TY - JOUR

T1 - On one boundary problem for nonlinear stationary controlled system

AU - Kvitko, Alexander

AU - Yakusheva, Daria

PY - 2019/4/3

Y1 - 2019/4/3

N2 - The object of study is nonlinear stationary controlled system of ordinary differential equations with constant disturbance in the right part. The problem of constructing the synthesising control function providing the transfer of this system from the initial state to the origin is considered. The sufficiently simple for numerical implementation algorithm of solution of the above-mentioned problem is obtained. It is shown that for local null controllability of the considered system, it is sufficient that the conditions of the Kalman's type were satisfied. In addition, the estimates restricting the choice of initial conditions and external disturbances under which the transfer is guaranteed are obtained. The main idea of the method of construction of the desired control function consists in reducing the original problem to stabilisation of a special kind linear non-stationary system and solving the Cauchy problem for an auxiliary system of ordinary differential equations closed by stabilising control. The simplicity of the realisation of this algorithm is determined by the construction of the auxiliary system and its stabilisation that could be obtained by analytical methods. The effectiveness of the method is illustrated by solving the problem of crane control and its numerical simulation.

AB - The object of study is nonlinear stationary controlled system of ordinary differential equations with constant disturbance in the right part. The problem of constructing the synthesising control function providing the transfer of this system from the initial state to the origin is considered. The sufficiently simple for numerical implementation algorithm of solution of the above-mentioned problem is obtained. It is shown that for local null controllability of the considered system, it is sufficient that the conditions of the Kalman's type were satisfied. In addition, the estimates restricting the choice of initial conditions and external disturbances under which the transfer is guaranteed are obtained. The main idea of the method of construction of the desired control function consists in reducing the original problem to stabilisation of a special kind linear non-stationary system and solving the Cauchy problem for an auxiliary system of ordinary differential equations closed by stabilising control. The simplicity of the realisation of this algorithm is determined by the construction of the auxiliary system and its stabilisation that could be obtained by analytical methods. The effectiveness of the method is illustrated by solving the problem of crane control and its numerical simulation.

KW - Boundary conditions

KW - control functions

KW - local null controllability

KW - nonlinear systems

KW - stabilisation

KW - NULL CONTROLLABILITY

KW - INTEGRODIFFERENTIAL-SYSTEMS

KW - SETS

KW - ADAPTIVE-CONTROL

KW - ATTAINABILITY

KW - CRANE

UR - http://www.scopus.com/inward/record.url?scp=85029439327&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/one-boundary-problem-nonlinear-stationary-controlled-system

U2 - 10.1080/00207179.2017.1370727

DO - 10.1080/00207179.2017.1370727

M3 - Article

AN - SCOPUS:85029439327

VL - 92

SP - 828

EP - 839

JO - International Journal of Control

JF - International Journal of Control

SN - 0020-7179

IS - 4

ER -