Geodesic
A maximum principle for optimal control problems with state and mixed constraints
Haider Ali Biswas, Md.1 ; de Pinho, Maria do Rosario2 
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
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 939-957

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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.

DOI : 10.1051/cocv/2014047
Classification : 49K15, 34A60
Keywords: Optimal control, state and mixed constraints, maximum principle

Haider Ali Biswas, Md. 1 ; de Pinho, Maria do Rosario 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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     title = {A maximum principle for optimal control problems with state and mixed constraints},
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Haider Ali Biswas, Md.; de Pinho, Maria do Rosario. A maximum principle for optimal control problems with state and mixed constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 939-957. doi: 10.1051/cocv/2014047

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