Modified optimal energy and initial memory of fractional continuous-time linear systems

Signal Processing

Volumn 91, Issue 3, 2011, Pages 379-385

  Mozyrska, Dorota ^a   Torres, Delfim F M ^b  

^a BIALYSTOK UNIVERSITY OF TECHNOLOGY   (Poland)

^b UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

Fractional derivatives; Initial memory; Memory states; Minimality

Indexed keywords

CONTINUOUS-TIME LINEAR SYSTEMS; FRACTIONAL DERIVATIVES; FRACTIONAL INTEGRALS; FRACTIONAL SYSTEMS; GRAMIANS; INITIAL MEMORY; MEMORY STATE; MINIMALITY; OPTIMAL ENERGY; STATE VARIABLES; STEERING FUNCTIONS; STEERING LAW; VALUE PROBLEMS;

LINEAR SYSTEMS;

CONTINUOUS TIME SYSTEMS;

EID: 78049334398     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2010.07.016     Document Type: Article

References (34)

1. R.L. Bagley, and R.A. Calico Fractional order state equations for the control of viscoelastics structures J. Guidance Control Dyn. 14 2 1991 304 311
2. M. Benchora, S. Hamani, and S.K. Ntouyas Boundary value problems for differential equations with fractional order Surv. Math. Appl. 3 2008 1 12
3. M. Bettayeb, S. Djennoune, A note on the controllability and the observability of fractional dynamical systems, in: Proceedings of the 2nd IFAC Workshop on Fractional Differentiation and its Applications, Porto, Portugal, July 1921, 2006.
4. L. Debnath Integral Transforms and their Applications 1995 CRC Press Florida
5. A. Erdlyi (Ed.), Higher Transcendental Functions, vol. 1, McGraw-Hill, New York, 1955.
6. T.T. Hartley, C.F. Lorenzo, A solution to the fundamental linear fractional order differential equation, NASA/TP-1998-208693, 1998.
7. T.T. Hartley, C.F. Lorenzo, Fractional system identification: an approach using continuous order distributions, NASA/TM-1999-209640, 1999.
8. T.T. Hartley, C.F. Lorenzo, Control of initialized fractional-order systems, NASA/TM-2002-211377, 2002.
9. T.T. Hartley, and C.F. Lorenzo Dynamics and control of initialized fractional-order systems Nonlinear Dyn. 29 2002 201 233
10. N. Heymans, and I. Podlubny Physical interpretation of initial conditions for fractional differential equations with RiemannLiouville fractional derivatives Rheol. Acta 37 2005 1 7
11. R. Hilfer (Ed.), Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
12. T. Kaczorek Fractional positive continuous-time linear systems and their reachability Int. J. Appl. Math. Comput. Sci. 18 2 2008 223 228
13. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V., Amsterdam, 2006.
14. C.F. Lorenzo, T.T. Hartley, Initialization, conceptualization, and application in the generalized (fractional) calculus, NASA TP-1998-208415, 1998.
15. C.F. Lorenzo, and T.T. Hartley Initialised fractional calculus Int. J. Appl. Math. 3 3 2000 249 265
16. C.F. Lorenzo, and T.T. Hartley Initialization of fractional-order operators and fractional differential equations J. Comput. Nonlinear Dyn. 3 2 2008 9 art. no. 021101
17. C.F. Lorenzo, T.T. Hartley, Initialization of fractional differential equations: background and theory, in: 2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007 5 PART B, 2008, pp. 13251333.
18. K.S. Miller, and B. Ross An Introduction to the Fractional Calculus and Fractional Differential Equations 1993 Wiley New York
19. D. Mozyrska, and D.F.M. Torres Minimal modified energy control for fractional linear control systems with the Caputo derivative Carpathian J. Math. 26 2 2010
20. K. Nishimoto Fractional Calculus 1984 Decartes Press Koriyama
21. K.B. Oldham, and J. Spanier The Fractional Calculus 1974 Academic Press New York
22. M.D. Ortigueira On the initial conditions in continuous-time fractional linear systems Signal Processing 83 11 2003 2301 2309
23. M.D. Ortigueira A coherent approach to non-integer order derivatives Signal Processing 86 10 2008 2505 2515
24. M.D. Ortigueira, and F.J. Coito System initial conditions vs derivative initial conditions Comput. Math. Appl. 59 5 2010 1782 1789
25. A. Oustaloup La drivation non entire 1995 Herms Paris
26. I. Podlubny, Fractional Differential Equations, Mathematics in Sciences and Engineering, vol. 198, Academic Press, San Diego, 1999.
27. J. Sabatier, O. Agrawal, and J. Tenreiro Machado Advances in Fractional Calculus: Theoretical Developments and Application in Physics and Engineering 2007 Springer Berlin
28. J. Sabatier, M. Merveillaut, R. Malti, and A. Oustaloup How to impose physically coherent initial conditions to a fractional system? Common Nonlinear Sci. Numer. Simulat. 15 2010 1318 1326
29. S.G. Samko, A.A. Kilbas, and O.I. Marichev Fractional Integrals and Derivatives: Theory and Applications 1993 Gordon and Breach Science Publishers S.A. Yverdon
30. E. Scalas Applications of continuous-time random walks in finance and economics Physica A 362 2 2006 225 239 (Pubitemid 43234049)
31. D. Sierociuk, and D. Dzieliski Fractional Kalman filter algorithm for the states parameters and order of fractional system estimation Int. J. Appl. Math. Comput. Sci. 16 1 2006 129 140
32. M. Vinagre, V. Feliu, Modeling and control of dynamic systems using fractional calculus: application to electrochemical processes and flexible structures, in: Proceedings of the 41st Conference Decision and Control, Las Vegas, NV, USA, 2002, pp. 214239.
33. M. Vinagre, C.A. Monje, A.J. Calderon, Fractional order systems and fractional order control actions, in: 3 IEEE CDC'02 TW#2: Fractional Calculus Applications in Automatic Control and Robotics, 2002.
34. J. Zabczyk Mathematical Control Theory, an Introduction 1995 Birkhuser Boston