Solving a nonhomogeneous linear system of interval differential equations

In most application problems, the exact values of the input parameters are unknown, but the intervals in which these values lie can be determined. In such problems, the dynamics of the system are described by an interval-valued differential equation. In this study, we present a new approach to nonho...

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Bibliographic Details
Published in:Soft computing (Berlin, Germany) Germany), 2018-06, Vol.22 (12), p.3817-3828
Main Authors: Gasilov, Nizami A., Emrah Amrahov, Şahin
Format: Article
Language:English
Subjects:
Artificial Intelligence
Calculus
Computational Intelligence
Control
Differential equations
Engineering
Existence theorems
Foundations
Inhomogeneous systems
Mathematical analysis
Mathematical Logic and Foundations
Mechatronics
Methods
Ordinary differential equations
Robotics
Uniqueness theorems
Variables
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Summary:In most application problems, the exact values of the input parameters are unknown, but the intervals in which these values lie can be determined. In such problems, the dynamics of the system are described by an interval-valued differential equation. In this study, we present a new approach to nonhomogeneous systems of interval differential equations. We consider linear differential equations with real coefficients, but with interval initial values and forcing terms that are sets of real functions. For each forcing term, we assume these real functions to be linearly distributed between two given real functions. We seek solutions not as a vector of interval-valued functions, as usual, but as a set of real vector functions. We develop a method to find the solution and establish an existence and uniqueness theorem. We explain our approach and solution method through an illustrative example. Further, we demonstrate the advantages of the proposed approach over the differential inclusion approach and the generalized differentiability approach.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-017-2818-x