arXiv subjects

Alexander Medvedev

Publications and source records attributed to Alexander Medvedev.

At least 19 recordsLinked to original sources

arXiv2026

Output Corridor Impulsive Control of First-order Continuous System with Non-local Attractivity Analysis

This paper addresses the design of an impulsive controller for a continuous scalar time-invariant linear plant that constitutes the simplest conceivable model of chemical kinetics. The model is ubiquitous in process control as well as pharmacometrics and readily generalizes to systems of Wiener structure. Given the impulsive nature of the feedback, the control problem formulation is particularly suited to discrete dosing applications in engineering and medicine, where both doses and inter-dose intervals are manipulated. Since the feedback controller acts at discrete time instants and employs both amplitude and frequency modulation, whereas the plant is continuous, the closed-loop system exhibits hybrid dynamics featuring complex nonlinear phenomena. The problem of confining the plant output to a predefined corridor of values is considered. The method at the heart of the proposed approach is to design a stable periodic solution, called a 1-cycle, whose one-dimensional orbit coincides with the predefined corridor. Conditions ensuring local and global attractivity of the 1-cycle are established. As a numerical illustration of the proposed approach, the problem of intravenous paracetamol dosing is considered.

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arXiv2026

Solvability of the Output Corridor Control Problem by Pulse-Modulated Feedback

The problem of maintaining the output of a positive time-invariant single-input single-output system within a predefined corridor of values is treated. For third-order plants possessing a certain structure, it is proven that the problem is always solvable under stationary conditions by means of pulse-modulated feedback. The obtained result is utilized to assess the feasibility of patient-specific pharmacokinetic-pharmacodynamic models with respect to patient safety. A population of Wiener models capturing the dynamics of a neuromuscular blockade agent is studied to investigate whether or not they can be driven into the desired output corridor by clinically acceptable sequential drug doses (boluses). It is demonstrated that low values of a parameter in the nonlinear pharmacodynamic part lie behind the detected model infeasibility.

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arXiv2025

Design of Cycles by Impulsive Feedback: Application to Discrete Dosing

The task of maintaining a predefined level of effect in a dynamical plant by applying periodic control actions often arises in, e.g., process control and medicine. When the state variables of the plant represent the concentrations of chemical substances and the control action constitutes an instantaneous introduction of a certain quantity of a chemical or drug, this control setup is referred to as a (discrete) dosing problem. The present paper examines an amplitude- and frequency-modulated impulsive controller that, under stationary conditions, generates a desired sequence of uniform and equidistant control impulses based on continuous measurements of the output of a smooth positive nonlinear time-invariant single-input single-output plant with Wiener structure. The controller design method is based on constructing and stabilizing the fixed point of a discrete map that describes the evolution of the state vector of the continuous plant between successive impulsive control action instants. Stability of the fixed point ensures the existence of a basin of attraction around the stationary trajectory, where solutions of the closed-loop system converge to the stationary solution after perturbation. The convergence rate is determined by the slopes of the amplitude and frequency modulation functions of the impulsive controller. The proposed controller is applied to dosing of the drug \emph{atracurium} in closed-loop neuromuscular blockade, and its performance is evaluated on a {database of patient-specific pharmacokinetic-pharmacodynamic models estimated from clinical data

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arXiv2025

Tissue Activation Calculation in Dual-lead Deep Brain Stimulation

Deep Brain Stimulation (DBS) is a well-established neurosurgical treatment aiming at symptom alleviation in a range of neurological and psychiatric diseases. Computational models of DBS are widely used to investigate the effects of stimulation on neural tissue, to explore stimulation targets and sweetspots, and ultimately, to aid clinicians in the DBS programming by calculating the stimulation parameters. Commonly, DBS is performed bilaterally, i.e. with one lead in each brain hemisphere, where computational models are solved independently for one lead at a time. This paper treats scenarios where multiple DBS leads are implanted in close proximity to one another, resulting in interacting electrical fields and, therefore, potentially overlapping stimulation spreads. In particular, a global dual-lead model is compared to approximations derived from single-lead approaches in a cohort of twelve multiple sclerosis (MS) tremor patients. It is concluded that simple superposition of volumes of tissue activated (VTAs) underestimates activation, while superposition of electric fields or activating functions leads to overestimation. It is concluded that given close proximity of DBS leads, the VTA cannot be computed individually as stimulation fields exhibit significant and complex interaction. The approach is extended to modeling two obsessive compulsive disorder patients with medially placed leads, where similar VTA discrepancies as in the MS patient cohort are observed.

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arXiv2025

Nonlinear dynamics in pulse-modulated feedback drug dosing

Pulse-modulated feedback is utilized in drug dosing to mimic sustained over a longer period of time manual discrete dose administration, the latter is in contrast with continuous drug infusion. The intermittent mode of dosing calls for a hybrid (continuous-discrete) modeling of the closed-loop system, where the pharmacokinetics and pharmacodynamics of the drug are captured by differential equations whereas the control law is described by difference equations. Hybrid dynamics are highly nonlinear which complicates formal design of pulse-modulated feedback. This paper demonstrates complex nonlinear dynamical phenomena arising in a simple control system of dosing a neuromuscular blockade agent in anesthesia. Along with the nominal periodic regimen, undesirable nonlinear behaviors, i.e. periodic solutions of high multiplicity, multistability, as well as deterministic chaos, are shown to exist. It is concluded that design of feedback drug dosing algorithms based on a hybrid paradigm has to be informed by a thorough bifurcation analysis in order to secure patient safety.

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arXiv2025

Mixed Integer Linear Programming for Active Contact Selection in Deep Brain Stimulation

Deep brain stimulation (DBS) programming remains a complex and time-consuming process, requiring manual selection of stimulation parameters to achieve therapeutic effects while minimizing adverse side-effects. This study explores mathematical optimization for DBS programming, using functional subdivisions of the subthalamic nucleus (STN) to define the desired activation profile. A Mixed Integer Linear Programming (MILP) framework is presented allowing for dissimilar current distribution across active contacts. MILP is compared to a Linear Programming (LP) approach in terms of computational efficiency and activation accuracy. Results from ten Parkinson's disease patients treated with DBS show that while MILP better matches the predefined stimulation target activation profile, LP solutions more closely resemble clinically applied settings, suggesting the profile may not fully capture clinically relevant patterns. Additionally, MILP's limitations are discussed, including its reliance on precisely defined target regions and its computational burden for larger target sets.

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arXiv2024

TuneS: Patient-specific model-based optimization of contact configuration in deep brain stimulation

Objective: The objective of this study is to develop and evaluate a systematic approach to optimize Deep Brain Stimulation (DBS) parameters, addressing the challenge of identifying patient-specific settings and optimal stimulation targets for various neurological and mental disorders. Methods: TuneS, a novel pipeline to predict clinically optimal DBS contact configurations based on predefined targets and constraints, is introduced. The method relies upon patient-specific models of stimulation spread and extends optimization beyond traditional neural structures to include automated, model-based targeting of streamlines. Results: Initial findings show that both the STN motor subdivision and STN motor streamlines are consistently engaged under clinical settings, while regions of avoidance receive minimal stimulation. Given these findings, the value of model-based contact predictions for assessing stimulation targets while observing anatomical constraints is demonstrated at the example of ten Parkinson's disease patients. The predicted settings were generally found to achieve higher target coverages while providing a better trade-off between maximizing target coverage and minimizing stimulation of regions associated with side effects. Conclusion: TuneS shows promise as a research tool, enabling systematic assessment of DBS target effectiveness and facilitating constraint-aware optimization of stimulation parameters. Significance: The presented pipeline offers a pathway to improve patient-specific DBS therapies and contributes to the broader understanding of effective DBS targeting strategies.

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arXiv2024

Fiber Activation by Bipolar Stimulation in Deep Brain Stimulation: A Patient Case Study

Deep Brain Stimulation (DBS) is a therapy widely used for treating the symptoms of neurological disorders. Electrical pulses are chronically delivered in DBS to a disease-specific brain target via a surgically implanted electrode. The stimulating contact configuration, stimulation polarity, as well as amplitude, frequency, and pulse width of the DBS pulse sequence are utilized to optimize the therapeutic effect. In this paper, the utility of therapy individualization by means of patient-specific mathematical modeling is investigated with respect to a specific case of a patient diagnosed with Essential Tremor (ET). Two computational models are compared in their ability to elucidate the impact of DBS stimulation on the dentato-rubrothalamic tract: (i) a conventional model of Volume of Tissue Activated (VTA) and (ii) a well-established neural fiber activation modeling framework known as OSS-DBS. The simulation results are compared with tremor measured in the patient under different DBS settings using a smartphone application. The findings of the study highlight that temporally static VTA models do not adequately describe the differences in the outcomes of bipolar stimulation settings with switched polarity, whereas neural fiber activation models hold potential in this regard. However, it is noted that neither of the investigated models fully accounts for the measured symptom pattern, particularly regarding a bilateral effect produced by unilateral stimulation.

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arXiv2024

Stability Properties of the Impulsive Goodwin's Oscillator in 1-cycle

The Impulsive Goodwin's Oscillator (IGO) is a mathematical model of a hybrid closed-loop system. It arises by closing a special kind of continuous linear positive time-invariant system with impulsive feedback, which employs both amplitude and frequency pulse modulation. The structure of IGO precludes the existence of equilibria, and all its solutions are oscillatory. With its origin in mathematical biology, the IGO also presents a control paradigm useful in a wide range of applications, in particular dosing of chemicals and medicines. Since the pulse modulation feedback mechanism introduces significant nonlinearity and non-smoothness in the closedloop dynamics, conventional controller design methods fail to apply. However, the hybrid dynamics of IGO reduce to a nonlinear, time-invariant discrete-time system, exhibiting a one-to-one correspondence between periodic solutions of the original IGO and those of the discrete-time system. The paper proposes a design approach that leverages the linearization of the equivalent discrete-time dynamics in the vicinity of a fixed point. A simple and efficient local stability condition of the 1-cycle in terms of the characteristics of the amplitude and frequency modulation functions is obtained.

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arXiv2023

Impulsive feedback control for dosing applications

This paper addresses a design procedure of pulse-modulated feedback control solving a dosing problem defined for implementation in a manual mode. Discrete dosing, as a control strategy, is characterized by exerting control action on the plant in impulsive manner at certain time instants. Dosing applications appear primarily in chemical industry and medicine where the control signal constitutes a sequence of (chemically or pharmacologically) active substance quantities (doses) administered to achieve a desired result. When the doses and the instants of their administration are adjusted as functions of some measured variable, a feedback control loop exhibiting nonlinear dynamics arises. The impulsive character of the interaction between the controller and the plant makes the resulting closed-loop system non-smooth. Limitations of the control law with respect to control goals are discussed. An application of the approach at hand to neuromuscular blockade in closed-loop anesthesia is considered in a numerical example.

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arXiv2023

Output corridor control via design of impulsive Goodwin's oscillator

In the Impulsive Goodwin's oscillator (IGO), a continuous positive linear time-invariant (LTI) plant is controlled by an amplitude- and frequency-modulated feedback into an oscillating solution. Self-sustained oscillations in the IGO model have been extensively used to portray periodic rhythms in endocrine systems, whereas the potential of the concept as a controller design approach still remains mainly unexplored. This paper proposes an algorithm to design the feedback of the IGO so that the output of the continuous plant is kept (at stationary conditions) within a pre-defined corridor, i.e. within a bounded interval of values. The presented framework covers single-input single-output LTI plants as well as positive Wiener and Hammerstein models that often appear in process and biomedical control. A potential application of the developed impulsive control approach to a minimal Wiener model of pharmacokinetics and pharmacodynamics of a muscle relaxant used in general anesthesia is discussed.

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arXiv2023

Neural Fiber Activation in Unipolar vs Bipolar Deep Brain Stimulation

Deep Brain Stimulation (DBS) is an established and powerful treatment method in various neurological disorders. It involves chronically delivering electrical pulses to a certain stimulation target in the brain in order to alleviate the symptoms of a disease. Traditionally, the effect of DBS on neural tissue has been modeled based on the geometrical intersection of the static Volume of Tissue Activated (VTA) and the stimulation target. Recent studies suggest that the Dentato-Rubro-Thalamic Tract (DRTT) may serve as a potential common underlying stimulation target for tremor control in Essential Tremor (ET). However, clinical observations highlight that the therapeutic effect of DBS, especially in ET, is strongly influenced by the dynamic DBS parameters such as pulse width and frequency, as well as stimulation polarity. This study introduces a computational model to elucidate the effect of the stimulation signal shape on the DRTT under neural input. The simulation results suggest that achieving a specific pulse amplitude threshold is necessary before eliciting the therapeutic effect through adjustments in pulse widths and frequencies becomes feasible. Longer pulse widths proved more likely to induce firing, thus requiring a lower stimulation amplitude. Additionally, the modulation effect of bipolar configurations on neural traffic was found to vary significantly depending on the chosen stimulation polarity and the direction of neural traffic. Further, bipolar configurations demonstrated the ability to selectively influence firing patterns in different fiber tracts.

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arXiv2023

Security Allocation in Networked Control Systems under Stealthy Attacks

This paper considers the problem of security allocation in a networked control system under stealthy attacks. The system is comprised of interconnected subsystems represented by vertices. A malicious adversary selects a single vertex on which to conduct a stealthy data injection attack with the purpose of maximally disrupting a distant target vertex while remaining undetected. Defense resources against the adversary are allocated by a defender on several selected vertices. First, the objectives of the adversary and the defender with uncertain targets are formulated in a probabilistic manner, resulting in an expected worst-case impact of stealthy attacks. Next, we provide a graph-theoretic necessary and sufficient condition under which the cost for the defender and the expected worst-case impact of stealthy attacks are bounded. This condition enables the defender to restrict the admissible actions to dominating sets of the graph representing the network. Then, the security allocation problem is solved through a Stackelberg game-theoretic framework. Finally, the obtained results are validated through a numerical example of a 50-vertex networked control system.

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arXiv2023

Closed-form expressions for the pure time delay in terms of the input and output Laguerre spectra

The pure time delay operator is considered in continuous and discrete time under the assumption of the input signal being integrable (summable) with square. By making use of a discrete convolution operator with polynomial Markov parameters, a common framework for handling the continuous and discrete case is set. Closed-form expressions for the delay value are derived in terms of the Laguerre spectra of the output and input signals. The expressions hold for any feasible value of the Laguerre parameter and can be utilized for e.g. building time-delay estimators that allow for non-persistent input. A simulation example is provided to illustrate the principle of Laguerre-domain time delay modeling and analysis.

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arXiv2023

Design of the Impulsive Goodwin's Oscillator: A Case Study

The impulsive Goodwin's oscillator (IGO) is a hybrid model composed of a third-order continuous linear part and a pulse-modulated feedback. This paper introduces a design problem of the IGO to admit a desired periodic solution. The dynamics of the continuous states represent the plant to be controlled, whereas the parameters of the impulsive feedback constitute design degrees of freedom. The design objective is to select the free parameters so that the IGO exhibits a stable 1-cycle with desired characteristics. The impulse-to-impulse map of the oscillator is demonstrated to always possess a positive fixed point that corresponds to the desired periodic solution; the closed-form expressions to evaluate this fixed point are provided. Necessary and sufficient conditions for orbital stability of the 1-cycle are presented in terms of the oscillator parameters and exhibit similarity to the problem of static output control. An IGO design procedure is proposed and validated by simulation. The nonlinear dynamics of the designed IGO are reviewed by means of bifurcation analysis. Applications of the design procedure to dosing problems in chemical industry and biomedicine are envisioned.

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arXiv2023

Robust One-Step Estimation of Impulsive Time Series

The paper deals with the estimation of a signal model in the form of the output of a continuous linear time-invariant system driven by a sequence of instantaneous impulses, i.e. an impulsive time series. This modeling concept arises in, e.g., endocrinology when episodic hormone secretion events and elimination rates are simultaneously estimated from sampled hormone concentration measurements. The pulsatile secretion is modeled with a train of Dirac impulses constituting the input to a linear plant, which represents stimulated hormone secretion and elimination. A previously developed one-step estimation algorithm effectively resolves the trade-off between data fit and impulsive input sparsity. The present work improves the algorithm so that it requires less manual tuning and produces more accurate results through the use of an information criterion. It is also extended to handle outliers and unknown basal levels that are commonly recognized issues in biomedical data. The algorithm performance is evaluated both theoretically and experimentally on synthetic and clinical data.

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arXiv2023

Optimal Detector Placement in Networked Control Systems under Cyber-attacks with Applications to Power Networks

This paper proposes a game-theoretic method to address the problem of optimal detector placement in a networked control system under cyber-attacks. The networked control system is composed of interconnected agents where each agent is regulated by its local controller over unprotected communication, which leaves the system vulnerable to malicious cyber-attacks. To guarantee a given local performance, the defender optimally selects a single agent on which to place a detector at its local controller with the purpose of detecting cyber-attacks. On the other hand, an adversary optimally chooses a single agent on which to conduct a cyber-attack on its input with the aim of maximally worsening the local performance while remaining stealthy to the defender. First, we present a necessary and sufficient condition to ensure that the maximal attack impact on the local performance is bounded, which restricts the possible actions of the defender to a subset of available agents. Then, by considering the maximal attack impact on the local performance as a game payoff, we cast the problem of finding optimal actions of the defender and the adversary as a zero-sum game. Finally, with the possible action sets of the defender and the adversary, an algorithm is devoted to determining the Nash equilibria of the zero-sum game that yield the optimal detector placement. The proposed method is illustrated on an IEEE benchmark for power systems.

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arXiv2023

Cycles in Impulsive Goodwin's Oscillators of Arbitrary Order

Existence of periodical solutions, i.e. cycles, in the Impulsive Goodwin's Oscillator (IGO) with the continuous part of an arbitrary order m is considered. The original IGO with a third-order continuous part is a hybrid model that portrays a chemical or biochemical system composed of three substances represented by their concentrations and arranged in a cascade. The first substance in the chain is introduced via an impulsive feedback where both the impulse frequency and weights are modulated by the measured output of the continuous part. It is shown that, under the standard assumptions on the IGO, a positive periodic solution with one firing of the pulse-modulated feedback in the least period also exists in models with any m >= 1. Furthermore, the uniqueness of this 1-cycle is proved for the IGO with m <= 10 whereas, for m > 10, the uniqueness can still be guaranteed under mild assumptions on the frequency modulation function.

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