A maximum principle for optimal control problems with state and mixed constraints
ESAIM: Control, Optimisation and Calculus of Variations, Volume 21 (2015) no. 4, pp. 939-957.

Here we derive a variant of the nonsmooth maximum principle for optimal control problems with both pure state and mixed state and control constraints. Our necessary conditions include a Weierstrass condition together with an Euler adjoint inclusion involving the joint subdifferentials with respect to both state and control, generalizing previous results in [M.d.R. de Pinho, M.M.A. Ferreira, F.A.C.C. Fontes, Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems. ESAIM: COCV 11 (2005) 614–632]. A notable feature is that our main results are derived combining old techniques with recent results. We use a well known penalization technique for state constrained problem together with an appeal to a recent nonsmooth maximum principle for problems with mixed constraints.

Received:
DOI: 10.1051/cocv/2014047
Classification: 49K15, 34A60
Keywords: Optimal control, state and mixed constraints, maximum principle
Haider Ali Biswas, Md. 1; do Rosario de Pinho, Maria 2

1 Mathematics Discipline, Science Engineering and Technology School, Khulna University, Khulna-9208, Bangladesh
2 Universidade do Porto, Faculadade de Engenharia, DEEC, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
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Haider Ali Biswas, Md.; do Rosario de Pinho, Maria. A maximum principle for optimal control problems with state and mixed constraints. ESAIM: Control, Optimisation and Calculus of Variations, Volume 21 (2015) no. 4, pp. 939-957. doi : 10.1051/cocv/2014047. http://www.numdam.org/articles/10.1051/cocv/2014047/

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