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Paper details
Number 1 - March 2021
Volume 31 - 2021
An approximate solution of the affine-quadratic control problem based on the concept of optimal damping
Evgeny I. Veremey
Abstract
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 integral quadratic 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.
Keywords
feedback, stability, damping control, functional, opt