Ulteriori informazioni
Distributed-order differential equations, a generalization of fractional calculus, are of increasing importance in many fields of science and engineering from the behaviour of complex dielectric media to the modelling of nonlinear systems.
This Brief will broaden the toolbox available to researchers interested in modeling, analysis, control and filtering. It contains contextual material outlining the progression from integer-order, through fractional-order to distributed-order systems. Stability issues are addressed with graphical and numerical results highlighting the fundamental differences between constant-, integer-, and distributed-order treatments. The power of the distributed-order model is demonstrated with work on the stability of noncommensurate-order linear time-invariant systems. Generic applications of the distributed-order operator follow: signal processing and viscoelastic damping of a mass-spring set up.
A new general approach to discretization of distributed-order derivatives and integrals is described. The Brief is rounded out with a consideration of likely future research and applications and with a number of MATLAB® codes to reduce repetitive coding tasks and encourage new workers in distributed-order systems.
Sommario
Introduction.- Distributed-order Linear Time-invariant System (DOLTIS) and Its Stability Analysis.- Noncommensurate Constant Orders as Special Cases of Doltis.- Distributed-order Filtering and Distributed-order Optimal Damping.- Numerical Solution of Differential Equations of Distributed Order.- Future Topics.- Appendix: MATLAB® Codes.
Info autore
Doctor YangQuan Chen has authored over 200 academic papers plus numerous technical reports. His current research interests include autonomous navigation and intelligent control of a team of unmanned ground vehicles, machine vision for control and automation, distributed control systems (MAS-net: mobile actuator-sensor networks), fractional-order control, interval computation, and iterative/repetitive/adaptive learning control. Currently, he serves as an Associate Editor for IEEE Control Systems Society, Conference Editorial Board (CSSCEB ). He was also an Associate Editor of ISA Review Board for AACC 's American Control Conference ( ACC2005 ). He has been the Co-Organizer and Instructor of the Tutorial Workshops on Fractional-order Calculus in Control and Robotics at IEEE 2002 Conference on Decision and Control (CDC 02), and Applied Fractional Calculus in Controls and Signal Processing at CDC 10 and a founding member of the ASME subcommittee on Fractional Dynamics .
Riassunto
Distributed-order differential equations, a generalization of fractional calculus, are of increasing importance in many fields of science and engineering from the behaviour of complex dielectric media to the modelling of nonlinear systems.
This Brief will broaden the toolbox available to researchers interested in modeling, analysis, control and filtering. It contains contextual material outlining the progression from integer-order, through fractional-order to distributed-order systems. Stability issues are addressed with graphical and numerical results highlighting the fundamental differences between constant-, integer-, and distributed-order treatments. The power of the distributed-order model is demonstrated with work on the stability of noncommensurate-order linear time-invariant systems. Generic applications of the distributed-order operator follow: signal processing and viscoelastic damping of a mass–spring set up.
A new general approach to discretization of distributed-order derivatives and integrals is described. The Brief is rounded out with a consideration of likely future research and applications and with a number of MATLAB® codes to reduce repetitive coding tasks and encourage new workers in distributed-order systems.
Testo aggiuntivo
From the book reviews:
“This book is a concise introduction to the theory and use of distributed-order systems. … Written at the level of first- or second-year graduate student, the book is well suited as a self-contained introduction to an emerging area of research and applications.” (IEEE Control Systems Magazine, October, 2013)
Relazione
From the book reviews:
"This book is a concise introduction to the theory and use of distributed-order systems. ... Written at the level of first- or second-year graduate student, the book is well suited as a self-contained introduction to an emerging area of research and applications." (IEEE Control Systems Magazine, October, 2013)
