Geodesic
On the existence of a Lipschitz feedback control in a control problem with state constraints
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 2, pp. 122-128

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We consider a nonlinear control system with state constraints given as a solution set for a finite system of nonlinear inequalities. The problem of constructing a feedback control that ensures the viability of trajectories of the closed system in a small neighborhood of the boundary of the state constraints is studied. Under some assumptions, the existence of a feedback control in the form of a Lipschitz function of the state of the system is proved.
Keywords: state constraints, feedback control, viability problem, invariance. 
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     author = {M. I. Gusev},
     title = {On the existence of a {Lipschitz} feedback control in a control problem with state constraints},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {122--128},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2016_22_2_a13/}
}
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M. I. Gusev. On the existence of a Lipschitz feedback control in a control problem with state constraints. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 2, pp. 122-128. http://geodesic.mathdoc.fr/item/TIMM_2016_22_2_a13/