메뉴 건너뛰기




Volumn 30, Issue 6, 1997, Pages 3843-3854

Numerical methods of nonlinear optimal control based on mathematical programming

Author keywords

Convex quadratic programming; Inexact Newton method; Infinite programming; Interior point method; Nonlinear programming; Optimal control; Quasi Newton method; Sequential quadratic programming

Indexed keywords


EID: 0043046995     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00327-6     Document Type: Article
Times cited : (1)

References (32)
  • 2
    • 0041499459 scopus 로고
    • Function-space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs
    • EDGE E. R. & POWERS W, F., Function-space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs, J. Optim. Theory Appl. 20, 455-479 (1976).
    • (1976) J. Optim. Theory Appl. , vol.20 , pp. 455-479
    • Edge, E.R.1    Powers, W.F.2
  • 4
    • 0042501265 scopus 로고
    • Dual variable metric algorithms for constrained optimization
    • HAN S. P., Dual variable metric algorithms for constrained optimization, SIAM J. Contr. Optim. 15, 546-565 (1977).
    • (1977) SIAM J. Contr. Optim. , vol.15 , pp. 546-565
    • Han, S.P.1
  • 6
    • 0025551667 scopus 로고
    • A solution of optimal control problems with terminal state equality constraints by quasi-Newton method
    • ITO S. & SHIMIZU K., A solution of optimal control problems with terminal state equality constraints by quasi-Newton method, Proc. 29th SICE Annual Conf. 2, 717-720 (1990).
    • (1990) Proc. 29th SICE Annual Conf. , vol.2 , pp. 717-720
    • Ito, S.1    Shimizu, K.2
  • 7
    • 0042182675 scopus 로고
    • Dual quasi-Newton algorithms for infinitely constrained optimization problems
    • ITO S. & SHIMIZU K., Dual quasi-Newton algorithms for infinitely constrained optimization problems (in Japanese). Trans. Soc. Instr. Contr. Engineers 27, 452-457 (1991).
    • (1991) Trans. Soc. Instr. Contr. Engineers , vol.27 , pp. 452-457
    • Ito, S.1    Shimizu, K.2
  • 8
    • 0000356344 scopus 로고
    • Inexact primal-dual interior point iteration for linear programs in function spaces
    • ITO S., KELLEY C. T. & SACHS E. W., Inexact primal-dual interior point iteration for linear programs in function spaces, Comp. Optim. Appl. 4, 189-202 (1995).
    • (1995) Comp. Optim. Appl. , vol.4 , pp. 189-202
    • Ito, S.1    Kelley, C.T.2    Sachs, E.W.3
  • 9
    • 0014585155 scopus 로고
    • A transformation technique for optimal control problems with a state variable inequality constraint
    • JACOBSON D. H. & LELE M. M., A transformation technique for optimal control problems with a state variable inequality constraint, IEEE Trans. Autom. Contr. AC-14, 457-464 (1969).
    • (1969) IEEE Trans. Autom. Contr. , vol.AC-14 , pp. 457-464
    • Jacobson, D.H.1    Lele, M.M.2
  • 10
    • 0023451450 scopus 로고
    • Quasi-Newton methods and unconstrained optimal control problems
    • KELLEY C. T. & SACHS E. W., Quasi-Newton methods and unconstrained optimal control problems, SIAM J. Contr. Optim. 25, 1503-1516 (1987).
    • (1987) SIAM J. Contr. Optim. , vol.25 , pp. 1503-1516
    • Kelley, C.T.1    Sachs, E.W.2
  • 12
    • 0014766408 scopus 로고
    • Conjugate direction methods for optimal control
    • LASDON L. S., Conjugate direction methods for optimal control, IEEE Trans. Autom. Contr. AC-15, 267-268 (1970).
    • (1970) IEEE Trans. Autom. Contr. , vol.AC-15 , pp. 267-268
    • Lasdon, L.S.1
  • 13
    • 0000940045 scopus 로고
    • Numerical solution of parabolic state constrained control problems using SQP- and interior-point-methods
    • Edited by W. W. HAGER, D. W. HEARN and P. M. PARDALOS Kluwer, Dordrecht
    • LEIBFRITZ F. & SACHS E. W., Numerical solution of parabolic state constrained control problems using SQP- and interior-point-methods, in Large Scale Optimization: State of the Art (Edited by W. W. HAGER, D. W. HEARN and P. M. PARDALOS), pp. 251-264, Kluwer, Dordrecht (1994).
    • (1994) Large Scale Optimization: State of the Art , pp. 251-264
    • Leibfritz, F.1    Sachs, E.W.2
  • 15
    • 0019040724 scopus 로고
    • A family of variable metric methods in function space, without exact line searches
    • MAYORGA R. V. & QUINTANA V. H., A family of variable metric methods in function space, without exact line searches, J. Optim. Theory Appl. 31, 303-329 (1980).
    • (1980) J. Optim. Theory Appl. , vol.31 , pp. 303-329
    • Mayorga, R.V.1    Quintana, V.H.2
  • 17
    • 0024665752 scopus 로고
    • Interior path following primal dual algorithms
    • MONTEIRO R. D. C. & ADLER I., Interior path following primal dual algorithms, Math. Prog. 44, 27-66 (1989).
    • (1989) Math. Prog. , vol.44 , pp. 27-66
    • Monteiro, R.D.C.1    Adler, I.2
  • 18
    • 0005413161 scopus 로고
    • The conjugate gradient method for optimal control problems with bounded control variables
    • PAGUREK B. & WOODSIDE C. M., The conjugate gradient method for optimal control problems with bounded control variables, Automatica 4, 337-349 (1968).
    • (1968) Automatica , vol.4 , pp. 337-349
    • Pagurek, B.1    Woodside, C.M.2
  • 19
    • 0014821831 scopus 로고
    • Computational experience with the Davidon method applied to optimal control problems
    • PIERSON B. L. & RAJTORA S. G., Computational experience with the Davidon method applied to optimal control problems, IEEE Trans. Sys. Sci. Cybern. SSC-6, 240-242 (1970).
    • (1970) IEEE Trans. Sys. Sci. Cybern. , vol.SSC-6 , pp. 240-242
    • Pierson, B.L.1    Rajtora, S.G.2
  • 20
    • 0016092681 scopus 로고
    • Clipping-off gradient algorithms to compute optimal controls with constrained magnitude
    • QUINTANA V. H. & DAVISON E. J., Clipping-off gradient algorithms to compute optimal controls with constrained magnitude, Int. J. Contr. 20, 243-255 (1974).
    • (1974) Int. J. Contr. , vol.20 , pp. 243-255
    • Quintana, V.H.1    Davison, E.J.2
  • 21
    • 0022718875 scopus 로고
    • Broyden's method in Hilbert space
    • SACHS E. W., Broyden's method in Hilbert space, Math. Prog. 35, 71-82 (1986).
    • (1986) Math. Prog. , vol.35 , pp. 71-82
    • Sachs, E.W.1
  • 22
    • 0022734381 scopus 로고
    • Constrained optimization methods in Hilbert spaces and their applications to optimal control problems with functional inequality constraints
    • SHIMIZU K., FUJIMAKI S. & ISHIZUKA Y., Constrained optimization methods in Hilbert spaces and their applications to optimal control problems with functional inequality constraints, IEEE Trans. Autom. Contr. AC-31, 559-564 (1986).
    • (1986) IEEE Trans. Autom. Contr. , vol.AC-31 , pp. 559-564
    • Shimizu, K.1    Fujimaki, S.2    Ishizuka, Y.3
  • 23
    • 0026403162 scopus 로고
    • Constrained optimization in Banach space and a generalized dual quasi-Newton algorithm for state-constrained optimal control problems
    • Boston
    • SHIMIZU K. & ITO S., Constrained optimization in Banach space and a generalized dual quasi-Newton algorithm for state-constrained optimal control problems, Proc. 1991 Amer. Contr. Conf. 1, 364-369, Boston (1991).
    • (1991) Proc. 1991 Amer. Contr. Conf. , vol.1 , pp. 364-369
    • Shimizu, K.1    Ito, S.2
  • 24
    • 0042501267 scopus 로고
    • Satisfactory optimal control - Formulation and algorithm
    • SHIMIZU K. & ITO S., Satisfactory optimal control - formulation and algorithm, Proc. 2nd Euro. Contr. Conf. 3, 1404-1409 (1993).
    • (1993) Proc. 2nd Euro. Contr. Conf. , vol.3 , pp. 1404-1409
    • Shimizu, K.1    Ito, S.2
  • 25
    • 0028439434 scopus 로고
    • Constrained optimization in Hilbert space and a generalized dual quasi-Newton algorithm for state-constrained optimal control problems
    • SHIMIZU K. & ITO S., Constrained optimization in Hilbert space and a generalized dual quasi-Newton algorithm for state-constrained optimal control problems, IEEE Trans. Autom. Contr. AC-39, 982-986 (1994).
    • (1994) IEEE Trans. Autom. Contr. , vol.AC-39 , pp. 982-986
    • Shimizu, K.1    Ito, S.2
  • 26
    • 84909773473 scopus 로고
    • Complementarity-enforcing centered Newton method for mathematical programming: Global method
    • Edited by K. TONE, The Institute of Statistical Mathematics. Tokyo
    • TANABE K., Complementarity-enforcing centered Newton method for mathematical programming: global method, in Cooperative Research Report 5 (Edited by K. TONE), pp. 118-144, The Institute of Statistical Mathematics. Tokyo (1987).
    • (1987) Cooperative Research Report , vol.5 , pp. 118-144
    • Tanabe, K.1
  • 27
    • 0042000440 scopus 로고
    • Centered Newton method for linear programming and quadratic programming
    • TANABE K., Centered Newton method for linear programming and quadratic programming, Proc. 8th Math. Prog. Symp. Japan 131-152 (1987).
    • (1987) Proc. 8th Math. Prog. Symp. Japan , pp. 131-152
    • Tanabe, K.1
  • 28
    • 0014781977 scopus 로고
    • Davidon's method for minimization problems in Hilbert space with an application to control problems
    • TOKUMARU H., ADACHI N. & GOTO K., Davidon's method for minimization problems in Hilbert space with an application to control problems, SIAM J. Contr. 8, 163-178 (1970).
    • (1970) SIAM J. Contr. , vol.8 , pp. 163-178
    • Tokumaru, H.1    Adachi, N.2    Goto, K.3
  • 29
    • 0014767739 scopus 로고
    • Optimization using conjugate gradient methods
    • TRIPATHI S. S. & NARENDRA K. S., Optimization using conjugate gradient methods, IEEE Trans. Autom. Contr. AC-15, 268-270 (1970).
    • (1970) IEEE Trans. Autom. Contr. , vol.AC-15 , pp. 268-270
    • Tripathi, S.S.1    Narendra, K.S.2
  • 30
    • 0016974617 scopus 로고
    • Variable metric methods in Hilbert space with applications to control problems
    • TURNER P. R. & HUNTLEY E., Variable metric methods in Hilbert space with applications to control problems, J. Optim. Theory Appl. 19, 381-400 (1976).
    • (1976) J. Optim. Theory Appl. , vol.19 , pp. 381-400
    • Turner, P.R.1    Huntley, E.2
  • 31
    • 0043002101 scopus 로고
    • Direct-prediction quasi-Newton methods in Hilbert space with applications to control problems
    • TURNER P. R. & HUNTLEY E., Direct-prediction quasi-Newton methods in Hilbert space with applications to control problems, J. Optim. Theory Appl. 21, 199-211 (1977).
    • (1977) J. Optim. Theory Appl. , vol.21 , pp. 199-211
    • Turner, P.R.1    Huntley, E.2
  • 32
    • 0027576638 scopus 로고
    • Interior point methods for optimal control of discrete-time systems
    • WRIGHT S. J., Interior point methods for optimal control of discrete-time systems, J. Optim. Theory Appl. 77, 161-174 (1993).
    • (1993) J. Optim. Theory Appl. , vol.77 , pp. 161-174
    • Wright, S.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.