On dynamical reconstruction of an input in a linear system under measuring a part of coordinates

2018 ◽  
Vol 26 (3) ◽  
pp. 395-410 ◽  
Author(s):  
Vyacheslav I. Maksimov
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Unknown Input ◽  
Phase Coordinates ◽  
Guaranteed Control ◽  
Dynamical Reconstruction

AbstractThe problem of reconstructing an unknown input under measuring a part of phase coordinates of a system of ordinary differential equations is considered. We propose a solving algorithm that is stable to perturbations and is based on the combination of ideas from the theory of dynamical inversion and the theory of guaranteed control. The algorithm consists of two blocks: the block of dynamical reconstruction of unmeasured coordinates and the block of dynamical reconstruction of an input.

On dynamical reconstruction of boundary and distributed inputs in a Schlögl equation

2019 ◽  
Vol 27 (6) ◽  
pp. 877-889
Author(s):  
Vyacheslav I. Maksimov
Keyword(s):  
Convergence Rate ◽  
Unknown Input ◽  
Phase Coordinates ◽  
Guaranteed Control ◽  
Dynamical Reconstruction

Abstract The problem of reconstructing an unknown input under measuring a phase coordinates of a Schlögl equation is considered. We propose a solving algorithm that is stable to perturbations and is based on the combination of ideas from the theory of dynamical inversion and the theory of guaranteed control. The convergence rate of the algorithm is obtained.

scholarly journals Linearization of Two Second-Order Ordinary Differential Equations via Fiber Preserving Point Transformations

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Sakka Sookmee ◽  
Sergey V. Meleshko
Keyword(s):  
Linear System ◽  
General Solution ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Point Transformations ◽  
Constant Coefficients ◽  
Linearizable System

The necessary form of a linearizable system of two second-order ordinary differential equations y1″=f1(x,y1,y2,y1′,y2′), y2″=f2(x,y1,y2,y1′,y2′) is obtained. Some other necessary conditions were also found. The main problem studied in the paper is to obtain criteria for a system to be equivalent to a linear system with constant coefficients under fiber preserving transformations. A linear system with constant coefficients is chosen because of its simplicity in finding the general solution. Examples demonstrating the procedure of using the linearization theorems are presented.

scholarly journals GREEN’S MATRICES FOR FIRST ORDER DIFFERENTIAL SYSTEMS WITH NONLOCAL CONDITIONS∗

2017 ◽  
Vol 22 (2) ◽  
pp. 213-227
Author(s):  
Gailė Paukštaitė ◽  
Artūras Štikonas
Keyword(s):  
Differential Equation ◽  
Linear System ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Green's Function ◽  
Nonlocal Conditions ◽  
Differential Systems ◽  
First Order ◽  
Green’S Matrix ◽  
Explicit Representations

In this paper, we investigate the linear system of first order ordinary differential equations with nonlocal conditions. Green’s matrices, their explicit representations and properties are considered as well. We present the relation between the Green’s matrix for the system and the Green’s function for the differential equation. Several examples are also given.

On the ξ-Exponentially Asymptotic Stability of Linear Systems of Generalized Ordinary Differential Equations

2001 ◽  
Vol 8 (4) ◽  
pp. 645-664
Author(s):  
M. Ashordia ◽  
N. Kekelia
Keyword(s):  
Asymptotic Stability ◽  
Linear System ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Systems ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Nondecreasing Function ◽  
Necessary And Sufficient ◽  
Generalized Ordinary Differential Equations

Abstract Necessary and sufficient conditions and effective sufficient conditions are established for the so-called ξ-exponentially asymptotic stability of the linear system 𝑑𝑥(𝑡) = 𝑑𝘈(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡), where and are respectively matrix- and vector-functions with bounded variation components, on every closed interval from [0, +∞[ and ξ : [0, +∞[ → [0, +∞[ is a nondecreasing function such that .

On a New Approach to the Solution of the Nonlinear Filtering Equation of Jump Processes

1996 ◽  
Vol 10 (1) ◽  
pp. 153-163 ◽  
Author(s):  
Kaisheng Fan
Keyword(s):  
Linear System ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Nonlinear Filtering ◽  
Jump Processes ◽  
Algebraic Equations ◽  
Normalization Procedure ◽  
New Approach ◽  
Partially Observed ◽  
On Line

An implementable on-line approach to solve the nonlinear filtering equation for a partially observed system in which both the state and observation processes are jump processes is presented. By making use of the special structure of jump processes, the new method allows us to obtain the solution of the resulting nonlinear filtering equation from solving a linear system of ordinary differential equations and a linear system of algebraic equations recursively and via a simple normalization procedure.

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