Simulation studies on the boundary stabilization and disturbance rejection for fractional diffusion-wave equation

• Published in: 2004 American Control Conference Proceedings; Volume 6 of 6 Vol. 6; pp. 5010 - 5015 vol.6
• Main Authors: Jinsong Liang, Yangquan Chen, Fullmer, R.
• Format: Conference Proceeding Journal Article
• Language: English
• Published: Piscataway NJ IEEE 01.01.2004; Evanston IL American Automatic Control Council
• Subjects: Aerodynamics; Aerospace engineering; Applied sciences; Calculus; Computational modeling; Computer science; control theory; systems; Control systems; Control theory. Systems; Exact sciences and technology; Integrodifferential equations; Numerical simulation; Partial differential equations; Stress; Velocity control; Wave equation; Disturbance rejection; Diffusion equation; Stabilization; Fractional derivative
• ISBN: 9780780383357; 0780383354
• ISSN: 0743-1619
• DOI: 10.23919/ACC.2004.1384644

A class of evolution systems described by the one-dimensional fractional diffusion-wave equation subject to a boundary controller at the boundary is considered. Both boundary stabilization and disturbance rejection are considered. This paper, for the first, has confirmed, via hybrid symbolic and numerical simulation studies, that the existing two schemes for boundary stabilization and disturbance rejection for (integer order) wave/beam equations are still valid for fractional order diffusion-wave equations. The problem definition, the hybrid symbolic and numerical simulation techniques, outlines of the methods for boundary stabilization and disturbance rejection are presented together with extensive simulation results. Different dynamic behaviors are revealed for different fractional orders which create new future research opportunities.