메뉴 건너뛰기




Volumn 34, Issue 3, 2013, Pages 253-274

Solution of linear optimal control problems with time delay using a composite Chebyshev finite difference method

Author keywords

Chebyshev Gauss Lobatto points; composite Chebyshev finite difference; delay; hybrid functions; optimal control

Indexed keywords

CHEBYSHEV; CHEBYSHEV-GAUSS-LOBATTO POINTS; DELAY; HYBRID FUNCTIONS; OPTIMAL CONTROLS;

EID: 84876283681     PISSN: 01432087     EISSN: 10991514     Source Type: Journal    
DOI: 10.1002/oca.2019     Document Type: Article
Times cited : (23)

References (42)
  • 3
    • 0034187599 scopus 로고    scopus 로고
    • Numerical solution of time-delay optimal control problems by iterative dynamic programming
    • Chen CL, Sun DY, Chang CY,. Numerical solution of time-delay optimal control problems by iterative dynamic programming. Optimal Control Applications and Methods 2000; 21: 91-105.
    • (2000) Optimal Control Applications and Methods , vol.21 , pp. 91-105
    • Chen, C.L.1    Sun, D.Y.2    Chang, C.Y.3
  • 4
    • 0037187982 scopus 로고    scopus 로고
    • Optimal control method with time delay in control
    • Cai G, Huang J,. Optimal control method with time delay in control. Journal of Sound and Vibration 2002; 251: 383-394.
    • (2002) Journal of Sound and Vibration , vol.251 , pp. 383-394
    • Cai, G.1    Huang, J.2
  • 5
    • 0037457761 scopus 로고    scopus 로고
    • Resonances of a non-linear s.d.o.f. system with two time delays in linear feedback control
    • Ji JC, Leung AYT,. Resonances of a non-linear s.d.o.f. system with two time delays in linear feedback control. Journal of Sound and Vibration 2002; 253: 985-1000.
    • (2002) Journal of Sound and Vibration , vol.253 , pp. 985-1000
    • Ji, J.C.1    Leung, A.Y.T.2
  • 7
    • 31344436881 scopus 로고    scopus 로고
    • A less conservative robust stability test for linear uncertain time-delay systems
    • Lin C, Wang QG, Lee TH,. A less conservative robust stability test for linear uncertain time-delay systems. IEEE Transactions on Automatic Control 2006; 51 (1): 87-91.
    • (2006) IEEE Transactions on Automatic Control , vol.51 , Issue.1 , pp. 87-91
    • Lin, C.1    Wang, Q.G.2    Lee, T.H.3
  • 8
    • 55749104718 scopus 로고    scopus 로고
    • A survey of linear matrix inequality techniques in stability analysis of delay systems
    • Xu S, Lam J,. A survey of linear matrix inequality techniques in stability analysis of delay systems. International Journal of Systems Science 2008; 39 (12): 1095-1113.
    • (2008) International Journal of Systems Science , vol.39 , Issue.12 , pp. 1095-1113
    • Xu, S.1    Lam, J.2
  • 9
    • 44649190536 scopus 로고    scopus 로고
    • Further results on adaptive robust control of uncertain time-delay systems
    • Xu S, Feng G,. Further results on adaptive robust control of uncertain time-delay systems. IET Control Theory and Applications 2008; 2 (5): 402-408.
    • (2008) IET Control Theory and Applications , vol.2 , Issue.5 , pp. 402-408
    • Xu, S.1    Feng, G.2
  • 10
    • 70350273381 scopus 로고    scopus 로고
    • Guaranteed cost control for uncertain neutral stochastic systems via dynamic output feedback controllers
    • Xu S, Lam J, Shi P, Boukas EK, Zou Y,. Guaranteed cost control for uncertain neutral stochastic systems via dynamic output feedback controllers. Journal of Optimization Theory and Applications 2009; 143: 207-223.
    • (2009) Journal of Optimization Theory and Applications , vol.143 , pp. 207-223
    • Xu, S.1    Lam, J.2    Shi, P.3    Boukas, E.K.4    Zou, Y.5
  • 11
    • 77953248580 scopus 로고    scopus 로고
    • Predictive control for a class of distributed delay systems using Chebyshev polynomials
    • Mahboobi Esfanjani R, Nikravesh SKY,. Predictive control for a class of distributed delay systems using Chebyshev polynomials. International Journal of Computer Mathematics 2010; 87 (7): 1591-1602.
    • (2010) International Journal of Computer Mathematics , vol.87 , Issue.7 , pp. 1591-1602
    • Mahboobi Esfanjani, R.1    Nikravesh, S.K.Y.2
  • 12
    • 0038992398 scopus 로고
    • The maximum principle in the theory of optimal process with time-lags
    • Kharatishvili GL,. The maximum principle in the theory of optimal process with time-lags. Doklady Akademii Nauk SSSR 1961; 136: 39-42.
    • (1961) Doklady Akademii Nauk SSSR , vol.136 , pp. 39-42
    • Kharatishvili, G.L.1
  • 15
    • 0020877912 scopus 로고
    • Solution and parameter estimation of linear time-invariant delay systems using Laguerre polynomial expansion
    • Kung FC, Lee H,. Solution and parameter estimation of linear time-invariant delay systems using Laguerre polynomial expansion. Journal of Dynamic Systems, Measurement, and Control 1983; 105: 297-301.
    • (1983) Journal of Dynamic Systems, Measurement, and Control , vol.105 , pp. 297-301
    • Kung, F.C.1    Lee, H.2
  • 16
    • 0022146627 scopus 로고
    • Shifted Legendre series solution and parameter estimation of linear delayed systems
    • Lee H, Kung FC,. Shifted Legendre series solution and parameter estimation of linear delayed systems. International Journal of Systems Science 1985; 16: 1249-1256.
    • (1985) International Journal of Systems Science , vol.16 , pp. 1249-1256
    • Lee, H.1    Kung, F.C.2
  • 17
    • 0022059118 scopus 로고
    • Analysis, parameter estimation and optimal control of time-delay systems via Chebyshev series
    • Horng IR, Chou JH,. Analysis, parameter estimation and optimal control of time-delay systems via Chebyshev series. International Journal of Control 1985; 41: 1221-1234.
    • (1985) International Journal of Control , vol.41 , pp. 1221-1234
    • Horng, I.R.1    Chou, J.H.2
  • 19
    • 0029394109 scopus 로고
    • The pseudospectral Legendre method for discretizing optimal control problems
    • Elnagar G, Kazemi MA, Razzaghi M,. The pseudospectral Legendre method for discretizing optimal control problems. IEEE Transactions on Automatic Control 1995; 40 (10): 1793-1796.
    • (1995) IEEE Transactions on Automatic Control , vol.40 , Issue.10 , pp. 1793-1796
    • Elnagar, G.1    Kazemi, M.A.2    Razzaghi, M.3
  • 20
    • 0032473255 scopus 로고    scopus 로고
    • Pseudospectral Legendre-based optimal computation of nonlinear constrained variational problems
    • Elnagar GN, Kazemi MA,. Pseudospectral Legendre-based optimal computation of nonlinear constrained variational problems. Journal of Computational and Applied Mathematics 1997; 88: 363-375.
    • (1997) Journal of Computational and Applied Mathematics , vol.88 , pp. 363-375
    • Elnagar, G.N.1    Kazemi, M.A.2
  • 21
    • 0036154549 scopus 로고    scopus 로고
    • Direct trajectory optimization by a Chebyshev pseudospectral method
    • Fahroo F, Ross IM,. Direct trajectory optimization by a Chebyshev pseudospectral method. Journal of Guidance, Control, and Dynamics 2002; 25: 160-166.
    • (2002) Journal of Guidance, Control, and Dynamics , vol.25 , pp. 160-166
    • Fahroo, F.1    Ross, I.M.2
  • 22
    • 4344637586 scopus 로고    scopus 로고
    • Pseudospectral methods for optimal motion planning of differentially flat systems
    • Ross IM, Fahroo F,. Pseudospectral methods for optimal motion planning of differentially flat systems. IEEE Transactions on Automatic Control 2004; 49: 1410-1413.
    • (2004) IEEE Transactions on Automatic Control , vol.49 , pp. 1410-1413
    • Ross, I.M.1    Fahroo, F.2
  • 24
    • 33746056457 scopus 로고    scopus 로고
    • A pseudospectral method for the optimal control of constrained feedback linearizable systems
    • Gong Q, Kang W, Ross IM,. A pseudospectral method for the optimal control of constrained feedback linearizable systems. IEEE Transactions on Automatic Control 2006; 51 (7): 1115-1129.
    • (2006) IEEE Transactions on Automatic Control , vol.51 , Issue.7 , pp. 1115-1129
    • Gong, Q.1    Kang, W.2    Ross, I.M.3
  • 25
    • 42949106980 scopus 로고    scopus 로고
    • The Chebyshev-Legendre collocation method for a class of optimal control problems
    • Zhang W, Ma H,. The Chebyshev-Legendre collocation method for a class of optimal control problems. International Journal of Computer Mathematics 2008; 85 (2): 225-240.
    • (2008) International Journal of Computer Mathematics , vol.85 , Issue.2 , pp. 225-240
    • Zhang, W.1    Ma, H.2
  • 26
    • 65349145908 scopus 로고    scopus 로고
    • The Chebyshev-Legendre method for discretizing optimal control problems
    • Zhang W, Ma H., The Chebyshev-Legendre method for discretizing optimal control problems. Journal of Shanghai University (English Edition) 2009; 13 (2): 113-118.
    • (2009) Journal of Shanghai University (English Edition) , vol.13 , Issue.2 , pp. 113-118
    • Zhang, W.1    Ma, H.2
  • 27
    • 79952610615 scopus 로고    scopus 로고
    • A numerical method for solving nonsmooth optimal control problems (in Chinese)
    • Zhang W,. A numerical method for solving nonsmooth optimal control problems (in Chinese). Applied Mathematics-A Journal of Chinese Universities (A Series) 2009; 24 (2): 207-220.
    • (2009) Applied Mathematics - A Journal of Chinese Universities (A Series) , vol.24 , Issue.2 , pp. 207-220
    • Zhang, W.1
  • 28
    • 79952595340 scopus 로고    scopus 로고
    • An efficient Chebyshev algorithm for the solution of optimal control problems
    • Ma H, Qin T, Zhang W,. An efficient Chebyshev algorithm for the solution of optimal control problems. IEEE Transactions on Automatic Control 2011; 56 (3): 675-680.
    • (2011) IEEE Transactions on Automatic Control , vol.56 , Issue.3 , pp. 675-680
    • Ma, H.1    Qin, T.2    Zhang, W.3
  • 29
    • 0012496848 scopus 로고    scopus 로고
    • Direct method for variational problems via hybrid of block-pulse and Chebyshev functions
    • Razzaghi M, Marzban HR,. Direct method for variational problems via hybrid of block-pulse and Chebyshev functions. Mathematical Problems in Engineering 2000; 6: 85-97.
    • (2000) Mathematical Problems in Engineering , vol.6 , pp. 85-97
    • Razzaghi, M.1    Marzban, H.R.2
  • 30
    • 0345854818 scopus 로고    scopus 로고
    • A hybrid domain analysis for systems with delays in state and control
    • Razzaghi M, Marzban HR,. A hybrid domain analysis for systems with delays in state and control. Mathematical Problems in Engineering 2001; 7: 337-353.
    • (2001) Mathematical Problems in Engineering , vol.7 , pp. 337-353
    • Razzaghi, M.1    Marzban, H.R.2
  • 33
    • 1842502575 scopus 로고    scopus 로고
    • Optimal control of linear delay systems via hybrid of block-pulse and Legendre polynomials
    • Marzban HR, Razzaghi M,. Optimal control of linear delay systems via hybrid of block-pulse and Legendre polynomials. Journal of the Franklin Institute 2004; 341 (3): 279-293.
    • (2004) Journal of the Franklin Institute , vol.341 , Issue.3 , pp. 279-293
    • Marzban, H.R.1    Razzaghi, M.2
  • 34
    • 29144499130 scopus 로고    scopus 로고
    • Analysis of time delay systems via hybrid of block-pulse functions and Taylor series
    • Marzban HR, Razzaghi M,. Analysis of time delay systems via hybrid of block-pulse functions and Taylor series. Journal of Vibration and Control 2005; 11: 1455-1468.
    • (2005) Journal of Vibration and Control , vol.11 , pp. 1455-1468
    • Marzban, H.R.1    Razzaghi, M.2
  • 35
    • 33644589006 scopus 로고    scopus 로고
    • Solution of multi-delay systems using hybrid of block-pulse functions and Taylor series
    • Marzban HR, Razzaghi M,. Solution of multi-delay systems using hybrid of block-pulse functions and Taylor series. Journal of Sound and Vibration 2006; 292: 954-963.
    • (2006) Journal of Sound and Vibration , vol.292 , pp. 954-963
    • Marzban, H.R.1    Razzaghi, M.2
  • 39
    • 0000624238 scopus 로고
    • A method for numerical integration on an automatic computer
    • Clenshaw CW, Curtis AR,. A method for numerical integration on an automatic computer. Numerische Mathematik 1960; 2: 197-205.
    • (1960) Numerische Mathematik , vol.2 , pp. 197-205
    • Clenshaw, C.W.1    Curtis, A.R.2
  • 40
    • 0037448159 scopus 로고    scopus 로고
    • Chebyshev finite difference approximation for the boundary value problems
    • Elbarbary EME,. Chebyshev finite difference approximation for the boundary value problems. Applied Mathematics and Computation 2003; 139: 513-523.
    • (2003) Applied Mathematics and Computation , vol.139 , pp. 513-523
    • Elbarbary, E.M.E.1
  • 41
    • 0017943998 scopus 로고
    • Hereditary control problems: Numerical methods based on averaging approximations
    • Banks HT, Burns JA,. Hereditary control problems: numerical methods based on averaging approximations. SIAM Journal of Control and Optimization 1978; 16 (2): 169-208.
    • (1978) SIAM Journal of Control and Optimization , vol.16 , Issue.2 , pp. 169-208
    • Banks, H.T.1    Burns, J.A.2
  • 42
    • 0020844889 scopus 로고
    • Optimal control of linear systems with delays in state and control via Walsh functions
    • Palanisamy KR, Rao GP,. Optimal control of linear systems with delays in state and control via Walsh functions. IEEE Proceedings 1983; 130 (6): 300-312.
    • (1983) IEEE Proceedings , vol.130 , Issue.6 , pp. 300-312
    • Palanisamy, K.R.1    Rao, G.P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.