Geodesic
On the existence of admissible processes for control systems with mixed constraints
Vestnik rossijskih universitetov. Matematika, Tome 28 (2023) no. 143, pp. 227-235 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A control system with mixed equality-type constraints and end-point constraints is considered. In terms of the generalized Jacobian (Clarke's derivative) with respect to the control variable of the mapping defining the constraints, sufficient conditions for the existence of continuous admissible positional controls are obtained. The proof of the corresponding theorem is based on reducing the control system to a boundary value problem for an ordinary differential equation via a nonlocal implicit function theorem. This problem is then reduced to the problem of finding a fixed point of a continuous mapping defined on a finite-dimensional closed ball and to applying an analogue of Brouwer's fixed point theorem. In addition, a control system with mixed inequality-type constraints and end-point constraints is studied. In terms of the first derivatives with respect to the control variable of the functions that define the constraints, sufficient conditions for the existence of continuous admissible positional controls are also obtained. The proof of the corresponding theorem is carried out by passing from a system of smooth inequality-type constraints to one locally Lipschitz equality-type constraint.
Keywords: control systems, mixed constraints, positional controls, Clarke’s derivative, implicit function. 
@article{VTAMU_2023_28_143_a1,
     author = {N. S. Borzov and Z. T. Zhukovskaya},
     title = {On the existence of admissible processes for control systems with mixed constraints},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {227--235},
     year = {2023},
     volume = {28},
     number = {143},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2023_28_143_a1/}
}
TY  - JOUR
AU  - N. S. Borzov
AU  - Z. T. Zhukovskaya
TI  - On the existence of admissible processes for control systems with mixed constraints
JO  - Vestnik rossijskih universitetov. Matematika
PY  - 2023
SP  - 227
EP  - 235
VL  - 28
IS  - 143
UR  - http://geodesic.mathdoc.fr/item/VTAMU_2023_28_143_a1/
LA  - ru
ID  - VTAMU_2023_28_143_a1
ER  - 
%0 Journal Article
%A N. S. Borzov
%A Z. T. Zhukovskaya
%T On the existence of admissible processes for control systems with mixed constraints
%J Vestnik rossijskih universitetov. Matematika
%D 2023
%P 227-235
%V 28
%N 143
%U http://geodesic.mathdoc.fr/item/VTAMU_2023_28_143_a1/
%G ru
%F VTAMU_2023_28_143_a1
N. S. Borzov; Z. T. Zhukovskaya. On the existence of admissible processes for control systems with mixed constraints. Vestnik rossijskih universitetov. Matematika, Tome 28 (2023) no. 143, pp. 227-235. http://geodesic.mathdoc.fr/item/VTAMU_2023_28_143_a1/

[1] F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley, N.Y., 1983 | MR | Zbl

[2] A. V. Arutyunov, S. E. Zhukovskiy, “Smoothing procedure for lipschitzian equations and continuity of solutions”, Journal of Optimization Theory and Applications, 2023 | MR

[3] A. V. Arutyunov, S. E. Zhukovskiy, “On nonlinear boundary value problems for differential inclusions”, Differential Equaitions, 2023

[4] J. Warga, Optimal Control of Differential and Functional Equations, Academic Press, N.Y., 1972 | MR | Zbl

[5] H. Cartan, Differential Calculus, Kershaw Publ. Company, London, 1971 | MR

[6] A. Granas, J. Dugundji, Fixed Point Theory, Springer Verlag, New York, 2003 | MR | Zbl