메뉴 건너뛰기




Volumn 17, Issue 7, 2011, Pages 1034-1041

Fractional optimal control problems: A pseudo-state-space approach

Author keywords

Fractional order system; Optimal control; Riemann Liouville fractional derivatives; State space

Indexed keywords

CONTROL VARIABLE; DYNAMIC CONSTRAINTS; DYNAMICAL EQUATION; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL ORDER; FRACTIONAL-ORDER SYSTEMS; METHODOLOGY AND TECHNIQUES; NUMERICAL EXAMPLE; NUMERICAL TECHNIQUES; OPTIMAL CONTROL PROBLEM; OPTIMAL CONTROLS; PERFORMANCE INDICES; RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES; STATE-SPACE;

EID: 80052623902     PISSN: 10775463     EISSN: 17412986     Source Type: Journal    
DOI: 10.1177/1077546310373618     Document Type: Article
Times cited : (56)

References (39)
  • 1
    • 0036701004 scopus 로고    scopus 로고
    • Formulation of Euler-Lagrange equations for fractional variational problems
    • Agrawal OP (2002) Formulation of Euler-Lagrange equations for fractional variational problems. Mathematical Analysis and Applications 272: 368-379.
    • (2002) Mathematical Analysis and Applications , vol.272 , pp. 368-379
    • Agrawal, O.P.1
  • 2
    • 15544379439 scopus 로고    scopus 로고
    • A general formulation and solution scheme for fractional optimal control problems
    • DOI 10.1007/s11071-004-3764-6
    • Agrawal OP (2004) A general formulation and solution scheme for fractional optimal control problems. Nonlinear Dynamics 38: 323-337. (Pubitemid 40400624)
    • (2004) Nonlinear Dynamics , vol.38 , Issue.1-4 , pp. 323-337
    • Agrawal, O.P.1
  • 3
    • 34748901185 scopus 로고    scopus 로고
    • A hamiltonian formulation and a direct numerical scheme for fractional optimal control problems
    • DOI 10.1177/1077546307077467
    • Agrawal OP (2007) A Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems. Journal of Vibration and Control 13: 1269-1281. (Pubitemid 47482812)
    • (2007) JVC/Journal of Vibration and Control , vol.13 , Issue.9-10 , pp. 1269-1281
    • Agrawal, O.P.1    Baleanu, D.2
  • 5
    • 0026124343 scopus 로고
    • Fractional order state equations for the control of viscoelastic structures
    • Bagley RL and Calico RA (1991) Fractional order state equations for the control of viscoelastic structures. Journal of Guidance, Control, and Dynamics 14(2): 304-311.
    • (1991) Journal of Guidance, Control, and Dynamics , vol.14 , Issue.2 , pp. 304-311
    • Bagley, R.L.1    Calico, R.A.2
  • 7
    • 4043139312 scopus 로고    scopus 로고
    • Lagrangians with linear velocities within Riemann-Liouville fractional derivatives
    • Baleanu D and Avkar T (2004) Lagrangians with linear velocities within Riemann-Liouville fractional derivatives. Nuovo Cimento Della Societa Italiana Di Fisica B -General Physics Relativity Astronomy and Mathematical Physics and Methods 119: 73-79. (Pubitemid 39057448)
    • (2004) Nuovo Cimento della Societa Italiana di Fisica B , vol.119 , Issue.1 , pp. 73-79
    • Baleanu, D.1    Avkar, T.2
  • 8
    • 62849085116 scopus 로고    scopus 로고
    • A central difference numerical scheme for fractional optimal control problems
    • Baleanu D, Defterli O and Agrawal OP (2009) A central difference numerical scheme for fractional optimal control problems. Journal of Vibration and Control 15: 583-597.
    • (2009) Journal of Vibration and Control , vol.15 , pp. 583-597
    • Baleanu, D.1    Defterli, O.2    Agrawal, O.P.3
  • 9
    • 82155162739 scopus 로고    scopus 로고
    • Numerical method for solving fractional optimal control problems
    • 30 August-2 September, California: San Diego, CA, ASME Paper No. DETC 2009-87008
    • Biswas RK and Sen S (2009) Numerical method for solving fractional optimal control problems, in Proceedings of the IDETC/CIE 2009, 30 August-2 September, California: San Diego, CA, ASME Paper No. DETC 2009-87008.
    • (2009) Proceedings of the IDETC/CIE 2009
    • Biswas, R.K.1    Sen, S.2
  • 14
    • 34147203638 scopus 로고
    • Relaxation and retardation functions of the Maxwell Model with fractional derivatives
    • Friedrich CH (1991) Relaxation and retardation functions of the Maxwell Model with fractional derivatives. Rheologica Acta 30: 151-158.
    • (1991) Rheologica Acta , vol.30 , pp. 151-158
    • Friedrich, C.H.1
  • 15
    • 0036650827 scopus 로고    scopus 로고
    • Dynamics and control of initialized fractional-order systems
    • DOI 10.1023/A:1016534921583, Fractional Order Calculus and Its Applications
    • Hartley TT and Lorenzo CF (2002) Dynamics and control of initialized fractional-order systems. Nonlinear Dynamics 29: 201-233. (Pubitemid 34945399)
    • (2002) Nonlinear Dynamics , vol.29 , Issue.1-4 , pp. 201-233
    • Hartley, T.T.1    Lorenzo, C.F.2
  • 16
    • 15544366107 scopus 로고    scopus 로고
    • A frequency-domain approach to optimal fractional-order damping
    • DOI 10.1007/s11071-004-3747-7
    • Hartley TT and Lorenzo CF (2004) A frequency domain approach to optimal fractional order damping. Nonlinear Dynamics 38: 69-84. (Pubitemid 40400608)
    • (2004) Nonlinear Dynamics , vol.38 , Issue.1-4 , pp. 69-84
    • Hartley, T.T.1    Lorenzo, C.F.2
  • 17
    • 70349224466 scopus 로고    scopus 로고
    • Fractional-order Euler-Lagrange equations and formulation of Hamiltonian equations
    • Herzallah MAE and Baleanu D (2009) Fractional-order Euler-Lagrange equations and formulation of Hamiltonian equations. Nonlinear Dynamics 58(1-2): 385-391.
    • (2009) Nonlinear Dynamics , vol.58 , Issue.1-2 , pp. 385-391
    • Mae, H.1    Baleanu, D.2
  • 19
    • 0037047631 scopus 로고    scopus 로고
    • Stationarity-conservation laws for fractional differential equations with variable coefficients
    • DOI 10.1088/0305-4470/35/31/311, PII S0305447002353848
    • Klimek M (2002) Stationary conservation laws for fractional differential equations with variable coefficients. Journal of Physics A: Mathematical and General 35: 6675-6693. (Pubitemid 37049354)
    • (2002) Journal of Physics A: Mathematical and General , vol.35 , Issue.31 , pp. 6675-6693
    • Klimek, M.1
  • 20
    • 47249142051 scopus 로고    scopus 로고
    • Formulation of a state equation including fractional-order state vectors
    • Kuroda M (2008) Formulation of a state equation including fractional-order state vectors. Journal of Computational and Nonlinear Dynamics 3(2): 21202.
    • (2008) Journal of Computational and Nonlinear Dynamics , vol.3 , Issue.2 , pp. 21202
    • Kuroda, M.1
  • 22
    • 3042776917 scopus 로고    scopus 로고
    • Fractional calculus in bioengineering, Parts 1-3
    • Magin RL (2004) Fractional calculus in bioengineering, Parts 1-3. Critical Reviews of Biomedical Engineering 32(1): 1-377.
    • (2004) Critical Reviews of Biomedical Engineering , vol.32 , Issue.1 , pp. 1-377
    • Magin, R.L.1
  • 25
    • 14844283120 scopus 로고    scopus 로고
    • Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives
    • DOI 10.1016/j.jmaa.2004.09.043, PII S0022247X04008005
    • Muslih SI and Baleanu D (2005a) Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives. Journal of Mathematical Analysis and Applications 304: 599-606. (Pubitemid 40350289)
    • (2005) Journal of Mathematical Analysis and Applications , vol.304 , Issue.2 , pp. 599-606
    • Muslih, S.I.1    Baleanu, D.2
  • 26
    • 21644464298 scopus 로고    scopus 로고
    • Formulation of Hamiltonian equations for fractional variational problems
    • DOI 10.1007/s10582-005-0067-1
    • Muslih SI and Baleanu D (2005b) Formulation of Hamiltonian equations for fractional variational problems. Czechoslovak Journal of Physics 55: 633-642. (Pubitemid 40937431)
    • (2005) Czechoslovak Journal of Physics , vol.55 , Issue.6 , pp. 633-642
    • Muslih, S.I.1    Baleanu, D.2
  • 29
    • 0031118929 scopus 로고    scopus 로고
    • Diophantine type fractional derivative representation of structural hysteresis Part I: Formulation
    • Padovan J and Sawicki JT (1997) Diophantine type fractional derivative representation of structural dynamics. Computational Mechanics 19(5): 335-340. (Pubitemid 127565985)
    • (1997) Computational Mechanics , vol.19 , Issue.5 , pp. 335-340
    • Padovan, J.1    Sawicki, J.T.2
  • 32
    • 0343715573 scopus 로고    scopus 로고
    • State space representation for fractional order controllers
    • Raynaud H-F and Zerganoh A (2000) State space representation for fractional order controllers. Automatica 36(7): 1017-1021.
    • (2000) Automatica , vol.36 , Issue.7 , pp. 1017-1021
    • Raynaud, H.-F.1    Zerganoh, A.2
  • 34
    • 4243530410 scopus 로고    scopus 로고
    • Mechanics with fractional derivatives
    • Riewe F (1997) Mechanics with fractional derivatives. Physical Review E 55: 3582-3592.
    • (1997) Physical Review e , vol.55 , pp. 3582-3592
    • Riewe, F.1
  • 35
    • 0030867045 scopus 로고    scopus 로고
    • Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids
    • Rossikhin YA and Shitikova MV (1997) Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids. Applied Mechanics Review 50: 15-67. (Pubitemid 127645586)
    • (1997) Applied Mechanics Reviews , vol.50 , Issue.1 , pp. 15-67
    • Rossikhin, Y.A.1    Shitikova, M.V.2
  • 37
    • 19944384253 scopus 로고    scopus 로고
    • Fractional Ginzburg-Landau equation for fractal media
    • DOI 10.1016/j.physa.2005.02.047, PII S0378437105002293
    • Tarasov VE and Zaslavsky GM (2005) Fractional Ginzburg- Landau equation for fractal media. Physica A-Statistical Mechanics and Its Applications 354: 249-261. (Pubitemid 40752473)
    • (2005) Physica A: Statistical Mechanics and its Applications , vol.354 , Issue.1-4 , pp. 249-261
    • Tarasov, V.E.1    Zaslavsky, G.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.