메뉴 건너뛰기




Volumn 49, Issue 4, 2011, Pages 1498-1522

Convergence results for smooth regularizations of hybrid nonlinear optimal control problems

Author keywords

Hybrid control; Optimal control; Orbit transfer with eclipse; Regularization; Shooting method

Indexed keywords

HYBRID CONTROLS; OPTIMAL CONTROLS; ORBIT TRANSFER WITH ECLIPSE; REGULARIZATION; SHOOTING METHOD;

EID: 80052697941     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/100809209     Document Type: Article
Times cited : (54)

References (34)
  • 1
    • 28444476416 scopus 로고    scopus 로고
    • Control theory from the geometric viewpoint
    • Control Theory and Optimization, II, Springer-Verlag, Berlin
    • A. AGRACHEV and Y. SACHKOV, Control Theory from the Geometric Viewpoint, Encyclopaedia Math. Sci. 87, Control Theory and Optimization, II, Springer-Verlag, Berlin, 2004.
    • (2004) Encyclopaedia Math. Sci. , vol.87
    • Agrachev, A.1    Sachkov, Y.2
  • 2
    • 33746034500 scopus 로고    scopus 로고
    • A benchmark for optimal control problem solvers for hybrid nonlinear systems
    • DOI 10.1016/j.automatica.2006.04.005, PII S0005109806001531
    • M. ALAMIR, A benchmark for optimal control problem solvers for hybrid nonlinear systems, Automatica J. IFAC, 42(2006), pp. 1593-1598. (Pubitemid 44080728)
    • (2006) Automatica , vol.42 , Issue.9 , pp. 1593-1598
    • Alamir, M.1
  • 3
    • 25644455408 scopus 로고
    • Etude locale de l'ensemble des points critiques d'un problème d'optimisation paramétré
    • PH. ANTOINE and H. ZOUAKI, Etude locale de l'ensemble des points critiques d'un problème d'optimisation paramétré, C. R. Acad. Sci. Paris Sér. I Math., 310(1990), pp. 587-590.
    • (1990) C. R. Acad. Sci. Paris Sér. I Math. , vol.310 , pp. 587-590
    • Antoine, Ph.1    Zouaki, H.2
  • 6
    • 34548056910 scopus 로고    scopus 로고
    • Mécanique céleste et contrôle des véhicules spatiaux
    • Springer-Verlag, Berlin
    • B. BONNARD, L. FAUBOURG, and E. TRÉLAT, Mécanique céleste et contrôle des véhicules spatiaux, Math. Appl. (Berlin) 51, Springer-Verlag, Berlin, 2006.
    • (2006) Math. Appl. (Berlin) , vol.51
    • Bonnard, B.1    Faubourg, L.2    Trélat, E.3
  • 7
    • 0031701911 scopus 로고    scopus 로고
    • A unified framework for hybrid control: Model and optimal control theory
    • PII S0018928698009258
    • M. S. BRANICKY, V. S. BORKAR, and S. K. MITTER, A unified framework for hybrid control: Model and optimal control theory, IEEE Trans. Automat. Control, 43(1998), pp. 31-45. (Pubitemid 128743101)
    • (1998) IEEE Transactions on Automatic Control , vol.43 , Issue.1 , pp. 31-45
    • Branicky, M.S.1    Borkar, V.S.2    Mitter, S.K.3
  • 8
    • 55849090281 scopus 로고    scopus 로고
    • Optimal control problems on stratified domains
    • A. BRESSAN and Y. HUONG, Optimal control problems on stratified domains, Netw. Heterog. Media, 2(2007), pp. 313-331.
    • (2007) Netw. Heterog. Media , vol.2 , pp. 313-331
    • Bressan, A.1    Huong, Y.2
  • 10
    • 17644427854 scopus 로고    scopus 로고
    • Semiconcave functions, hamilton-jacobi equations, and optimal control
    • Birkhäuser Boston, Inc., Boston, MA
    • P. CANNARSA and C. SINESTRARI, Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control, Progr. Nonlinear Differential Equations Appl. 58, Birkhäuser Boston, Inc., Boston, MA, 2004.
    • (2004) Progr. Nonlinear Differential Equations Appl. , vol.58
    • Cannarsa, P.1    Sinestrari, C.2
  • 11
    • 0003287433 scopus 로고
    • Optimization-theory and applications. Problems with ordinary differential equations
    • Springer-Verlag, New York
    • L. CESARI, Optimization-Theory and Applications. Problems with Ordinary Differential Equations, Appl. Math. 17, Springer-Verlag, New York, 1983.
    • (1983) Appl. Math. , vol.17
    • Cesari, L.1
  • 12
    • 19244367902 scopus 로고
    • The relationship between the maximum principle and dynamic programming
    • F. H. CLARKE and R. B. VINTER, The relationship between the maximum principle and dynamic programming, SIAM J. Control Optim., 25(1987), pp. 1291-1311.
    • (1987) SIAM J. Control Optim. , vol.25 , pp. 1291-1311
    • Clarke, F.H.1    Vinter, R.B.2
  • 13
  • 14
    • 51149110483 scopus 로고    scopus 로고
    • The hybrid maximum principle is a consequence of Pontryagin maximum principle
    • A. V. DMITRUK and A. M. KAGANOVICH, The hybrid maximum principle is a consequence of Pontryagin maximum principle, Systems Control Lett., 57(2008), pp. 964-970.
    • (2008) Systems Control Lett. , vol.57 , pp. 964-970
    • Dmitruk, A.V.1    Kaganovich, A.M.2
  • 15
    • 0035247459 scopus 로고    scopus 로고
    • Optimal control for engines with electro-ionic propulsion under constraint of eclipse
    • DOI 10.1016/S0094-5765(00)00158-2, PII S0094576500001582
    • CH. FERRIER and R. EPENOY, Optimal control for engines with electro-ionic propulsion under constraint of eclipse, Acta Astronaut., 48(2001), pp. 181-192. (Pubitemid 32335168)
    • (2001) Acta Astronautica , vol.48 , Issue.4 , pp. 181-192
    • Ferrier, C.H.1    Epenoy, R.2
  • 17
    • 33645788599 scopus 로고    scopus 로고
    • Homotopy method for minimum consumption orbit transfer problem
    • J. GERGAUD and T. HABERKORN, Homotopy method for minimum consumption orbit transfer problem, ESAIM Cont. Optim. Calc. Var., 12(2006), pp. 294-310.
    • (2006) ESAIM Cont. Optim. Calc. Var. , vol.12 , pp. 294-310
    • Gergaud, J.1    Haberkorn, T.2
  • 18
    • 9944247187 scopus 로고    scopus 로고
    • Low thrust minimum fuel orbital transfer: An homotopic approach
    • J. GERGAUD, T. HABERKORN, and P. MARTINON, Low thrust minimum fuel orbital transfer: An homotopic approach, J. Guidance Cont. Dyn., 27(2004), pp. 1046-1060.
    • (2004) J. Guidance Cont. Dyn. , vol.27 , pp. 1046-1060
    • Gergaud, J.1    Haberkorn, T.2    Martinon, P.3
  • 21
    • 34248156187 scopus 로고    scopus 로고
    • Using switching detection and variational equations for the shooting method
    • DOI 10.1002/oca.794
    • P. MARTINON and J. GERGAUD, Using switching detection and variational equations for the shooting me t hod, Optimal Control Appl. Methods, 28(2007), pp. 95-116. (Pubitemid 46716565)
    • (2007) Optimal Control Applications and Methods , vol.28 , Issue.2 , pp. 95-116
    • Martinon, P.1    Gergaud, J.2
  • 23
    • 33845380556 scopus 로고    scopus 로고
    • An optimal control approach for hybrid systems
    • DOI 10.3166/ejc.9.449-458
    • P. RIEDINGER, C. IUNG, and F. KRATZ, An optimal control approach for hybrid systems, European J. Control, 9(2003), pp. 449-458. (Pubitemid 44895219)
    • (2003) European Journal of Control , vol.9 , Issue.5 , pp. 449-458
    • Riedinger, P.1    Iung, C.2    Kratz, F.3
  • 24
    • 17444430784 scopus 로고    scopus 로고
    • Morse-Sard type results in sub-Riemannian geometry
    • DOI 10.1007/s00208-004-0622-2
    • L. RIFFORD and E. TRÉLAT, Morse-Sard type results in sub-Riemannian geometry, Math. Ann., 332(2005), pp. 145-159. (Pubitemid 40550201)
    • (2005) Mathematische Annalen , vol.332 , Issue.1 , pp. 145-159
    • Rifford, L.1    Trelat, E.2
  • 25
    • 74249110334 scopus 로고    scopus 로고
    • On the stabilization problem for nonholonomic distributions
    • L. RIFFORD and E. TRÉLAT, On the stabilization problem for nonholonomic distributions, J. J. Eur. Math. Soc (JEMS), 11(2009), pp. 223-255.
    • (2009) J. J. Eur. Math. Soc (JEMS) , vol.11 , pp. 223-255
    • Rifford, L.1    Trélat, E.2
  • 26
    • 70249100644 scopus 로고    scopus 로고
    • Reformulations and algorithms for the optimization of switching decisions in nonlinear optimal control
    • S. SAGER, Reformulations and algorithms for the optimization of switching decisions in nonlinear optimal control, J. Process Control, 19(2009), pp. 1238-1247.
    • (2009) J. Process Control , vol.19 , pp. 1238-1247
    • Sager, S.1
  • 27
    • 34648846630 scopus 로고    scopus 로고
    • On the hybrid optimal control problem: Theory and algorithms
    • DOI 10.1109/TAC.2007.904451
    • M. S. SHAIKH and P. E. CAINES, On the hybrid optimal control problem: Theory and algorithms, IEEE Trans. Automat. Control, 52(2007), pp. 1587-1603. (Pubitemid 47456070)
    • (2007) IEEE Transactions on Automatic Control , vol.52 , Issue.9 , pp. 1587-1603
    • Shaikh, M.S.1    Caines, P.E.2
  • 28
    • 78149257173 scopus 로고    scopus 로고
    • Smooth regularization of bang-bang optimal control problems
    • C. J. SILVA and E. TRÉLAT, Smooth regularization of bang-bang optimal control problems, IEEE Trans. Automat. Control, 55(2010), pp. 2488-2499.
    • (2010) IEEE Trans. Automat. Control , vol.55 , pp. 2488-2499
    • Silva, C.J.1    Trélat, E.2
  • 32
    • 0001222585 scopus 로고    scopus 로고
    • Some properties of the value function and its level sets for affine control systems with quadratic cost
    • E. TRÉLAT, Some properties of the value function and its level sets for affine control systems with quadratic cost, J. Dyn. Cont. Syst., 6(2000), pp. 511-541.
    • (2000) J. Dyn. Cont. Syst. , vol.6 , pp. 511-541
    • Trélat, E.1
  • 33
    • 84972814157 scopus 로고
    • Strong convergence results related to strict convexity
    • A. VISINTIN, Strong convergence results related to strict convexity, Comm. Partial Differential Equations, 9(1984), pp. 439-466.
    • (1984) Comm. Partial Differential Equations , vol.9 , pp. 439-466
    • Visintin, A.1
  • 34
    • 0037126506 scopus 로고    scopus 로고
    • Optimal control of switched systems via nonlinear optimization based on direct differentiation of value functions
    • X. XU and P. J. ANTSAKLIS, Optimal control of switched systems via nonlinear optimization based on direct differentiation of value functions, Internat. J. Control, 75(2002), pp. 1406-1426.
    • (2002) Internat. J. Control , vol.75 , pp. 1406-1426
    • Xu, X.1    Antsaklis, P.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.