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Modeling of Cerebral Blood Flow Autoregulation Using Mathematical Control Theory
Mathematics. 2022. Vol. 10. No. 12. Article 2060.
Golubev A., Kovtanyuk A., Lampe R.
A mathematical model of cerebral blood flow in the form of a dynamical system is studied.
The cerebral blood flow autoregulation modeling problem is treated as a nonlinear control problem
and the potential and applicability of the nonlinear control theory techniques are analyzed in this
respect. It is shown that the cerebral hemodynamics model in question is differentially flat. Then,
the integrator backstepping approach combined with barrier Lyapunov functions is applied to
construct the control laws that recover the cerebral autoregulation performance of a healthy human.
Simulation results confirm the good performance and flexibility of the suggested cerebral blood flow
autoregulation design. The conducted research should enrich our understanding of the mathematics
behind the cerebral blood flow autoregulation mechanisms and medical treatments to compensate
for impaired cerebral autoregulation, e.g., in preterm infants.
Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407
In this paper, we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that, in some cases, this boundary is sharp. ...
Added: May 19, 2026
Жакупов О. Б., European Journal of Mathematics 2025 Vol. 11 Article 84
We provide examples of smooth three-dimensional Fano complete intersections of degree 2, 4, 6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute ...
Added: May 18, 2026
Lerman L. M., Turaev D. V., Regular and Chaotic Dynamics 2026 Vol. 31 No. 3 P. 349–369
We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic H´enonlike map and study bifurcations of the ...
Added: May 15, 2026
Aleskerov F. T., Yakuba V. I., Khutorskaya O. et al., Springer, 2026.
The book contains new models of bibliometric analysis based on centrality measures in network analysis, pattern analysis and stability analysis. A distinctive feature of these centrality measures is that they account for the parameters of vertices and group influence of vertices to a vertex. This reveals specific groups of publications, authors, terms, journals and affiliations ...
Added: May 15, 2026
Kuptsov P., Panyushev A., Stankevich N., Chaos 2026 Vol. 36 No. 5 Article 053138
We develop a machine-learning approach to reproduce the behavior of two versions of the van der Pol oscillator exhibiting a subcritical Andronov–Hopf bifurcation, with or without a codimension-2 Bautin point. We construct a neural-network model that functions as a recur rent map and train it on short segments of oscillator trajectories. The results show that, ...
Added: May 15, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Lebedev V., Journal of Mathematical Analysis and Applications 2026 Vol. 563 No. 2 Article 130787
It is known that for every continuous real-valued
function $f$ on the circle $\mathbb T=\mathbb R/2\pi\mathbb Z$ there exists a
change of variable, i.e., a self-homeomorphism $h$ of $\mathbb T$, such that
the superposition $f\circ h$ is in the Sobolev space $W_2^{1/2}(\mathbb T)$.
We obtain new results on simultaneous improvement of functions by a single
change of variable in relation ...
Added: May 14, 2026
Blokh A., Oversteegen L., Selinger N. et al., Arnold Mathematical Journal 2025 Vol. 12 No. 1 P. 1–40
We describe a model for the boundary of the connectedness locus of the parameter space of cubic symmetric polynomials. We show that there exists a monotone continuous function from the connectedness locus to the model which is a homeomorphism if the former is locally connected. ...
Added: May 13, 2026
Petrov I., Автоматика и телемеханика 2026 № 6 С. 82–118
Системам связанных агентов и сетевому управлению посвящено большое число отечественных и зарубежных исследований. Исторически, наибольший интерес в теории управления возникал к усредняющим системам и, в частности, к задаче консенсуса. Однако сетевое взаимодействие может характеризоваться более специфическими функциями, отражающими зависимость от действий соседей по сети, что особенно явно проявляется в моделях стратегического взаимодействия на сети, которое ...
Added: May 12, 2026
М.: ООО «Макс Пресс», 2026.
В настоящем сборнике представлены тезисы докладов участников семинара "Интеграция основного и дополнительного физико-математического образования", проходившего 11 февраля 2026 года в ГБОУ Школа №2007 ФМШ г. москвы, а также другие публикации, посвящённые вопросам дополнительного физико-математического образования. ...
Added: May 11, 2026
Novikov R., V. N. Sivkin, Inverse Problems 2026 Vol. 42 No. 4 Article 045009
We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for
the Helmholtz equation in an exterior region in Rd, d ⩾ 2. In this region, we consider a hyperplane X with sufficiently large distance s from the origin in Rd. We give two-point local formulas
for approximate recovering the radiation ...
Added: May 11, 2026
Hecht M., Hofmann P., Wicaksono D. et al., IMA Journal of Numerical Analysis 2026 Vol. 00 P. 1–30
Recent advances in Bernstein—Walsh theory have extended Bernstein’s Theorem to multiple dimensions, stating that a multivariate function can be approximated with a geometric rate in a downward-closed polynomial space if and only if it is analytic in a generalized Bernstein polyellipse. To compute approximations of this class of functions—which we term Bos–Levenberg–Trefethen–(BLT) functions—we extend the ...
Added: May 11, 2026
Kelbert M., Kalimulina E. Y., Entropy 2026 Vol. 28 Article 536
We study binary hypothesis testing for i.i.d. observations under a multiplicative context
weight. For the optimal weighted total loss, defined as the sum of weighted type-I and typeII losses, we prove the logarithmic asymptotic L∗n = exp{−nDwC (P,Q) + o(n)}, n →∞, where Dw
C is the weighted Chernoff information. The single-letter form of the exponent
relies on ...
Added: May 7, 2026
N. Belousov, L. Cherepanov, Derkachov S. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 44
We prove equivalence of two integral representations for the wave functions of hyperbolic Calogero–Sutherland system. For this we study two families of Baxter operators related to hyperbolic Calogero–Sutherland and rational Ruijsenaars models; the first one as a limit from hyperbolic Ruijsenaars system, while the second one independently. Besides, computing asymptotics of integral representations and also ...
Added: May 6, 2026
Alexeeva T., Kuznetsov N., Lobachev M. et al., , in: Recent Developments in Model-Based and Data-Driven Methods for Advanced Control and DiagnosisIssue 467: ACD 2022.: Cham: Springer, 2023. P. 225–234.
Added: January 10, 2024
Alexey E. Golubev, , in: 16th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB).: IEEE, 2022. P. 1–3.
A mathematical model of cerebral blood flow in the form of a dynamical system is considered. The cerebral blood flow
regulation problem is treated as a control problem. A nonlinear dynamics inversion based approach is applied to construct the relevant control laws which should help us understand the mathematics behind the cerebral blood flow autoregulation mechanism ...
Added: February 4, 2023
A.E. Golubev, Дальневосточный математический журнал 2022 Vol. 22 No. 2 P. 170–175
A mathematical model of cerebral blood flow in the form of a system of nonlinear ordinary differential equations is studied. The cerebral blood flow autoregulation modeling problem is formulated as an output regulation automatic control problem. The nonlinear dynamics inversion based approach is applied to reveal the controllability properties of the model and construct the ...
Added: February 4, 2023
Golubev A., Glazkov T. V., , in: Proceedings of the Workshop on Mathematical Modeling and Scientific Computing: Focus on Complex Processes and Systems — dedicated to the memory of Nikolai Botkin (MMSC 2020).: CEUR Workshop Proceedings, 2020. Ch. 2783 P. 113–127.
Added: November 18, 2021
Golubev A., Utkina N. V., , in: Proceedings of 2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference), STAB 2020.: IEEE, 2020.
In this note we deal with analytical time polynomial based motion planning considerations. A class of differentially flat affine dynamical systems that can be rendered as a set of second-order controlled subsystems is analyzed. It is shown that state and input box constraints can be readily accounted for by proper choice of time of motion ...
Added: November 18, 2021
Golubev A., Nay T., Gorbunov A. V. et al., AIP Conference Proceedings 2019 Vol. 2116 Article 380004
In this note we deal with control of a quadrocopter in a horizontal plane under state constraints in the form of a labyrinth. An algorithm to construct the programmed motion of the quadrocopter in a flat labyrinth is proposed. A full rigid body model of the flying vehicle that doesn't assume smallness of the Euler ...
Added: November 18, 2021
Glazkov T. V., Golubev A., Gorbunov A. V. et al., AIP Conference Proceedings 2019 Vol. 2116 Article 380003
This paper deals with trajectory tracking control of a quadcopter in a horizontal plane. A full rigid body model of the flying vehicle that doesn't assume smallness of the Euler angles is considered. For synthesis of the tracking control the nonlinear dynamics inversion approach is used. Three different control strategies with restrictions on the orientation ...
Added: November 18, 2021
Glazkov T. V., Golubev A., AIP Conference Proceedings 2019 Vol. 2195 Article 020007
In this paper we deal with nonlinear control design for Parrot Mambo or Parrot Rolling Spider quadcopters using Simulink Support Package for Parrot Minidrones. A full rigid body model of the flying vehicle that doesn't assume smallness of the Euler angles is considered. For synthesis of the control the nonlinear dynamics inversion and integrator backstepping ...
Added: November 18, 2021
Golubev A., Krishchenko A. P., Utkina N. V., IFAC-PapersOnLine 2019 Vol. 52 No. 16 P. 724–729
This paper deals with missile longitudinal dynamics control. The angle of attack tracking problem is considered for an unpowered flight phase of a short range tail-controlled missile with the zero engine thrust. For the control synthesis, a simplified missile dynamics model that includes the actuator dynamics is used. The tracking control law is designed using ...
Added: November 18, 2021
Golubev A., Botkin N. D., Krishchenko A. P., IFAC-PapersOnLine 2019 Vol. 52 No. 16 P. 712–717
In this paper, we deal with the problem of aircraft take-off control in the presence of a windshear. A simplified point mass nonlinear model of aircraft dynamics assuming the flight in a vertical plane is used. A reference trajectory is constructed to satisfy the altitude, relative path inclination and relative velocity state constraints. An integrator ...
Added: November 18, 2021