Geodesic
On flexibility of constraints system under approximation of optimal control problems
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 59 (2022), pp. 114-130

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For finite-dimensional mathematical programming problems (approximating problems) being obtained by a parametric approximation of control functions in lumped optimal control problems with functional equality constraints, we introduce concepts of rigidity and flexibility for a system of constraints. The rigidity in a given admissible point is treated in the sense that this point is isolated for the admissible set; otherwise, we call a system of constraints as flexible in this point. Under using a parametric approximation for a control function with the help of quadratic exponentials (Gaussian functions) and subject to some natural hypotheses, we establish that in order to guarantee the flexibility of constraints system in a given admissible point it suffices to increase the dimension of parameter space in the approximating problem. A test of our hypotheses is illustrated by an example of the soft lunar landing problem.
Keywords: lumped optimal control problems with functional equality constraints, parametric approximation of control, rigidity and flexibility of constraints system, Gaussian functions, quadratic exponentials. 
@article{IIMI_2022_59_a7,
     author = {A. V. Chernov},
     title = {On flexibility of constraints system under approximation of optimal control problems},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {114--130},
     publisher = {mathdoc},
     volume = {59},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2022_59_a7/}
}
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A. V. Chernov. On flexibility of constraints system under approximation of optimal control problems. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 59 (2022), pp. 114-130. http://geodesic.mathdoc.fr/item/IIMI_2022_59_a7/