Geodesic
Optimal control of a~nonlinear singular system with state constraints
Matematičeskie zametki, Tome 60 (1996) no. 4, pp. 511-518

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A control system described by a nonlinear equation of parabolic type is considered in the situation where there may be no global solution. A particular optimal control problem subject to state constraints is studied. A proof of the existence of an optimal control is presented. The penalty method is used to obtain necessary conditions for optimal control. A proof of the convergence of this method is given. The successive approximation method is used to obtain an approximate solution for the conditions derived. 
@article{MZM_1996_60_4_a3,
     author = {S. Ya. Serovaǐskiǐ},
     title = {Optimal control of a~nonlinear singular system with state constraints},
     journal = {Matemati\v{c}eskie zametki},
     pages = {511--518},
     publisher = {mathdoc},
     volume = {60},
     number = {4},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_4_a3/}
}
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S. Ya. Serovaǐskiǐ. Optimal control of a~nonlinear singular system with state constraints. Matematičeskie zametki, Tome 60 (1996) no. 4, pp. 511-518. http://geodesic.mathdoc.fr/item/MZM_1996_60_4_a3/