Fractional Order Calculus Day at Utah State University Round Table Discussions

1. Fractional Order Calculus Day at Utah State UniversityRound Table Discussions YangQuan Chen, Acting Director Center for Self-Organizing and Intelligent Systems (CSOIS), Dept. of Electrical and Computer Engineering Utah State University E: yqchen@ece.usu.edu; T: (435)797-0148; F: (435)797-3054 W: http://www.csois.usu.edu/people/yqchen April 19, 2005.

2. Outline • FOC related events: 2005 – ASME 2nd Symposium on Fractional Derivatives & Their Applications (ASME DETC FDTA05, organizers: Profs. Om Prakash Agrawal, Jocelyn Sabatier and J. A. Tenreiro Machado); 2006 – the 2nd IFAC FDA06: Workshop on Fractional Differentiation & its Applications (http://www.gecad.isep.ipp.pt/FDA06/; Chair: Stefan Samko and co-Chair: Blas M. Vinagre) • NSF Partnership grant proposal (leading PI: Prof. Om Prakash Agrawal) • Research directions, IP issues, industry interests Fractional Order Calculus Day at Utah State University

3. NSF International Collaboration for the Advancement of Research and Education on Fractional Derivatives & Their Applications (FDTA) • US Team • Om P. Agrawal, Mechanical Engineering, Southern Illinois Univ., Carbondale, IL 62901 • B. N. Narahari Achar, Dept. of Physics, The Univ. of Memphis, Memphis, TN 38152 • Anil K. Bajaj, Mechanical Engineering, Purdue Univ., West Lafayette, IN 47907-1288 • Gary Bohannan, Wavelength Electronics, Inc., 51 Evergreen Drive, Bozeman, MT 59715 • YangQuan Chen, Electrical & Computer Engineering, Utah State Univ., Logan, UT 84322 • Patricia Davies, Mechanical Engineering, Purdue Unive., West Lafayette, IN 47907-2088 • John W. Hanneken, Department of Physics, The Univ. of Memphis, Memphis, TN 38152 • Tom T. Hartley, Electrical Engineering, The Univ. of Akron, Akron, Ohio 44325-3904 • Carl F. Lorenzo, NASA, Glenn Research Center, Cleveland, Ohio 44135 • Richard L. Magin, Dept. of Bioengineering, Univ. of Illinois at Chicago, Chicago, IL Fractional Order Calculus Day at Utah State University

4. International Team • J. A. Tenreiro Machado, ISEP - Institute of Engineering of Porto, Dept. of Electrotechnical Engineering, Rua Dr. Antonio Bernardino de Almeida, 4200-072 Porto, Portugal • Shunji Manabe, 1-8-12 Kataseyama, Fujisawa-shi, Kanagawa 251-0033, Japan • Raoul Nigmatullin, Department of Theoretical Physics, Kazan University, 18 Kremlyovskaya St., Kazan 420008, Republic of Tatarstan, Russian Federation • Alain Oustaloup, Equipe CRONE – LAP – ENSERB, Université Bordeaux 1, 351, cours de la Libération, 33405, Talence Cédex, France • Igor Podlubny, Dept. of Informatics and Process Control, BERG Faculty, Technical University of Kosice, B. Nemcovej 3, 04200 Kosice, Slovakia • Jocelyn Sabatier, LAP Université Bordeaux 1, 351, Cours de la Libération, 33405 Talence cedex, France • Nobuyuki Shimizu, Dr. Eng., Iwaki Meisei University, Department of Mechanical Engineering, 5-5-1 Chuodai Iino, Iwaki-shi, 970-8551 Japan • Blas M. Vinagre, Automatic Control Group, Dept. of Electronics and Electromechanical Engineering, Industrial Engineering School, University of Extremadura, Avda. de Elvas, s/n 06071 Badajoz, Spain • Dingyu Xue, Director, Institute of Robotics and Artificial Intelligent, School of Information Science and Engineering, Northeastern Universtiy, Shenyang 110004, China Fractional Order Calculus Day at Utah State University

5. Executive Summary • This proposal outlines a set of objectives to initiate collaboration between the U.S. and the international teams for the advancement of research and education on Fractional Derivatives and Their Applications (FDTAs). The U.S. team consists of 10 researchers from academia, business, and government research labs. The international team consists of 9 members from China, France, India, Japan, Portugal, Spain, and Slovakia. These members are actively involved in the application of fractional derivatives to problems in engineering, science, mathematics, and biomedical and biomechanics. Their biography and curriculum vita, and the rationale for having a large group are given in Supplementary Documents and Project Description sections. Fractional Order Calculus Day at Utah State University

6. Broad research areas to be investigated under this project are 1) Fractional control of engineering systems, 2) Fundamental explorations of the mechanical, electrical, and thermal constitutive relations and other properties of various engineering materials such as viscoelastic polymers, foam, gel, and animal tissues, and their engineering and scientific applications, 3) Advancement of Calculus of Variations and Optimal Control to fractional dynamic systems, 4) Fundamental understanding of wave and diffusion phenomenon, their measurements and verifications, 5) Analytical and numerical tools and techniques, 6) Bioengineering and biomedical applications, 7) Thermal modeling of engineering systems such as brakes and machine tools, 8) Fractional trigonometry and fractional hyperboletry, and 9) Image and signal processing. Details of the objectives are described in the Project Description section. • The education component of the project includes, 1) Development of courseware packages and their integration into existing courses, 2) Training of graduates and undergraduates in the field by involving them in research, 3) Establishment of faculty/student exchange programs to enhance research and international cultural experiences of individuals, 4) Training of research and educational community by organizing tutorials, seminars, workshops, and summer courses, and 5) Dissemination of outcome of research and education components by publishing papers in professional research and education journals, conference proceedings, and on the web. Fractional Order Calculus Day at Utah State University

7. The members will meet once each year to identify research and educational issues, to form partnerships to accomplish a task, and to discuss the outcomes of their efforts. Some topics may be investigated by multiple members/groups to allow diversity in approaches. Although the group will identify the broader topic, an individual will have full autonomy to pursue his/her approach. A website will be developed to allow members to communicate with each other. Agrawal will be in charge of the overall coordination, logistic, and reporting to NSF. • The project will bring about important fundamental theoretical as well as applied discoveries, and many newly trained researchers in the field. It will also bring about new efficient consumer products and new software companies. The rationale for these claims is discussed in the Project Description section. The project will also help the members form a consortium or a federation that will identify the future research issues, set guidelines and standards, and promote research and education in the field. Fractional Order Calculus Day at Utah State University

8. Discussions • Research directions, IP issues, industry interests Fractional Order Calculus Day at Utah State University

9. Porous media • TDR, measuring multiple physical parameters • Dynamic systems identification • Structurally known but parametrically unknown • Moving sensor w/ fixed spatial resolution – on-the-fly, fixed time interval. GPS-fedback. • Input design (excitation signal design) Fractional Order Calculus Day at Utah State University

10. A new viewpoint? • FOC helps to understand the “distributed parameter systems” with “lumped parameter dynamic system” viewpoint? • Modeling purpose dependent • Bottom-up vs. top-down Fractional Order Calculus Day at Utah State University

11. Industry concerns • FOC into a product? Demo first. • “Publish or perish” vs. “sale or fail”. • It takes time to get into a product. Fractional Order Calculus Day at Utah State University