proposed algorithm efficiently solves the boundary-value problem and produces a well-behaved
solution of the Cauchy problem.
__________
Translated from Prikladnaya Matematika i Informatika, No. 23, pp. 24–35, 2006. 相似文献
12.
The general construction for finding all “essentially different” nonlinearities in equations of mathematical physics is exemplified
by the inverse problem of the Grad–Shafranov equation. We present an algorithm that allows one to recover relatively fast
all essentially different sought-for nonlinear right-hand sides of the Grad–Shafranov equation. We present the first example
of a domain with smooth boundary for which the inverse problem has at most one solution in the class of affine functions,
and also in the class of exponential functions. We select some subset of simply connected domains that model, in some sense,
the so-called doublet configurations, for which the inverse problem has at least two essentially different solutions in the
class of analytic functions. In the concluding subsection of the paper, we indicate a method of recovery, from boundary data,
of all essentially different nonlinearities in equations of mathematical physics of considerably general kind, which includes
a system of equations that describes combustion and detonation processes. 相似文献
13.
V. I. Maksimov 《Differential Equations》2014,50(3):362-371
For a parabolic equation, we consider the problem of constructing a feedback control synthesis algorithm ensuring that the solution of a given equation shadows the solution of another equation with unknown right-hand side. We suggest a noise-immune algorithm based on the extremal shift method well known in guaranteed control theory. 相似文献
14.
In this work, we study the problem of the determination of the non-linearity in a parabolic equation from measurements over its solution. This corresponds to an usual physical situation, in which the parameter depends on the state of the system (for instance, the heat conduction coefficient depends on the temperature). We first state the problem as a control problem, for which we show the existence of a solution, and we calculate the derivative of the criterion with respect to the nonlinearity without any assumption on the algebraic form of this latter. We finally give a numerical application of the algorithm, which shows that the situation which is here taken in account (estimation of a parameter function depending on the state) is much better, from the identification point of view, than the usually studied situation for distributed system (estimation of a parameter function depending on space and/or time variables). 相似文献
15.
N. A. Krasovskii A. M. Taras’ev 《Proceedings of the Steklov Institute of Mathematics》2010,269(1):174-185
We address the problem of optimal reconstruction of the values of a linear operator on ℝ
d
or ℤ
d
from approximate values of other operators. Each operator acts as the multiplication of the Fourier transform by a certain
function. As an application, we present explicit expressions for optimal methods of reconstructing the solution of the heat
equation (for continuous and difference models) at a given instant of time from inaccurate measurements of this solution at
other time instants. 相似文献
16.
We construct a sequence of branching particle systems α
n
convergent in measure to the solution of the Kushner–Stratonovitch equation. The algorithm based on this result can be used
to solve numerically the filtering problem. We prove that the rate of convergence of the algorithm is of order n
?. This paper is the third in a sequence, and represents the most efficient algorithm we have identified so far.
Received: 4 February 1997 / Revised version: 26 October 1998 相似文献
17.
We characterize functions satisfying a dissipative inequality associated with a control problem. Such a characterization
is provided in terms of an epicontingent solution, or a viscosity supersolution to a partial differential equation called
Isaacs' equation. Links between supersolutions and epicontingent solutions to Isaacs' equation are studied. Finally, we derive
(possibly discontinuous) disturbance attenuation feedback of the H
∞
problem from contingent formulation of Isaacs' equation.
Accepted 20 January 1998 相似文献
18.
The inverse problem of determining a spacewise dependent heat source, together with the initial temperature for the parabolic heat equation, using the usual conditions of the direct problem and information from two supplementary temperature measurements at different instants of time is studied. These spacewise dependent temperature measurements ensure that this inverse problem has a unique solution, despite the solution being unstable, hence the problem is ill-posed. We propose an iterative algorithm for the stable reconstruction of both the initial data and the source based on a sequence of well-posed direct problems for the parabolic heat equation, which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for a typical benchmark test example, which has the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure gives accurate numerical approximations in relatively few iterations. 相似文献
19.
We consider a reaction–diffusion parabolic problem on branched structures. The Hodgkin–Huxley reaction–diffusion equations
are formulated on each edge of the graph. The problems are coupled by some conjugation conditions at branch points. It is
important to note that two different types of the flux conservation equations are considered. The first one describes a conservation
of the axial currents at branch points, and the second equation defines the conservation of the current flowing at the soma
in neuron models. We study three different types of finite-difference schemes. The fully implicit scheme is based on the backward
Euler algorithm. The stability and convergence of the discrete solution is proved in the maximum norm, and the analysis is
done by using the maximum principle method. In order to decouple computations at each edge of the graph, we consider two modified
schemes. In the predictor algorithm, the values of the solution at branch points are computed by using an explicit approximation
of the conservation equations. The stability analysis is done using the maximum principle method. In the predictor–corrector
method, in addition to the previous algorithm, the values of the solution at the branch points are recomputed by an implicit
algorithm, when the discrete solution is obtained on each subdomain. The stability of this algorithm is investigated numerically.
The results of computational experiments are presented. 相似文献
20.
In this paper, an iterative algorithm is constructed for solving linear matrix equation AXB = C over generalized centro-symmetric matrix X. We show that, by this algorithm, a solution or the least-norm solution of the matrix equation AXB = C can be obtained within finite iteration steps in the absence of roundoff errors; we also obtain the optimal approximation
solution to a given matrix X
0 in the solution set of which. In addition, given numerical examples show that the iterative method is efficient. 相似文献