Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-05T18:26:57.575Z Has data issue: false hasContentIssue false
  • English
  • Français

Unmaximized inclusion necessary conditions for nonconvexconstrained optimal control problems

Published online by Cambridge University Press:  15 September 2005

Maria do Rosário de Pinho ,
Maria Margarida Ferreira  and
Fernando Fontes
Maria do Rosário de Pinho
Affiliation:
ISR and DEEC, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal; mrpinho@fe.up.pt; mmf@fe.up.pt
Maria Margarida Ferreira
Affiliation:
ISR and DEEC, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal; mrpinho@fe.up.pt; mmf@fe.up.pt
Fernando Fontes
Affiliation:
Officina Mathematica, Universidade do Minho, 4800-058 Guimarães, Portugal; ffontes@mct.uminho.pt
Get access

Abstract

Necessary conditions of optimality in the form ofUnmaximized Inclusions (UI) are derived for optimal controlproblems with state constraints. The conditions presented heregeneralize earlier optimality conditions to problems that may benonconvex. The derivation of UI-type conditions in the absence of the convexity assumption is of particularimportance when deriving necessary conditions for constrainedproblems. We illustrate this feature by establishing, as anapplication, optimality conditions for problems that in additionto state constraints incorporate mixed state-control constraints.

Keywords

Optimal controlstate constraintsnonsmooth analysisEuler-Lagrange inclusion.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 4 , October 2005 , pp. 614 - 632
Copyright
© EDP Sciences, SMAI, 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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).
F.H. Clarke, Optimization and Nonsmooth Analysis. Wiley, New York (1983). Reprinted as Vol. 5 of Classics Appl. Math. SIAM, Philadelphia (1990).
de Pinho, M.d.R., Ferreira, M.M.A. and Fontes, F.A.C.C., An Euler-Lagrange inclusion for optimal control problems with state constraints. J. Dynam. Control Syst. 8 (2002) 23–45. CrossRef
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).
de Pinho, M.d.R. and Ilchmann, A., Weak maximum principle for optimal control problems with mixed constraints. Nonlinear Anal. Theory Appl. 48 (2002) 1179–1196. CrossRef
de Pinho, M.d.R. and Vinter, R.B., An Euler-Lagrange inclusion for optimal control problems. IEEE Trans. Aut. Control 40 (1995) 1191–1198. CrossRef
de Pinho, M.d.R. and Vinter, R.B., Necessary conditions for optimal control problems involving nonlinear differential algebraic equations. J. Math. Anal. Appl. 212 (1997) 493–516. CrossRef
de Pinho, M.d.R., Vinter, R.B. and Zheng, H., A maximum principle for optimal control problems with mixed constraints. IMA J. Math. Control Inform. 18 (2001) 189–205. CrossRef
Mordukhovich, B.S., Maximum principle in problems of time optimal control with nonsmooth constraints. J. Appl. Math. Mech. 40 (1976) 960–969. CrossRef
B.S. Mordukhovich, Approximation Methods in Problems of Optimization and Control. Nakua, Moscow; the 2nd edition to appear in Wiley-Interscience (1988).
R.T. Rockafellar and B. Wets, Variational Analysis. Springer, Berlin (1998).
R.B. Vinter, Optimal Control. Birkhauser, Boston (2000).