Geodesic
On the Solution of the Trajectory Survival Problem for a~Nonlinear Dynamical System
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 262 (2008), pp. 146-155

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Nonlinear control systems possessing the flatness property are encountered in many applied mathematical models. In this paper, a trajectory survival problem is considered for a specific nonlinear system that possesses the above property. A method based on the properties of the system is proposed for constructing a control that solves the trajectory survival problem when the controlled object moves to the goal set within a bounding set containing an obstacle. Results of numerical calculations of the control and the trajectory of a system with a given initial position are presented. 
@article{TM_2008_262_a10,
     author = {L. N. Luk'yanova},
     title = {On the {Solution} of the {Trajectory} {Survival} {Problem} for {a~Nonlinear} {Dynamical} {System}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {146--155},
     publisher = {mathdoc},
     volume = {262},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2008_262_a10/}
}
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L. N. Luk'yanova. On the Solution of the Trajectory Survival Problem for a~Nonlinear Dynamical System. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control, Tome 262 (2008), pp. 146-155. http://geodesic.mathdoc.fr/item/TM_2008_262_a10/