Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems

Maria do Rosário de Pinho; Maria Margarida Ferreira; Fernando Fontes

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 11, Issue: 4, page 614-632
  • ISSN: 1292-8119

Abstract

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Necessary conditions of optimality in the form of Unmaximized Inclusions (UI) are derived for optimal control problems with state constraints. The conditions presented here generalize earlier optimality conditions to problems that may be nonconvex. The derivation of UI-type conditions in the absence of the convexity assumption is of particular importance when deriving necessary conditions for constrained problems. We illustrate this feature by establishing, as an application, optimality conditions for problems that in addition to state constraints incorporate mixed state-control constraints.

How to cite

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Maria do Rosário de Pinho, Ferreira, Maria Margarida, and Fontes, Fernando. "Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems." ESAIM: Control, Optimisation and Calculus of Variations 11.4 (2010): 614-632. <http://eudml.org/doc/90780>.

@article{MariadoRosáriodePinho2010,
abstract = { Necessary conditions of optimality in the form of Unmaximized Inclusions (UI) are derived for optimal control problems with state constraints. The conditions presented here generalize earlier optimality conditions to problems that may be nonconvex. The derivation of UI-type conditions in the absence of the convexity assumption is of particular importance when deriving necessary conditions for constrained problems. We illustrate this feature by establishing, as an application, optimality conditions for problems that in addition to state constraints incorporate mixed state-control constraints. },
author = {Maria do Rosário de Pinho, Ferreira, Maria Margarida, Fontes, Fernando},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Optimal control; state constraints; nonsmooth analysis; Euler-Lagrange inclusion.; optimal control; Euler-Lagrange inclusion},
language = {eng},
month = {3},
number = {4},
pages = {614-632},
publisher = {EDP Sciences},
title = {Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems},
url = {http://eudml.org/doc/90780},
volume = {11},
year = {2010},
}

TY - JOUR
AU - Maria do Rosário de Pinho
AU - Ferreira, Maria Margarida
AU - Fontes, Fernando
TI - Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 11
IS - 4
SP - 614
EP - 632
AB - Necessary conditions of optimality in the form of Unmaximized Inclusions (UI) are derived for optimal control problems with state constraints. The conditions presented here generalize earlier optimality conditions to problems that may be nonconvex. The derivation of UI-type conditions in the absence of the convexity assumption is of particular importance when deriving necessary conditions for constrained problems. We illustrate this feature by establishing, as an application, optimality conditions for problems that in addition to state constraints incorporate mixed state-control constraints.
LA - eng
KW - Optimal control; state constraints; nonsmooth analysis; Euler-Lagrange inclusion.; optimal control; Euler-Lagrange inclusion
UR - http://eudml.org/doc/90780
ER -

References

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  1. K.E. Brenen, S.L. Campbell and L.R. Petzold, Numerical Solution of Initial-Value Problems in Differential Algebraic Equations. Classics Appl. Math. SIAM, Philadelphia (1996).  
  2. F.H. Clarke, Optimization and Nonsmooth Analysis. Wiley, New York (1983). Reprinted as Vol. 5 of Classics Appl. Math. SIAM, Philadelphia (1990).  
  3. M.d.R. de Pinho, M.M.A. Ferreira and F.A.C.C. Fontes, An Euler-Lagrange inclusion for optimal control problems with state constraints. J. Dynam. Control Syst.8 (2002) 23–45.  Zbl1027.49019
  4. M.d.R. de Pinho, M.M.A. Ferreira and F.A.C.C. Fontes, Necessary conditions in Euler-Lagrange inclusion form for constrained nonconvex optimal control problems, in Proc. of the 10th Mediterranean Conference on Control and Automation. Lisbon, Portugal (2002).  Zbl1027.49019
  5. M.d.R. de Pinho and A. Ilchmann, Weak maximum principle for optimal control problems with mixed constraints. Nonlinear Anal. Theory Appl.48 (2002) 1179–1196.  Zbl1019.49024
  6. M.d.R. de Pinho and R.B. Vinter, An Euler-Lagrange inclusion for optimal control problems. IEEE Trans. Aut. Control40 (1995) 1191–1198.  Zbl0827.49014
  7. M.d.R. de Pinho and R.B. Vinter, Necessary conditions for optimal control problems involving nonlinear differential algebraic equations. J. Math. Anal. Appl.212 (1997) 493–516.  Zbl0891.49013
  8. M.d.R. de Pinho, R.B. Vinter and H. Zheng, A maximum principle for optimal control problems with mixed constraints. IMA J. Math. Control Inform.18 (2001) 189–205.  Zbl1103.49307
  9. B.S. Mordukhovich, Maximum principle in problems of time optimal control with nonsmooth constraints. J. Appl. Math. Mech.40 (1976) 960–969.  Zbl0362.49017
  10. B.S. Mordukhovich, Approximation Methods in Problems of Optimization and Control. Nakua, Moscow; the 2nd edition to appear in Wiley-Interscience (1988).  
  11. R.T. Rockafellar and B. Wets, Variational Analysis. Springer, Berlin (1998).  
  12. R.B. Vinter, Optimal Control. Birkhauser, Boston (2000).  Zbl0952.49001

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