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Fractional derivatives of convex Lyapunov functions and control problems in fractional order systems
- Source :
- Fractional Calc. Appl. Anal., Fractional Calculus and Applied Analysis
- Publication Year :
- 2018
- Publisher :
- De Gruyter, 2018.
-
Abstract
- The paper is devoted to the development of control procedures with a guide for conflict-controlled dynamical systems described by ordinary fractional differential equations with the Caputo derivative of an order $\alpha \in (0, 1).$ For the case when the guide is in a certain sense a copy of the system, a mutual aiming procedure between the initial system and the guide is elaborated. The proof of proximity between motions of the systems is based on the estimate of the fractional derivative of the superposition of a convex Lyapunov function and a function represented by the fractional integral of an essentially bounded measurable function. This estimate can be considered as a generalization of the known estimates of such type. An example is considered which illustrates the workability of the proposed control procedures.<br />Comment: Submitted to "Fract. Calc. Appl. Anal."
- Subjects :
- Lyapunov function
0209 industrial biotechnology
Measurable function
Dynamical systems theory
Generalization
FRACTIONAL DIFFERENTIAL EQUATION
02 engineering and technology
01 natural sciences
CONTROL PROBLEM
GUIDE
symbols.namesake
Superposition principle
020901 industrial engineering & automation
Classical Analysis and ODEs (math.CA)
FOS: Mathematics
Applied mathematics
0101 mathematics
Mathematics - Optimization and Control
Mathematics
Applied Mathematics
010102 general mathematics
Function (mathematics)
Fractional calculus
LYAPUNOV FUNCTION
Optimization and Control (math.OC)
Mathematics - Classical Analysis and ODEs
DIFFERENTIAL GAME
Bounded function
DISTURBANCES
symbols
Analysis
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Fractional Calc. Appl. Anal., Fractional Calculus and Applied Analysis
- Accession number :
- edsair.doi.dedup.....236256fdf6fa32e07bf1d3b7ecb6ad54