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## On Optimal Anisotropy-Based Control Problem for Discrete-Time Descriptor Systems

P. 661-666.

Belov A. A., Andrianova O.

This paper is dedicated to optimal state-feedback

control problem for discrete-time descriptor systems in presence

of “colored” noise with known mean anisotropy level. Here

“colored” noise stands for a stationary Gaussian sequence,

generated by a linear shaping filter from the Gaussian white

noise sequence. The control goal is to find a state feedback

control law which makes the closed-loop system admissible and

minimizes its a-anisotropic norm (mean anisotropy level a is

known).

Belov A. A., Andrianova O., , in: PROCEEDINGS OF 2016 INTERNATIONAL CONFERENCE “STABILITY AND OSCILLATIONS OF NONLINEAR CONTROL SYSTEMS” (PYATNITSKIY’S CONFERENCE). .: IEEE, 2016.. P. 1-4.

In this paper, linear discrete-time descriptor systems
with norm-bounded parametric uncertainties are under consideration. The input signal is supposed to be a “colored” noise with
bounded mean anisotropy. Sufficient conditions of anisotropic
norm boundedness for such class of systems are given. ...

Added: February 6, 2018

Belov A., Andrianova O., Automation and Remote Control 2016 Vol. 77 No. 10 P. 1741-1755

A computationally efficient method for the design of a suboptimal anisotropic con- troller for discrete descriptor systems based on convex optimization methods is proposed. Nu- merical examples are given. ...

Added: October 20, 2017

Andrianova O., Belov A., Kurdyukov A., Journal of Computer and Systems Sciences International 2015 Vol. 54 No. 1 P. 27-38

A class of systems, described by algebraic-difference equations, is under consideration. Such systems are called descriptor (singular). For these systems the conditions of anisotropic norm boundedness are obtained. Anisotropic norm describes the root mean square gain of the system with respect to random Gaussian stationary disturbances, which are characterized by mean anisotropy. The conditions are ...

Added: October 19, 2017

Andrianova O., Kurdyukov A., Kustov A. Y., Journal of Computer and Systems Sciences International 2015 Vol. 54 No. 5 P. 10-23

Linear stationary discrete-time descriptor systems with input sequences of random Gaussian nonzero-mean vectors with bounded mean anisotropy are under consideration. Conditions of anisotropic norm boundedness for such systems are given in terms of generalized discrete-time algebraic Riccati equations (GDARE) and linear matrix inequalities (LMI). On basis of these results, the algorithm of anisotropic norm computation ...

Added: October 20, 2017

Max press, 2018

This collection of articles contain materials of the talks presented at the International Conference "Systems Analysis: Modeling and Control" in memory of Academician A.V. Kryazhimskiy, Moscow, May 31 - June 1, 2018 ...

Added: June 18, 2018

Junca M., Moreno-Franco H. A., Pérez J. et al., Advances in Applied Probability 2019 Vol. 51 No. 3 P. 633-666

We consider de Finetti’s problem for spectrally one-sided Lévy risk models with control strategies that are absolutely continuous with respect to the Lebesgue measure. Furthermore, we consider the version with a constraint on the time of ruin. To characterize the solution to the aforementioned models, we first solve the optimal dividend problem with a terminal ...

Added: March 25, 2018

Belov A., Andrianova O., IFAC-PapersOnLine 2017 Vol. 50 No. 1 P. 15471-15476

The paper deals with linear discrete-time time-invariant (LDTI) descriptor systems with norm-bounded parametric uncertainties. The input signal is supposed to be a “colored” noise with bounded mean anisotropy. Sufficient conditions of anisotropic norm boundedness for such class of systems are given. The control design procedure, based on these conditions, is proposed. Numerical example is given. ...

Added: October 19, 2017

Suboptimal Anisotropy-based Control for Linear Discrete-time Systems with Norm-bounded Uncertainties

Andrianova O., Belov A. A., , in: 2018 14th International Conference "Stability and Oscillations of Nonlinear Control Systems" (Pyatnitskiy's Conference) (STAB). .: IEEE, 2018.. P. 1-4.

In this paper, suboptimal anisotropy-based control
for linear discrete-time systems with norm-bounded parametric uncertainties is designed. State-feedback and static outputfeedback control laws, that guarantee a known level of rejection
of random input disturbances, are constructed. A numerical
example is given. ...

Added: July 16, 2018

Belov A., Andrianova O., IFAC-PapersOnLine 2015 Vol. 48 No. 11 P. 372-377

The paper presents a solution of anisotropy-based suboptimal controller design problem for descriptor systems. The goal is to design a state feedback and full information control for the system such that the closed-loop system is admissible, and its anisotropic norm (mean anisotropy level is set) is bounded by a given positive real value. A numerical ...

Added: October 20, 2017

Belov A. A., Andrianova O., International Journal of Systems Science 2019 Vol. 50 No. 6 P. 1303-1312

This paper deals with a state feedback H ∞ control problem for linear time-invariant discrete-time
descriptor systems with norm-bounded parametric uncertainties. To this end, bounded real lemma
(BRL) is extended on the class of uncertain descriptor systems. The control design procedure based
on the conditions of BRL for uncertain descriptor systems is proposed. Numerical examples are
included to illustrate ...

Added: May 2, 2019

Presnova A., Journal of Physics: Conference Series 2019 No. 1163 P. 1-6

The mathematical model describing the dynamics of HIV in the human body is a nonlinear system of differential equations. This model takes into account the effect of drugs on the body. Thus, it is possible to obtain ”optimal” treatment regimens for patients, which cause minimal harm to the body. In the work for constructing suboptimal ...

Added: March 28, 2019

Belov A. A., Andrianova O., , in: PROCEEDINGS OF 2016 INTERNATIONAL CONFERENCE “STABILITY AND OSCILLATIONS OF NONLINEAR CONTROL SYSTEMS” (PYATNITSKIY’S CONFERENCE). .: IEEE, 2016.. P. 1-4.

In this paper, linear discrete-time systems with
Gaussian input disturbances are considered. Input sequences are
characterized by nonzero mean and bounded mean anisotropy.
Suboptimal control law, which guarantees stability of the closedloop system and boundedness of its anisotropic norm, is designed. ...

Added: February 6, 2018

Belov A., Andrianova O., , in: Proceedings of the 2017 21st International Conference on Process Control, PC 2017. .: IEEE, 2017.. P. 12-17.

In this paper, anisotropy-based control problem with
regional pole assignment for descriptor systems is investigated.
The purpose is to find a state-feedback control law, which guarantees desirable disturbance attenuation level from stochastic
input with unknown covariance to controllable output of the
closed-loop system, and ensures, that all finite eigenvalues of
the closed-loop system belong to the given region inside the
unit ...

Added: February 6, 2018

Romero-Severson E., Bulla I., Serea O. S. et al., Mathematical Medicine and Biology 2018 Vol. 35 No. 4 P. 469-491

This article is about numerical control of HIV propagation. The contribution of the article is threefold: first, a novel model of HIV propagation is proposed; second, the methods from numerical optimal control are successfully applied to the developed model to compute optimal control profiles; finally, the computed results are applied to the real problem yielding ...

Added: October 8, 2019

Andrianova O., Belov A. A., European Journal of Control 2018 No. 42 P. 38-48

In this paper, linear discrete-time time-invariant (LDTI) normal and descriptor systems with norm-bounded parametric uncertainties are under consideration. The input signal is supposed to be a “colored” noise with bounded
known mean anisotropy level (spectral color). The conditions of anisotropic
norm boundedness for such class of systems are derived. The algorithm is
based on convex optimization technique. A ...

Added: June 10, 2018

Manita L., Ronzhina M., , in: Оптимальное управление и дифференциальные игры : Материалы Международной конференции, посвященной 110-летиюсо дня рождения Льва Семеновича Понтрягина, Москва, 12–14 декабря 2018 г.. .: М.: МАКС Пресс, 2018.. P. 171-172.

We consider a linear model of a rotating Timoshenko beam. We show that for some initial conditions, the solutions of the minimization problem for the deviation of the beam from the equilibrium state have Fuller singularities. ...

Added: May 15, 2020

Belov A., Andrianova O., IFAC-PapersOnLine 2017 Vol. 50 No. 1 P. 15483-15487

This paper deals with a state feedback H∞ control problem for linear discrete-time time-invariant (LDTI) uncertain descriptor systems. Considered systems contain norm-bounded parametric uncertainties in all matrices. Bounded real lemma (BRL) for descriptor systems with all known matrices is extended on the class of uncertain systems. The control design procedure based on the conditions of BRL for ...

Added: October 20, 2017

Kelbert M., Moreno-Franco H. A., SIAM Journal on Control and Optimization 2019 Vol. 57 No. 3 P. 2185-2213

In this paper, we guarantee the existence and uniqueness (in the almost everywhere
sense) of the solution to a Hamilton-Jacobi-Bellman (HJB) equation with gradient
constraint and a partial integro-di erential operator whose Levy measure has bounded
variation. This type of equation arises in a singular control problem, where the state
process is a multidimensional jump-di usion with jumps of ...

Added: February 13, 2019

Azhmyakov V., Abstract and Applied Analysis 2016 Vol. 2016 Article 2091526

This paper proposes a new theoretic approach to a specific interaction of continuous and discrete dynamics in switched control systems known as a Zeno behaviour. We study executions of switched control systems with affine structure that admit infinitely many discrete transitions on a finite time interval. Although the real world processes do not present the ...

Added: October 30, 2021

Andrianova O., Белов А. А., , in: 2019 23rd International Conference on System Theory, Control and Computing (ICSTCC). .: IEEE, 2019.. P. 455-460.

The problem of robust admissibilization with guaranteed random disturbance attenuation level for discrete-time
time-invariant (LDTI) descriptor systems with norm-bounded
uncertainties is considered. The input disturbance is supposed
to be a stationary Gaussian sequence with bounded mean
anisotropy level. The solutions to analysis and robust statefeedback control problems are formulated in terms of matrix
inequalities. The obtained conditions are convex over ...

Added: December 5, 2019

Presnova A., Afanasiev V., , in: IFAC-PapersOnLine. Vol. 51. Issue 32.: Editions Elsevier, 2018.. Ch. 45. P. 428-433.

The problem of optimal control is formulated for a class of nonlinear objects that can be represented as objects with a linear structure and parameters that depend on the state. The linear structure of the transformed nonlinear system and the quadratic functional of quality allow for the synthesis of optimal control, i.e. parameters of the ...

Added: November 4, 2018

Andrianova O., Наука и образование: научное издание МГТУ им. Н.Э. Баумана 2014 P. 160-174

The paper presents a novel concept of anisotropy-based analysis for linear discrete-time descriptor systems with nonzero-mean input signals. Descriptor systems are a general case of normal systems. They contain both differential (difference) equations and algebraic equations. In this paper, the algorithm for mean anisotropy computation of the Gaussian stationary random sequence with nonzero mean (we ...

Added: October 20, 2017

Robust Anisotropy-Based Control for Uncertain Descriptor Systems with Transient Response Constraints

Andrianova O., Belov A. A., IFAC-PapersOnLine 2018 Vol. 51 No. 32 P. 515-520

In this paper, a problem of robust anisotropy-based control with regional pole assignment for descriptor systems with norm-bounded parametric uncertainties is concerned. The goal is to find a state-feedback control law, which guarantees desirable disturbance attenuation level from stochastic input with unknown covariance to controllable output of the closed-loop system, and ensures, that all finite ...

Added: December 16, 2018

Junca M., Moreno-Franco H. A., Pérez J., Risks 2019 Т. 7 № 1 С. 1-24

We consider the optimal bail-out dividend problem with fixed transaction cost for a Lévy risk model with a constraint on the expected present value of injected capital. To solve this problem, we first consider the optimal bail-out dividend problem with transaction cost and capital injection and show the optimality of reflected (c_1,c_2) -policies. We then ...

Added: September 27, 2019