scholarly journals THE THEOREM OF AVERAGING IN THE CONDITION OF UNLIMETED SPEED FOR ALMOST-PERIODIC FUNCTIONS

2017 ◽  
Vol 19 (3) ◽  
pp. 53-57
Author(s):  
O.P. Filatov
Keyword(s):  
Differential Inclusion ◽  
Initial Conditions ◽  
Dimensional Space ◽  
Finite Dimensional Space ◽  
Almost Periodic ◽  
Independent Variables ◽  
Finite Dimensional ◽  
All Solutions ◽  
Independent Variable ◽  
The Right

It is proved that the limit of maximal mean is an independent variable of initial conditions if an axis exists from the convex hull of a set of permitted speeds out of a finite-dimensional space and the components of direction vector of the axis are the independent variables with respect to a spectrum of almost-periodic function. The set of permitted speeds is the right hand of differential inclusion. The limit of maximal mean is taken over all solutions of the Couchy problem for the differential inclusion.

scholarly journals THE THEOREM OF AVERAGING FOR THE ALMOST-PERIODIC FUNCTIONS

2017 ◽  
Vol 18 (6) ◽  
pp. 100-112
Author(s):  
O.P. Filatov
Keyword(s):  
Differential Inclusion ◽  
Initial Conditions ◽  
Dimensional Space ◽  
Compact Set ◽  
Finite Dimensional Space ◽  
Almost Periodic ◽  
Finite Dimensional ◽  
All Solutions ◽  
Independent Variable ◽  
The Right

It is proved that the limit of maximal mean is an independent variable of initial conditions if a vector exists from the convex hull of a compact set out of a finite-dimensional space and the components of vector are independent variables with respect to the spectrum of almost-periodic function. The compact set is the right hand of differential inclusion. The limit of maximal mean is taken over all solutions of the Couchy problem for the differential inclusion.

scholarly journals DIFFERENCE-DIFFERENTIAL GAME OF CONVERGENCE - EVASION IN HILBERT SPACE, II

2017 ◽  
Vol 20 (10) ◽  
pp. 74-83
Author(s):  
V.L. Pasikov
Keyword(s):  
Hilbert Space ◽  
Dimensional Space ◽  
Dynamic Game ◽  
Continuous Functions ◽  
Scientific School ◽  
Finite Dimensional Space ◽  
Space Of Continuous Functions ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
The Right

For conflict operated differential system with delay studying of dynamic game of convergence - evasion relatively functional goal set, now regarding evasion and solution of a problem of existence of alternative in the case under consideration is continued. In the work realization of condition of saddle point relatively to the right part of operated system is not supposed. Earlier similar tasks were set and solved for finite-dimensional space at scientific school of the academicianN.N. Krasovsky. For a case of infinite-dimensional space of continuous functions similar tasks were considered by the author. In the suggested work at theorem proving about convergence - evasion, the norm of Hilbert space is used.

scholarly journals Value Function and Optimal Control of Differential Inclusions

2015 ◽  
Vol 61 (1) ◽  
pp. 181-193 ◽  
Author(s):  
Tzanko Donchev ◽  
Ammara Nosheen
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Unique Solution ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Value Function ◽  
Dimensional Space ◽  
Finite Dimensional Space ◽  
Finite Dimensional ◽  
The Value Function

Abstract Optimal control system described by differential inclusion with continuous and one sided Perron right-hand side in a finite dimensional space is studied in the paper. We prove that the value function is the unique solution of a proximal Hamilton-Jacobi inequalities.

DUAL FORMULATION OF OPTIMAL PROBLEM FOR CONTINUOUS-TIME SYSTEMS

2005 ◽  
Vol 02 (03) ◽  
pp. 251-258
Author(s):  
HANLIN HE ◽  
QIAN WANG ◽  
XIAOXIN LIAO
Keyword(s):  
Objective Function ◽  
Continuous Time ◽  
Dimensional Space ◽  
Finite Dimensional Space ◽  
Error Response ◽  
Infinite Dimensional ◽  
Dual Formulation ◽  
Finite Dimensional ◽  
Continuous Time Systems ◽  
Time Systems

The dual formulation of the maximal-minimal problem for an objective function of the error response to a fixed input in the continuous-time systems is given by a result of Fenchel dual. This formulation probably changes the original problem in the infinite dimensional space into the maximal problem with some restrained conditions in the finite dimensional space, which can be researched by finite dimensional space theory. When the objective function is given by the norm of the error response, the maximum of the error response or minimum of the error response, the dual formulation for the problems of L1-optimal control, the minimum of maximal error response, and the minimal overshoot etc. can be obtained, which gives a method for studying these problems.

Estimation of the Hankel Singular Values of Fractional-Order Systems

2009 ◽  
Author(s):  
Jay L. Adams ◽  
Robert J. Veillette ◽  
Tom T. Hartley
Keyword(s):  
Fractional Order ◽  
Dimensional Space ◽  
Ritz Method ◽  
Singular Values ◽  
Finite Dimensional Space ◽  
Fractional Order Systems ◽  
Norm Estimates ◽  
Finite Dimensional ◽  
Hankel Singular Values ◽  
Hankel Norm

This paper applies the Rayleigh-Ritz method to approximating the Hankel singular values of fractional-order systems. The algorithm is presented, and estimates of the first ten Hankel singular values of G(s) = 1/(sq+1) for several values of q ∈ (0, 1] are given. The estimates are computed by restricting the operator domain to a finite-dimensional space. The Hankel-norm estimates are found to be within 15% of the actual values for all q ∈ (0, 1].

Series in a Finite-Dimensional Space

1997 ◽  
pp. 13-27
Author(s):  
Mikhail I. Kadets ◽  
Vladimir M. Kadets
Keyword(s):  
Dimensional Space ◽  
Finite Dimensional Space ◽  
Finite Dimensional

Alternating projections and interpolation of stationary processes

1992 ◽  
Vol 29 (4) ◽  
pp. 921-931 ◽  
Author(s):  
Mohsen Pourahmadi
Keyword(s):  
Missing Values ◽  
Stationary Process ◽  
Dimensional Space ◽  
Stationary Processes ◽  
Finite Dimensional Space ◽  
Alternating Projections ◽  
Von Neumann ◽  
Finite Dimensional ◽  
Explicit Formulae ◽  
Linear Interpolator

By using the alternating projection theorem of J. von Neumann, we obtain explicit formulae for the best linear interpolator and interpolation error of missing values of a stationary process. These are expressed in terms of multistep predictors and autoregressive parameters of the process. The key idea is to approximate the future by a finite-dimensional space.

Well Posedness

2012 ◽  
Author(s):  
G. F. Roach ◽  
I. G. Stratis ◽  
A. N. Yannacopoulos
Keyword(s):  
Variational Formulation ◽  
Eigenvalue Problems ◽  
Dimensional Space ◽  
Well Posedness ◽  
Finite Dimensional Space ◽  
Chiral Media ◽  
Exterior Problems ◽  
Finite Dimensional ◽  
Time Harmonic ◽  
Interior Domain

This chapter presents rigorous mathematical results concerning the solvability and well posedness of time-harmonic problems for complex electromagnetic media, with a special emphasis on chiral media. It also presents some results concerning eigenvalue problems in cavities filled with complex electromagnetic materials. The chapter also studies the behaviour of the interior domain problem for a chiral medium in the limit of low chirality. Next, it presents some comments related to the well posedness and solvability of exterior problems. Finally, using an appropriate finite-dimensional space and the variational formulation of the discretised version of the original boundary value problem, this chapter obtains numerical methods for the solution of the Maxwell equations for chiral media.

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