arXiv subjects

Roman Chertovskih

Publications and source records attributed to Roman Chertovskih.

At least 19 recordsLinked to original sources

arXiv2026

Time-optimal elevator control with higher-order state constraints: analysis and computation of boundary contacts

In this paper, we consider the classical time-optimal elevator problem in the presence of higher-order state constraints. The main contribution is a constructive indirect solution framework based on a Pontryagin Maximum Principle specifically formulated for higher-order constrained systems. First, we derive specialized optimality conditions and analyze the resulting structure of extremal trajectories. Second, we show that the infinite-dimensional optimal control problem can be transformed into a finite-dimensional system of nonlinear algebraic equations involving switching times, boundary-contact times, and multiplier parameters. This provides a computationally efficient procedure for calculating candidate optimal trajectories using standard nonlinear equation solvers. Third, we characterize the geometry of boundary contacts and explain the emergence of contact-chattering phenomena in higher-order constrained systems. In particular, we show that normal extremals cannot evolve along the constraint boundary for a positive amount of time, although sequences of boundary contacts may accumulate indefinitely. The proposed approach is demonstrated on a fourth-order elevator model, and the computed solutions are independently verified using a direct IPOPT-based optimization method.

math.OC↗

arXiv2026

Predicting Radial Velocities from Rossiter-McLaughlin Time Series Observations

The Rossiter-McLaughlin (RM) effect produces apparent radial velocity (RV) shifts through line-profile distortions caused by a transiting planet blocking different regions of the rotating stellar surface. Because the underlying orbital RV trend can be estimated from out-of-transit observations, RM sequences provide a controlled laboratory for studying flux-induced RV variations. We compiled a sample of 1171 ESPRESSO observations of 13 targets obtained during 21 RM observing nights and trained machine-learning models to reconstruct a reference RV trend from observed RVs, line-profile diagnostics, and activity indicators. Predictive performance varied substantially among stars and depended on both the strength of the RM signal and the similarity of the target star to the training sample. Applications to Sun-as-a-star observations and Proxima Centauri recovered known periodicities but did not fully remove the activity-induced variability. Larger and more diverse datasets will be required to assess the potential of this approach for mitigating activity-induced RV signals.

physics.gen-ph↗

arXiv2026

Transition to chaos in two-dimensional Rayleigh-Bénard convection: the role of the magnetic field

The impact of an externally imposed magnetic field on numerical simulations of two-dimensional Rayleigh-Bénard convection (RBC) is investigated. Initially, the RBC model is examined in the absence of a magnetic field to establish a baseline. Then, a background magnetic field is introduced, and its influence on the transition to chaos is explored. For the purely hydrodynamic case and a range of the reduced Rayleigh number, the system exhibits traveling rolls which, after an attractor-merging crisis, give way to chaotic traveling rolls. Upon imposing a background magnetic field, there is a notable increase in the occurrence of traveling roll dynamics. Furthermore, the presence of the magnetic field favors the splitting/breaking of convective rolls, indicating a possible mechanism for transition to two-dimensional turbulence, with the structure of the convection cell being disrupted. A detailed analysis of the velocity field reveals that the collision between a saddle point and the center of a convective roll restores the system's original topology, with two symmetric kinetic vortices. During this collision, a magnetic vortex splits in two as a result of a magnetic reconnection. This behavior occurs intermittently in time.

physics.flu-dyn↗

arXiv2026

Bilevel optimization for smart irrigation control: a framework for enhancing water-use efficiency in agriculture

Global warming has intensified water scarcity, posing a critical challenge for the agricultural sector, where seasonal demand often leads to significant wastage. This work addresses the need for efficient water management by proposing a smart irrigation control system based on a bilevel optimization algorithm. The framework aims to minimize water consumption across multiple fields simultaneously or, under supply constraints, to distribute available water equitably to minimize deviations from required levels. To achieve this, the problem is modeled hierarchically: the upper level acts as a central controller managing daily water limits and field-wise allocation, while the lower level acts as a centralized scheduler determining the optimal cooperative irrigation execution across all fields. This structure ensures that both global resource constraints and local irrigation needs are met efficiently. Preliminary results from digital simulation tools suggest that the proposed framework significantly improves water-use efficiency and supports sustainable irrigation practices, particularly in water-constrained scenarios.

math.OC↗

arXiv2026

Exact Cost-Increment Formula for Optimal Control of Semilinear Evolution Equations

We address optimal control of semilinear evolution equations on Banach spaces with finitely many control channels, a framework encompassing a broad class of infinite-dimensional dynamical systems, arising in many applications. For this setting, we derive an exact and global formula quantifying the increment of the cost functional with respect to an arbitrary reference control. This identity enables the design of monotone descent algorithms that require no linearization or step-size tuning. We further establish the existence of optimal controls and propose a practical sample-and-hold realization of the descent step suitable for numerical implementation. The effectiveness of the method is demonstrated on a controlled reaction-diffusion equation.

math.OC↗

arXiv2025

Indirect methods in optimal control on Banach spaces

This work focuses on indirect descent methods for optimal control problems governed by nonlinear ordinary differential equations in Banach spaces, viewed as abstract models of distributed dynamics. As a reference line, we revisit the classical schemes, rooted in Pontryagin's maximum principle, and highlight their sensitivity to local convexity and lack of monotone convergence. We then develop an alternative method based on exact cost-increment formulas and finite-difference probes of the terminal cost. We show that our method exhibits stable monotone convergence in numerical analysis of an Amari-type neural field control problem.

math.OC↗

arXiv2025

Optimizing Image Retrieval with an Extended b-Metric Space

This article provides a new approach on how to enhance data storage and retrieval in the Query By Image Content Systems (QBIC) by introducing the ${\rm NEM}_σ$ distance measure, satisfying the relaxed triangle inequality. By leveraging the concept of extended $b$-metric spaces, we address complex distance relationships, thereby improving the accuracy and efficiency of image database management. The use of ${\rm NEM}_σ$ facilitates better scalability and accuracy in large-scale image retrieval systems, optimizing both the storage and retrieval processes. The proposed method represents a significant advancement over traditional distance measures, offering enhanced flexibility and precision in the context of image content-based querying. Additionally, we take inspiration from ice flow models using ${\rm NEM}_σ$ and ${\rm NEM}_r$, adding dynamic and location-based factors to better capture details in images.

math.OC↗

arXiv2025

Convolutional Attention in Betting Exchange Markets

This study presents the implementation of a short-term forecasting system for price movements in exchange markets, using market depth data and a systematic procedure to enable a fully automated trading system. The case study focuses on the UK to Win Horse Racing market during the pre-live stage on the world's leading betting exchange, Betfair. Innovative convolutional attention mechanisms are introduced and applied to multiple recurrent neural networks and bi-dimensional convolutional recurrent neural network layers. Additionally, a novel padding method for convolutional layers is proposed, specifically designed for multivariate time series processing. These innovations are thoroughly detailed, along with their execution process. The proposed architectures follow a standard supervised learning approach, involving model training and subsequent testing on new data, which requires extensive pre-processing and data analysis. The study also presents a complete end-to-end framework for automated feature engineering and market interactions using the developed models in production. The key finding of this research is that all proposed innovations positively impact the performance metrics of the classification task under examination, thereby advancing the current state-of-the-art in convolutional attention mechanisms and padding methods applied to multivariate time series problems.

q-fin.ST↗

arXiv2025

From Few-Shot Optimal Control to Few-Shot Learning

We present an approach to solving unconstrained nonlinear optimal control problems for a broad class of dynamical systems. This approach involves lifting the nonlinear problem to a linear ``super-problem'' on a dual Banach space, followed by a non-standard ``exact'' variational analysis, -- culminating in a descent method that achieves rapid convergence with minimal iterations. We investigate the applicability of this framework to mean-field control and discuss its perspectives for the analysis of information propagation in self-interacting neural networks.

math.OC↗

arXiv2024

What makes a steady flow to favour kinematic magnetic field generation: A statistical analysis

To advance our understanding of the magnetohydrodynamic (MHD) processes in liquid metals, in this paper we propose an approach combining the classical methods in the dynamo theory based on numerical simulations of the partial differential equations governing the evolution of the magnetic field with the statistical methods. In this study, we intend to answer the following ``optimization'' question: Can we find a statistical explanation what makes a flow to favour magnetic field generation in the linear regime (i.e. the kinematic dynamo is considered), where the Lorenz force is neglected? The flow is assumed to be steady and incompressible, and the magnetic field generation is governed by the magnetic induction equation. The behaviour of its solution is determined by the dominant (i.e. with the largest real part) eigenvalue of the magnetic induction operator. Considering an ensemble of 2193 randomly generated flows, we solved the kinematic dynamo problem and performed an attempt to find a correlation between the dominant eigenvalue and the standard quantities used in hydrodynamics -- vorticity and kinetic helicity. We have found that there is no visible relation between the property of the flow to be a kinematic dynamo and these quantities. This enables us to conclude that the problem requires a more elaborated approach to ``recognize'' if the flow is a dynamo or not; we plan to solve it using contemporary data-driven approach based on deep neural networks.

physics.flu-dyn↗

arXiv2024

Fixed Point Theory Analysis of a Lambda Policy Iteration with Randomization for the Ćirić Contraction Operator

We apply methods of the fixed point theory to a Lambda policy iteration with a randomization algorithm for weak contractions mappings. This type of mappings covers a broader range than the strong contractions typically considered in the literature, such as Ćirić contraction. Specifically, we explore the characteristics of reinforcement learning procedures developed for feedback control within the context of fixed point theory. Under relatively general assumptions, we identify the sufficient conditions for convergence with a probability of one in infinite-dimensional policy spaces.

math.OC↗

arXiv2024

On Minimum-Dispersion Control of Nonlinear Diffusion Processes

This work collects some methodological insights for numerical solution of a "minimum-dispersion" control problem for nonlinear stochastic differential equations, a particular relaxation of the covariance steering task. The main ingredient of our approach is the theoretical foundation called $\infty$-order variational analysis. This framework consists in establishing an exact representation of the increment ($\infty$-order variation) of the objective functional using the duality, implied by the transformation of the nonlinear stochastic control problem to a linear deterministic control of the Fokker-Planck equation. The resulting formula for the cost increment analytically represents a "law-feedback" control for the diffusion process. This control mechanism enables us to learn time-dependent coefficients for a predefined Markovian control structure using Monte Carlo simulations with a modest population of samples. Numerical experiments prove the vitality of our approach.

math.OC↗

arXiv2024

Optimal control of diffusion processes: $\infty$-order variational analysis and numerical solution

We tackle a nonlinear optimal control problem for a stochastic differential equation in Euclidean space and its state-linear counterpart for the Fokker-Planck-Kolmogorov equation in the space of probabilities. Our approach is founded on a novel concept of local optimality surpassing Pontryagin's minimum, originally crafted for deterministic optimal ensemble control problems. A key practical outcome is a rapidly converging numerical algorithm, which proves its feasibility for problems involving Markovian and open-loop strategies.

math.OC↗

arXiv2024

Transition to chaos and magnetic field generation in rotating Rayleigh-Bénard convection

Hydrodynamic and magnetohydrodynamic convective attractors in three-dimensional rotating Rayleigh-Bénard convection are studied numerically by varying the Taylor and Rayleigh numbers as control parameters. First, an analysis of hydrodynamic attractors and their bifurcations is conducted, where routes to chaos via quasiperiodicity are identified. Second, the behaviour of the magnetohydrodynamic system is investigated by introducing a seed magnetic field and measuring its growth or decay as a function of the Taylor number, while keeping the Rayleigh number fixed. Analysis of the attractors shows that rotation has a significant impact on magnetic field generation in Rayleigh-Bénard convection, with the critical magnetic Prandtl number changing nonmonotonically with the rotation rate. It is argued that a nonhysteretic blowout bifurcation with on-off intermittency is responsible for the transitions to dynamo.

physics.flu-dyn↗

arXiv2023

Optimal control of nonlocal continuity equations: numerical solution

The paper addresses an optimal ensemble control problem for nonlocal continuity equations on the space of probability measures. We admit the general nonlinear cost functional, and an option to directly control the nonlocal terms of the driving vector field. For this problem, we design a descent method based on Pontryagin's maximum principle (PMP). To this end, we derive a new form of PMP with a decoupled Hamiltonian system. Specifically, we extract the adjoint system of linear nonlocal balance laws on the space of signed measures and prove its well-posedness. As an implementation of the designed descent method, we propose an indirect deterministic numeric algorithm with backtracking. We prove the convergence of the algorithm and illustrate its modus operandi by treating a simple case involving a Kuramoto-type model of a population of interacting oscillators.

math.OC↗

arXiv2023

Optimal control of distributed ensembles with application to Bloch equations

Motivated by the problem of designing robust composite pulses for Bloch equations in the presence of natural perturbations, we study an abstract optimal ensemble control problem in a probabilistic setting with a general nonlinear performance criterion. The model under study addresses mean-field dynamics described by a linear continuity equation in the space of probability measures. For the resulting optimization problem, we derive an exact representation of the increment of the cost functional in terms of the flow of the driving vector field. Relying on the exact increment formula, a descent method is designed that is free of any internal line search. The numerical method is applied to solve new control problems for distributed ensembles of Bloch equations.

math.OC↗

arXiv2023

Optimization of external stimuli for populations of theta neurons via mean-field feedback control

We study a problem of designing ``robust'' external excitations for control and synchronization of an assembly of homotypic harmonic oscillators representing so-called theta neurons. The model of theta neurons (Theta model) captures, in main, the bursting behavior of spiking cells in the brain of biological beings, enduring periodic oscillations of the electric potential in their membrane. We study the following optimization problem: to design an external stimulus (control), which steers all neurons of a given population to their desired phases (i.e., excites/slows down its spiking activity) with the highest probability. This task is formulated as an optimal mean-field control problem for the local continuity equation in the space of probability measures. To solve this problem numerically, we propose an indirect deterministic descent method based on an exact representation of the increment (infinite-order variation) of the objective functional. We discuss some aspects of practical realization of the proposed method, and provide results of numerical experiments.

math.OC↗

arXiv2022

Gaussian-type density bounds for solutions to multidimensional backward SDEs and application to gene expression

We obtain upper and lower Gaussian-type bounds on the density of each component $Y^i_t$ of the solution $Y_t$ to a multidimensional non-Markovian backward SDE. Our approach is based on the Nourdin-Viens formula and a stochastic version of Wazewski's theorem on the positivity of the components of a solution to an ODE. Furthermore, we apply our results to stochastic gene expression; namely, we estimate the density of the law of the amount of protein generated by a gene in a gene regulatory network.

math.PR↗