Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 4, pp. 614-632.

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.

DOI : 10.1051/cocv:2005020
Classification : 49K15
Mots clés : optimal control, state constraints, nonsmooth analysis, Euler-Lagrange inclusion
de Pinho, Maria Do Rosário  ; Ferreira, Maria Margarida  ; Fontes, Fernando 1

1 Officina Mathematica, Universidade do Minho, 4800-058 Guimarães, Portugal
@article{COCV_2005__11_4_614_0,
     author = {de Pinho, Maria Do Ros\'ario and Ferreira, Maria Margarida and Fontes, Fernando},
     title = {Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {614--632},
     publisher = {EDP-Sciences},
     volume = {11},
     number = {4},
     year = {2005},
     doi = {10.1051/cocv:2005020},
     mrnumber = {2167877},
     zbl = {1081.49016},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/cocv:2005020/}
}
TY  - JOUR
AU  - de Pinho, Maria Do Rosário
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
PY  - 2005
SP  - 614
EP  - 632
VL  - 11
IS  - 4
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/cocv:2005020/
DO  - 10.1051/cocv:2005020
LA  - en
ID  - COCV_2005__11_4_614_0
ER  - 
%0 Journal Article
%A de Pinho, Maria Do Rosário
%A Ferreira, Maria Margarida
%A Fontes, Fernando
%T Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2005
%P 614-632
%V 11
%N 4
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/cocv:2005020/
%R 10.1051/cocv:2005020
%G en
%F COCV_2005__11_4_614_0
de Pinho, Maria Do Rosário; Ferreira, Maria Margarida; Fontes, Fernando. Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 4, pp. 614-632. doi : 10.1051/cocv:2005020. http://archive.numdam.org/articles/10.1051/cocv:2005020/

[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). | MR | Zbl

[2] F.H. Clarke, Optimization and Nonsmooth Analysis. Wiley, New York (1983). Reprinted as Vol. 5 of Classics Appl. Math. SIAM, Philadelphia (1990). | MR | Zbl

[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. | Zbl

[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). | Zbl

[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. | Zbl

[6] M.D.R. De Pinho and R.B. Vinter, An Euler-Lagrange inclusion for optimal control problems. IEEE Trans. Aut. Control 40 (1995) 1191-1198. | Zbl

[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. | Zbl

[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. | Zbl

[9] B.S. Mordukhovich, Maximum principle in problems of time optimal control with nonsmooth constraints. J. Appl. Math. Mech. 40 (1976) 960-969. | Zbl

[10] B.S. Mordukhovich, Approximation Methods in Problems of Optimization and Control. Nakua, Moscow; the 2nd edition to appear in Wiley-Interscience (1988). | MR | Zbl

[11] R.T. Rockafellar and B. Wets, Variational Analysis. Springer, Berlin (1998). | MR | Zbl

[12] R.B. Vinter, Optimal Control. Birkhauser, Boston (2000). | MR | Zbl

Cité par Sources :