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Volumn 32, Issue 4, 2011, Pages 476-502

An hp-adaptive pseudospectral method for solving optimal control problems

Author keywords

collocation methods; nonlinear optimization; pseudospectral methods

Indexed keywords

COLLOCATION METHOD; COMPUTATIONAL EFFORT; NON-LINEAR OPTIMIZATION; OPTIMAL CONTROL PROBLEM; POLYNOMIAL DEGREE; PSEUDO-SPECTRAL APPROXIMATION; PSEUDOSPECTRAL METHODS;

EID: 79958042822     PISSN: 01432087     EISSN: 10991514     Source Type: Journal    
DOI: 10.1002/oca.957     Document Type: Article
Times cited : (482)

References (44)
  • 2
    • 53349121945 scopus 로고    scopus 로고
    • Trajectory optimization using multiresolution techniques
    • Jain D, Tsiotras P,. Trajectory optimization using multiresolution techniques. Journal of Guidance, Control, and Dynamics 2008; 31 (5): 1424-1436.
    • (2008) Journal of Guidance, Control, and Dynamics , vol.31 , Issue.5 , pp. 1424-1436
    • Jain, D.1    Tsiotras, P.2
  • 3
    • 78649987066 scopus 로고    scopus 로고
    • A density-function based mesh refinement algorithm for solving optimal control problems
    • AIAA Paper 2009-2019, Seattle, Washington, April
    • Zhao Y, Tsiotras P,. A density-function based mesh refinement algorithm for solving optimal control problems. Infotech and Aerospace Conference, AIAA Paper 2009-2019, Seattle, Washington, April 2009.
    • (2009) Infotech and Aerospace Conference
    • Zhao, Y.1    Tsiotras, P.2
  • 4
    • 0031672836 scopus 로고    scopus 로고
    • Mesh refinement in direct transcription methods for optimal control
    • Betts JT, Huffman WP,. Mesh refinement in direct transcription methods for optimal control. Optimal Control Applications and Methods 1998; 19: 1-21. (Pubitemid 128725104)
    • (1998) Optimal Control Applications and Methods , vol.19 , Issue.1 , pp. 1-21
    • Betts, J.T.1    Huffman, W.P.2
  • 5
    • 0023397367 scopus 로고
    • On the optimization of differential-algebraic processes
    • Cuthrell JE, Biegler LT,. On the optimization of differential-algebraic processes. AIChe Journal 1987; 33 (8): 1257-1270.
    • (1987) AIChe Journal , vol.33 , Issue.8 , pp. 1257-1270
    • Cuthrell, J.E.1    Biegler, L.T.2
  • 6
    • 0002296262 scopus 로고
    • Simultaneous optimization and solution methods for batch reactor control profiles
    • Cuthrell JE, Biegler LT,. Simultaneous optimization and solution methods for batch reactor control profiles. Computers and Chemical Engineering 1989; 13 (1/2): 49-62.
    • (1989) Computers and Chemical Engineering , vol.13 , Issue.12 , pp. 49-62
    • Cuthrell, J.E.1    Biegler, L.T.2
  • 7
    • 0029394109 scopus 로고
    • The pseudospectral legendre method for discretizing optimal control problems
    • Elnagar G, Kazemi M, 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.2    Razzaghi, M.3
  • 8
    • 0031146526 scopus 로고    scopus 로고
    • A collocation-type method for linear quadratic optimal control problems
    • Elnagar G, Razzaghi M,. A collocation-type method for linear quadratic optimal control problems. Optimal Control Applications and Methods 1998; 18 (3): 227-235.
    • (1998) Optimal Control Applications and Methods , vol.18 , Issue.3 , pp. 227-235
    • Elnagar, G.1    Razzaghi, M.2
  • 9
    • 26944454165 scopus 로고    scopus 로고
    • Ph.D. Thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA
    • Benson DA,. A Gauss pseudospectral transcription for optimal control. Ph.D. Thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, 2004.
    • (2004) A Gauss Pseudospectral Transcription for Optimal Control
    • Benson, D.A.1
  • 10
    • 33845488897 scopus 로고    scopus 로고
    • Direct trajectory optimization and costate estimation via an orthogonal collocation method
    • DOI 10.2514/1.20478
    • Benson DA, Huntington GT, Thorvaldsen TP, Rao AV,. Direct trajectory optimization and costate estimation via an orthogonal collocation method. Journal of Guidance, Control, and Dynamics 2006; 29 (6): 1435-1440. (Pubitemid 44916718)
    • (2006) Journal of Guidance, Control, and Dynamics , vol.29 , Issue.6 , pp. 1435-1440
    • Benson, D.A.1    Huntington, G.T.2    Thorvaldsen, T.P.3    Rao, A.V.4
  • 14
    • 48349094967 scopus 로고    scopus 로고
    • Convergence rates for direct transcription of optimal control problems using collocation at Radau points
    • Kameswaran S, Biegler LT,. Convergence rates for direct transcription of optimal control problems using collocation at Radau points. Computational Optimization and Applications 2008; 41 (1): 81-126.
    • (2008) Computational Optimization and Applications , vol.41 , Issue.1 , pp. 81-126
    • Kameswaran, S.1    Biegler, L.T.2
  • 15
    • 78049296201 scopus 로고    scopus 로고
    • Direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal control problems via a Radau pseudospectral method
    • Published Online: October 6,. DOI: 10.1007/s10589-009-9291-0. Available from
    • Garg D, Patterson MA, Darby CL, Francolin C, Huntington GT, Hager WW, Rao AV,. Direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal control problems via a Radau pseudospectral method. Computational Optimization and Applications, Published Online: October 6, 2009. DOI: 10.1007/s10589-009-9291-0. Available from:.
    • (2009) Computational Optimization and Applications
    • Garg, D.1    Patterson, M.A.2    Darby, C.L.3    Francolin, C.4    Huntington, G.T.5    Hager, W.W.6    Rao, A.V.7
  • 16
    • 78049252960 scopus 로고    scopus 로고
    • A unified framework for the numerical solution of optimal control problems using pseudospectral methods
    • DOI: 10.1016/j.automatica.2010.06.048
    • Garg D, Patterson MA, Hager WW, Rao AV, Benson DA, Huntington GT,. A unified framework for the numerical solution of optimal control problems using pseudospectral methods. Automatica 2010; DOI: 10.1016/j.automatica.2010.06.048.
    • (2010) Automatica
    • Garg, D.1    Patterson, M.A.2    Hager, W.W.3    Rao, A.V.4    Benson, D.A.5    Huntington, G.T.6
  • 21
    • 0028734274 scopus 로고
    • The p and hpversion of the finite element method, basic principles and properties
    • Babuska I, Suri M,. The p and hpversion of the finite element method, basic principles and properties. SIAM Review 1994; 36: 578-632.
    • (1994) SIAM Review , vol.36 , pp. 578-632
    • Babuska, I.1    Suri, M.2
  • 22
    • 0345257516 scopus 로고
    • The h, p, and hpversions of the finite element method in 1 dimension. Part I. The error analysis of the p version
    • Gui W, Babuska I,. The h, p, and hpversions of the finite element method in 1 dimension. Part I. The error analysis of the p version. Numerische Mathematik 1986; 49: 577-612.
    • (1986) Numerische Mathematik , vol.49 , pp. 577-612
    • Gui, W.1    Babuska, I.2
  • 23
    • 34250122149 scopus 로고
    • The h, p, and hpversions of the finite element method in 1 dimension. Part II. The error analysis of the h and h-p versions
    • Gui W, Babuska I,. The h, p, and hpversions of the finite element method in 1 dimension. Part II. The error analysis of the h and h-p versions. Numerische Mathematik 1986; 49: 613-657.
    • (1986) Numerische Mathematik , vol.49 , pp. 613-657
    • Gui, W.1    Babuska, I.2
  • 24
    • 34250128680 scopus 로고
    • The h, p, and hpversions of the finite element method in 1 dimension. Part III. The adaptive h-p version
    • Gui W, Babuska I,. The h, p, and hpversions of the finite element method in 1 dimension. Part III. The adaptive h-p version. Numerische Mathematik 1986; 49: 659-683.
    • (1986) Numerische Mathematik , vol.49 , pp. 659-683
    • Gui, W.1    Babuska, I.2
  • 25
    • 40949159878 scopus 로고    scopus 로고
    • Hp-Adaptive least squares spectral element method for hyperbolic partial differential equations
    • DOI 10.1016/j.cam.2006.03.063, PII S0377042706007515
    • Galvao A, Gerritsma M, Maerschalk BD,. hp-Adaptive least-squares spectral element method for hyperbolic partial differential equations. Journal of Computational and Applied Mathematics 2008; 215 (2): 409-418. (Pubitemid 351410531)
    • (2008) Journal of Computational and Applied Mathematics , vol.215 , Issue.2 , pp. 409-418
    • Galvao, A.1    Gerritsma, M.2    De Maerschalck, B.3
  • 26
    • 34248338816 scopus 로고    scopus 로고
    • An adaptive least squares scheme for the burgers equation
    • Heinrichs W,. An adaptive least squares scheme for the burgers equation. Numerical Algorithms 2007; 44 (1): 1-10.
    • (2007) Numerical Algorithms , vol.44 , Issue.1 , pp. 1-10
    • Heinrichs, W.1
  • 27
    • 41149150404 scopus 로고    scopus 로고
    • Hp-adaptive least squares spectral element method for population balance equations
    • DOI 10.1016/j.apnum.2006.12.005, PII S0168927407000104
    • Dorao CA, Jakobsen HA,. hp-Adaptive least squares spectral element method for population balance equations. Applied Numerical Mathematics 2008; 58 (5): 563-576. (Pubitemid 351443040)
    • (2008) Applied Numerical Mathematics , vol.58 , Issue.5 , pp. 563-576
    • Dorao, C.A.1    Jakobsen, H.A.2
  • 30
    • 84856712408 scopus 로고    scopus 로고
    • A concept for operationally responsive space mission planning using aeroassisted orbital transfer
    • AIAA Paper RS6-2008-7309, Los Angeles, CA, April
    • Rao AV, Scherich AE, Cox S, Mosher TE,. A concept for operationally responsive space mission planning using aeroassisted orbital transfer. 2008 Responsive Space Conference, AIAA Paper RS6-2008-7309, Los Angeles, CA, April 2008.
    • (2008) 2008 Responsive Space Conference
    • Rao, A.V.1    Scherich, A.E.2    Cox, S.3    Mosher, T.E.4
  • 35
    • 0000967117 scopus 로고
    • On the problem of optimal thrust programming for a soft lunar landing
    • Meditch J,. On the problem of optimal thrust programming for a soft lunar landing. IEEE Transactions on Automatic Control 1964; 9 (4): 477-484.
    • (1964) IEEE Transactions on Automatic Control , vol.9 , Issue.4 , pp. 477-484
    • Meditch, J.1
  • 36
    • 0033116222 scopus 로고    scopus 로고
    • Dichotomic basis approach to solving hyper-sensitive optimal control problems
    • Rao AV, Mease KD,. Dichotomic basis approach to solving hyper-sensitive optimal control problems. Automatica 1999; 35 (4): 633-642.
    • (1999) Automatica , vol.35 , Issue.4 , pp. 633-642
    • Rao, A.V.1    Mease, K.D.2
  • 37
    • 0033632684 scopus 로고    scopus 로고
    • Eigenvector approximate dichotomic basis method for solving hyper-sensitive optimal control problems
    • Rao AV, Mease KD,. Eigenvector approximate dichotomic basis method for solving hyper-sensitive optimal control problems. Optimal Control Applications and Methods 2000; 21 (1): 1-19.
    • (2000) Optimal Control Applications and Methods , vol.21 , Issue.1 , pp. 1-19
    • Rao, A.V.1    Mease, K.D.2
  • 38
    • 0013051531 scopus 로고    scopus 로고
    • Application of a dichotomic basis method to performance optimization of supersonic aircraft
    • Rao AV,. Application of a dichotomic basis method to performance optimization of supersonic aircraft. Journal of Guidance, Control, and Dynamics 2000; 23 (3): 570-573.
    • (2000) Journal of Guidance, Control, and Dynamics , vol.23 , Issue.3 , pp. 570-573
    • Rao, A.V.1
  • 39
    • 0037269602 scopus 로고    scopus 로고
    • Riccati dichotomic basis method for solving hyper-sensitive optimal control problems
    • Rao AV,. Riccati dichotomic basis method for solving hyper-sensitive optimal control problems. Journal of Guidance, Control, and Dynamics 2003; 26 (1): 185-189.
    • (2003) Journal of Guidance, Control, and Dynamics , vol.26 , Issue.1 , pp. 185-189
    • Rao, A.V.1
  • 42
    • 0014604030 scopus 로고
    • Energy-state approximation in performance optimization of supersonic aircraft
    • Bryson AE, Desai MN, Hoffman WC,. Energy-state approximation in performance optimization of supersonic aircraft. AIAA Journal of Aircraft 1969; 6 (6): 481-488.
    • (1969) AIAA Journal of Aircraft , vol.6 , Issue.6 , pp. 481-488
    • Bryson, A.E.1    Desai, M.N.2    Hoffman, W.C.3
  • 43
    • 0029772390 scopus 로고    scopus 로고
    • Finite difference scheme for automatic costate calculation
    • Seywald H, Kumar RR,. Finite difference scheme for automatic costate calculation. Journal of Guidance, Control, and Dynamics 1996; 19 (4): 231-239. (Pubitemid 126535996)
    • (1996) Journal of Guidance, Control, and Dynamics , vol.19 , Issue.1 , pp. 231-239
    • Seywald, H.1    Kumar, R.R.2


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