arXiv subjects

Pavel Barkhayev

Publications and source records attributed to Pavel Barkhayev.

4 recordsLinked to original sources

arXiv2021

Implementation of the algorithm for constructing homogeneous approximations of nonlinear control systems

We present a 'calculator' for constructing a homogeneous approximation of nonlinear control systems, which is based on the algebraic approach developed by the authors in their previous papers. This approach mainly uses linear algebraic and combinatorial tools, so, it is perfectly adapted to computer realization. We describe the algorithm and discuss its capabilities and limitations. We present its implementation as a web application and show by example how this app works.

math.OC↗

arXiv2020

Minimum energy exact null-controllability problem for linear time-delay equations

We study the minimum energy null-controllability problem for differential equations with point-wise delays. For the equations of both neutral and retarded type we reduce the problem of finding the optimal control to a Volterra integral equation and solve it explicitly. We prove that for any initial state and any controllability time the corresponding optimal control belongs to the characteristic space generated by the equation's exponentials. Besides, we show that the proposed approach can be applied to the systems of retarded equations with one delay term.

math.OC↗

arXiv2019

Conditions of exact null controllability and the problem of complete stabilizability for time-delay systems

For a class of linear time-delay control systems satisfying the property of completability of the generalized eigenvectors we prove that the problems of complete stabilizability and exact null controllability are equivalent.

math.OC↗

arXiv2017

Exact null controllability, complete stabilizability and exact final observability: the case of neutral type systems

For abstract linear systems in Hilbert spaces we revisit the problems of exact controllability and complete stabilizability (stabilizability with an arbitrary decay rate), the latter property is equivalent to exact null controllability. We extend this result to the case when the feedback is not bounded. This enables the characterization of exact null controllability and complete stabilizability for neutral type systems. By duality, we obtain a result about continuous final observability.Illustrative examples are given.

math.OC↗