Geodesic
On the construction of a discontinuous piecewise affine synthesis in a target control problem
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 3, pp. 194-210

Voir la notice de l'article provenant de la source Math-Net.Ru

A new method is proposed for the approximate solution of problems of solvability and control synthesis for a nonlinear system of ordinary differential equations. The method is based on the piecewise linearization (hybridization) of equations and on the use of the dynamic programming approach and the comparison principle. The main idea is to construct piecewise affine value functions and a feedback control of a special form. Two cases are considered: when these functions are continuous and when they may have discontinuities on certain sets in the state space. In both cases, we obtain internal estimates for the solvability sets of the original nonlinear system and a feedback control that takes the system's state vector to the target set on a given finite time interval.
Keywords: nonlinear dynamics, control synthesis, dynamic programming, comparison principle, linearization, switched system, piecewise affine value function. 
@article{TIMM_2021_27_3_a15,
     author = {P. A. Tochilin and I. A. Chistyakov},
     title = {On the construction of a discontinuous piecewise affine synthesis in a target control problem},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {194--210},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2021_27_3_a15/}
}
TY  - JOUR
AU  - P. A. Tochilin
AU  - I. A. Chistyakov
TI  - On the construction of a discontinuous piecewise affine synthesis in a target control problem
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2021
SP  - 194
EP  - 210
VL  - 27
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2021_27_3_a15/
LA  - ru
ID  - TIMM_2021_27_3_a15
ER  - 
%0 Journal Article
%A P. A. Tochilin
%A I. A. Chistyakov
%T On the construction of a discontinuous piecewise affine synthesis in a target control problem
%J Trudy Instituta matematiki i mehaniki
%D 2021
%P 194-210
%V 27
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2021_27_3_a15/
%G ru
%F TIMM_2021_27_3_a15
P. A. Tochilin; I. A. Chistyakov. On the construction of a discontinuous piecewise affine synthesis in a target control problem. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 3, pp. 194-210. http://geodesic.mathdoc.fr/item/TIMM_2021_27_3_a15/