TY - JOUR

T1 - An approximate solution of the affine-quadratic control problem based on the concept of optimal damping

AU - Veremey, Evgeny I.

N1 - Publisher Copyright: © 2021 Evgeny I. Veremey, published by Sciendo.

PY - 2021/3/1

Y1 - 2021/3/1

N2 - The paper is devoted to a particular case of the nonlinear and nonautonomous control law design problem based on the application of the optimization approach. Close attention is paid to the controlled plants, which are presented by affine-control mathematical models characterized by integralquadratic functionals. The proposed approach to controller design is based on the optimal damping concept firstly developed by V.I. Zubov in the early 1960s. A modern interpretation of this concept allows us to construct effective numerical procedures of control law synthesis initially oriented to practical implementation. The main contribution is the proposition of a new methodology for selecting the functional to be damped. The central idea is to perform parameterization of a set of admissible items for this functional. As a particular case, a new method of this parameterization has been developed, which can be used for constructing an approximate solution to the classical optimization problem. Applicability and effectiveness of the proposed approach are confirmed by a practical numerical example.

AB - The paper is devoted to a particular case of the nonlinear and nonautonomous control law design problem based on the application of the optimization approach. Close attention is paid to the controlled plants, which are presented by affine-control mathematical models characterized by integralquadratic functionals. The proposed approach to controller design is based on the optimal damping concept firstly developed by V.I. Zubov in the early 1960s. A modern interpretation of this concept allows us to construct effective numerical procedures of control law synthesis initially oriented to practical implementation. The main contribution is the proposition of a new methodology for selecting the functional to be damped. The central idea is to perform parameterization of a set of admissible items for this functional. As a particular case, a new method of this parameterization has been developed, which can be used for constructing an approximate solution to the classical optimization problem. Applicability and effectiveness of the proposed approach are confirmed by a practical numerical example.

KW - damping control

KW - feedback

KW - functional

KW - optimization

KW - stability

UR - http://www.scopus.com/inward/record.url?scp=85104297243&partnerID=8YFLogxK

U2 - 10.34768/amcs-2021-0001

DO - 10.34768/amcs-2021-0001

M3 - Article

AN - SCOPUS:85104297243

VL - 31

SP - 5

EP - 15

JO - International Journal of Applied Mathematics and Computer Science

JF - International Journal of Applied Mathematics and Computer Science

SN - 1641-876X

IS - 1

ER -