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## An Algorithm for Optimizing a Nonlinear System, Based on the Behavior of the Hamiltonian on the Optimal Trajectory

P. 359-364.

### In book

Vol. 54. Issue 19. , Elsevier, 2021

Belov A. 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

Belov A. 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

Afanasiev V., Orlov P., Известия РАН. Теория и системы управления 2011 Т. 50 № 3 С. 13-22

An optimal control problem is formulated for a class of nonlinear systems for which there exists a coordinate representation (diffeomorphism) transforming the original system into a system with a linear main part and a nonlinear feedback. In this case the coordinate transformation significantly changes the form of original quadratic functional. The penalty matrices become dependent ...

Added: April 13, 2012

Kulagin N., Lerman L., Malkin A., Communications in Nonlinear Science and Numerical Simulation 2021 Vol. 93 Article 105525

Solitons and cavitons (the latter are localized solutions with singularities) for the nonlocal Whitham equations are studied. The fourth order differential equation for traveling waves with a parameter in front of the fourth derivative is reduced to a reversible Hamiltonian system defined on a two-sheeted four-dimensional space. Solutions of the system which stay on one ...

Added: September 16, 2020

Kazakov A., Lerman L. M., Kulagin N., Mathematical Modeling of Natural Phenomena 2013 Vol. 8 No. 5 P. 155-172

We demonstrate that a piecewise linear slow-fast Hamiltonian system with an equilibrium of the saddle-center type can have a sequence of small parameter values for which a one-round homoclinic orbit to this equilibrium exists. This contrasts with the well-known findings by Amick and McLeod and others that solutions of such type do not exist in ...

Added: March 29, 2015

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

Andrianova O., Belov 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

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

Afanasiev V., Автоматика и телемеханика 2011 № 4 С. 43-56

The theoretical fundamentals for solving the linear quadratic problems may be some times used to design the optimal control actions for the nonlinear systems. The method relying on the Riccati equation with state-dependent coefficients is promising and rapidly developing tools for design of the nonlinear controllers. The set of possible suboptimal solutions is generated by ...

Added: April 13, 2012

Dmitry Tonkonog, / Cornell University. Series math "arxiv.org". 2012.

Let (M,\omega) be a symplectic 2n-manifold and h_1,...,h_n be functionally independent commuting functions on M. We present a geometric criterion for a singular point P\in M (i.e. such that {dh_i(P)}_{i=1}^n are linearly dependent) to be non-degenerate in the sence of Vey-Eliasson.
Then we apply Fomenko's theory to study the neighborhood U of the singular Liouville fiber ...

Added: February 20, 2013

Eminov P. A., Sokolov V. V., RUDN Journal of Mathematics, Information Sciences and Physics 2010 No. 2(2) P. 163-167

The Hamiltonian description of ferrohydrodynamics equation for a ideal nonconducting compressible magnetic fluid with frozen-in magnetization is presented. ...

Added: December 31, 2012

Pechersky E., Pirogov S. A., Schütz G. M. et al., Moscow Mathematical Journal 2019 Vol. 19 No. 1 P. 107-120

We study a class of random processes on N particles which can be interpreted as stochastic model of luminescence. Each particle can stay in one of two states: Excited state or ground state. Any particle at ground state is excited with a constant rate (pumping). The number of excited particles decreases by means of photon emission through ...

Added: December 5, 2020

Presnova A., Качество. Инновации. Образование 2016 № 5 С. 33-41

Built parametric suboptimal control of supply of drugs using the method of algorithmic design in the problem of stabilization of the cells of the immune system in patients with the HIV. A mathematical model describing the dynamics of HIV in the human body represents a nonlinear system of differential equations. In this paper uses the ...

Added: May 25, 2016

Trifonov K., / Cornell University. Series arXiv "math". 2020. No. 3454820.

An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same level of a Hamiltonian and two non-symmetric heteroclinic orbits permuted by the involution. This is a co- dimension one structure and therefore ...

Added: December 26, 2020

Presnova A., Afanasiev V., IFAC-PapersOnLine 2019 Vol. 52 No. 17 P. 42-47

In this paper, we consider the issue of synthesizing optimal control of nonlinear dynamic systems in case of a problem with an unspecified time of the transition process. To solve this problem, an algorithmic method for constructing a suboptimal control is suggested. The basis of this method is the behavior of the Hamiltonian on the ...

Added: January 8, 2020

Belov 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., 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