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Medvedev, A. (2024). Closed-form expressions for the pure time delay in terms of the input and output Laguerre spectra. Automatica, 159, Article ID 111366.
Open this publication in new window or tab >>Closed-form expressions for the pure time delay in terms of the input and output Laguerre spectra
2024 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 159, article id 111366Article in journal (Refereed) Published
Abstract [en]

The pure time delay operator is considered in continuous and discrete time under the assumption of the input signal being integrable (summable) with square. Then the input and the output signals are uniquely given by their Laguerre spectra. It is shown that a discrete convolution operator with polynomial Markov parameters constitutes a common description of the delay operator in the continuous and discrete case. Closed-form expressions for the delay value in terms of the output and input Laguerre spectra are derived. 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 with perfect disturbance rejection.

Place, publisher, year, edition, pages
Elsevier, 2024
Keywords
Delay systems, Infinite-dimensional systems, Time-invariant systems
National Category
Control Engineering
Identifiers
urn:nbn:se:uu:diva-518033 (URN)10.1016/j.automatica.2023.111366 (DOI)001106929700001 ()
Funder
Swedish Research Council, 2019-04451
Available from: 2023-12-19 Created: 2023-12-19 Last updated: 2023-12-19Bibliographically approved
Proskurnikov, A. V., Runvik, H. & Medvedev, A. (2024). Cycles in Impulsive Goodwin's Oscillators of arbitrary order☆. Automatica, 159, Article ID 111379.
Open this publication in new window or tab >>Cycles in Impulsive Goodwin's Oscillators of arbitrary order☆
2024 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 159, article id 111379Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2024
Keywords
Discontinuous control, Hybrid and switched systems modeling
National Category
Control Engineering Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:uu:diva-518106 (URN)10.1016/j.automatica.2023.111379 (DOI)001107814400001 ()
Available from: 2024-01-02 Created: 2024-01-02 Last updated: 2024-01-02Bibliographically approved
Marin, R., Runvik, H., Medvedev, A. & Engblom, S. (2023). Bayesian Monitoring of COVID-19 in Sweden. Epidemics, 45, Article ID 100715.
Open this publication in new window or tab >>Bayesian Monitoring of COVID-19 in Sweden
2023 (English)In: Epidemics, ISSN 1755-4365, E-ISSN 1878-0067, Vol. 45, article id 100715Article in journal (Refereed) Published
Abstract [en]

In an effort to provide regional decision support for the public healthcare, we design a data-driven compartment-based model of COVID-19 in Sweden. From national hospital statistics we derive parameter priors, and we develop linear filtering techniques to drive the simulations given data in the form of daily healthcare demands. We additionally propose a posterior marginal estimator which provides for an improved temporal resolution of the reproduction number estimate as well as supports robustness checks via a parametric bootstrap procedure.

From our computational approach we obtain a Bayesian model of predictive value which provides important insight into the progression of the disease, including estimates of the effective reproduction number, the infection fatality rate, and the regional-level immunity. We successfully validate our posterior model against several different sources, including outputs from extensive screening programs. Since our required data in comparison is easy and non-sensitive to collect, we argue that our approach is particularly promising as a tool to support monitoring and decisions within public health.

Significance: Using public data from Swedish patient registries we develop a national-scale computational model of COVID-19. The parametrized model produces valuable weekly predictions of healthcare demands at the regional level and validates well against several different sources. We also obtain critical epidemiological insights into the disease progression, including, e.g., reproduction number, immunity and disease fatality estimates. The success of the model hinges on our novel use of filtering techniques which allows us to design an accurate data-driven procedure using data exclusively from healthcare demands, i.e., our approach does not rely on public testing and is therefore very cost-effective.

Place, publisher, year, edition, pages
Elsevier, 2023
Keywords
Bayesian forecasting, Public health situation awareness, Data-driven epidemics, Compartment-based model, Kalman filtering
National Category
Computational Mathematics Public Health, Global Health, Social Medicine and Epidemiology
Research subject
Scientific Computing
Identifiers
urn:nbn:se:uu:diva-473444 (URN)10.1016/j.epidem.2023.100715 (DOI)001077959200001 ()
Projects
eSSENCE - An eScience Collaboration
Funder
VinnovaSwedish Research Council FormasSwedish Research Council
Available from: 2022-04-27 Created: 2022-04-27 Last updated: 2023-10-26Bibliographically approved
Bro, V. & Medvedev, A. (2023). Continuous and discrete Volterra-Laguerre models with  delay for modeling of smooth pursuit eye movements. IEEE Transactions on Biomedical Engineering, 70(1), 97-104
Open this publication in new window or tab >>Continuous and discrete Volterra-Laguerre models with  delay for modeling of smooth pursuit eye movements
2023 (English)In: IEEE Transactions on Biomedical Engineering, ISSN 0018-9294, E-ISSN 1558-2531, Vol. 70, no 1, p. 97-104Article in journal (Refereed) Published
Abstract [en]

The mathematical modeling of the human smooth pursuit system from eye-tracking data is considered. Recently developed algorithms for the estimation of Volterra-Laguerre (VL) models with explicit time delay are applied in continuous and discrete time formulations to experimental data collected from Parkinsonian patients in different medication states and healthy controls. The discrete VL model with an explicit time delay and the method for its estimation are first introduced in this paper. The estimated parameters of a second-order VL model are shown to capture the ocular dynamics both in health and disease. The possibility of including the estimated time delay, along with the VL kernel parameters, into the set of the model parameters is explored. The results obtained in continuous VL modeling are compared with those in discrete time to discern the effects due to the sampling enforced by the eye tracker used for data acquisition.

Place, publisher, year, edition, pages
IEEE, 2023
National Category
Control Engineering
Identifiers
urn:nbn:se:uu:diva-460499 (URN)10.1109/TBME.2022.3185669 (DOI)000936179400010 ()35737630 (PubMedID)
Funder
Vinnova, 2018-01963Swedish Research Council, 2019-04451
Available from: 2021-12-07 Created: 2021-12-07 Last updated: 2023-04-03Bibliographically approved
Abdalmoaty, M. & Medvedev, A. (2023). Continuous Time-Delay Estimation From Sampled Measurements. Paper presented at 22nd World Congress of the International Federation of Automatic Control (IFAC), July 9-14, 2023, Yokohama, Japan. IFAC-PapersOnLine, 56(2), 6982-6987
Open this publication in new window or tab >>Continuous Time-Delay Estimation From Sampled Measurements
2023 (English)In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 56, no 2, p. 6982-6987Article in journal (Refereed) Published
Abstract [en]

An algorithm for continuous time-delay estimation from sampled output data and a known input of finite energy is presented. The continuous time-delay modeling allows for the estimation of subsample delays. The proposed estimation algorithm consists of two steps. First, the continuous Laguerre spectrum of the output (delayed) signal is estimated from discretetime (sampled) noisy measurements. Second, an estimate of the delay value is obtained via a Laguerre domain model using a continuous-time description of the input. The second step of the algorithm is shown to be intrinsically biased, the bias sources are established, and the bias itself is modeled. The proposed delay estimation approach is compared in a Monte-Carlo simulation with state-of-the-art methods implemented in time, frequency, and Laguerre domain demonstrating comparable or higher accuracy in the considered scenario.

Place, publisher, year, edition, pages
Elsevier, 2023
Keywords
Delay, continuous systems, sampled data, estimation, bias
National Category
Control Engineering
Identifiers
urn:nbn:se:uu:diva-533845 (URN)10.1016/j.ifacol.2023.10.534 (DOI)001122557300116 ()
Conference
22nd World Congress of the International Federation of Automatic Control (IFAC), July 9-14, 2023, Yokohama, Japan
Funder
Swedish Research Council, 2019-04451
Available from: 2024-07-01 Created: 2024-07-01 Last updated: 2024-07-01Bibliographically approved
Medvedev, A., Proskurnikov, A. V. & Zhusubaliyev, Z. T. (2023). Design of the Impulsive Goodwin's Oscillator: A Case Study. In: 2023 American Control Conference (ACC): . Paper presented at American Control Conference (ACC), MAY 31-JUN 2, 2023, San Diego, CA, USA (pp. 3572-3577). Institute of Electrical and Electronics Engineers (IEEE)
Open this publication in new window or tab >>Design of the Impulsive Goodwin's Oscillator: A Case Study
2023 (English)In: 2023 American Control Conference (ACC), Institute of Electrical and Electronics Engineers (IEEE), 2023, p. 3572-3577Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2023
Series
Proceedings of the American Control Conference, ISSN 0743-1619, E-ISSN 2378-5861
National Category
Control Engineering Computer Sciences Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:uu:diva-512440 (URN)10.23919/ACC55779.2023.10156389 (DOI)001027160303030 ()979-8-3503-2806-6 (ISBN)979-8-3503-2807-3 (ISBN)978-1-6654-6952-4 (ISBN)
Conference
American Control Conference (ACC), MAY 31-JUN 2, 2023, San Diego, CA, USA
Funder
Swedish Research Council, 2019-04451
Available from: 2023-09-26 Created: 2023-09-26 Last updated: 2023-09-26Bibliographically approved
Medvedev, A., Proskurnikov, A. V. & Zhusubaliyev, Z. T. (2023). Design of the Impulsive Goodwin's Oscillator in 1-cycle. Paper presented at 22nd World Congress of the International Federation of Automatic Control (IFAC), July 9-14, 2023, Yokohama, Japan. IFAC-PapersOnLine, 56(2), 6660-6665
Open this publication in new window or tab >>Design of the Impulsive Goodwin's Oscillator in 1-cycle
2023 (English)In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 56, no 2, p. 6660-6665Article in journal (Refereed) Published
Abstract [en]

This paper presents a systematic approach to design a hybrid oscillator that admits an orbitally stable periodic solution of a certain type with pre-defined parameters. The parsimonious structure of the Impulsive Goodwin's oscillator (IGO) is selected for the implementation due to its well-researched rich nonlinear dynamics. The IGO is a feedback interconnection of a positive third-order continuous-time LTI system and a nonlinear frequency and amplitude impulsive modulator. A design algorithm based on solving a bilinear matrix inequality is proposed yielding the slope values of the modulation functions that guarantee stability of the fixed point defining the designed periodic solution. Further, assuming Hill function parameterizaton of the pulse-modulated feedback, the parameters of those rendering the desired stationary properties are calculated. The character of perturbed solutions in vicinity of the fixed point is controlled through localization of the multipliers. The proposed design approach is illustrated by a numerical example. Bifurcation analysis of the resulting oscillator is performed to explore the nonlinear phenomena in vicinity of the designed dynamics.

Place, publisher, year, edition, pages
Elsevier, 2023
Keywords
Hybrid and switched systems modeling, Event-based control, Control in systems biology, Controller constraints and structure, Application of nonlinear analysis and design.
National Category
Control Engineering
Identifiers
urn:nbn:se:uu:diva-533858 (URN)10.1016/j.ifacol.2023.10.368 (DOI)001122557300065 ()
Conference
22nd World Congress of the International Federation of Automatic Control (IFAC), July 9-14, 2023, Yokohama, Japan
Funder
Swedish Research Council, 2019-04451
Available from: 2024-07-01 Created: 2024-07-01 Last updated: 2024-07-01Bibliographically approved
Nguyen, A. T., Coimbatore Anand, S., Teixeira, A. & Medvedev, A. (2023). Optimal Detector Placement in Networked Control Systems under Cyber-attacks with Applications to Power Networks. In: : . Paper presented at 22nd IFAC World Congress: Yokohama, Japan, July 9-14, 2023 (pp. 1820-1826). Elsevier
Open this publication in new window or tab >>Optimal Detector Placement in Networked Control Systems under Cyber-attacks with Applications to Power Networks
2023 (English)Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2023
National Category
Control Engineering
Identifiers
urn:nbn:se:uu:diva-518875 (URN)10.1016/j.ifacol.2023.10.1896 (DOI)
Conference
22nd IFAC World Congress: Yokohama, Japan, July 9-14, 2023
Available from: 2023-12-27 Created: 2023-12-27 Last updated: 2024-01-10Bibliographically approved
Nguyen, A. T., Teixeira, A. & Medvedev, A. (2022). A Single-Adversary-Single-Detector Zero-Sum Game in Networked Control Systems. Paper presented at 9th IFAC Conference on Networked Systems (NECSYS), JUL 05-07, 2022, Zurich, Switzerland. IFAC-PapersOnLine, 55(13), 49-54
Open this publication in new window or tab >>A Single-Adversary-Single-Detector Zero-Sum Game in Networked Control Systems
2022 (English)In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 55, no 13, p. 49-54Article in journal (Refereed) Published
Abstract [en]

This paper proposes a game-theoretic approach to address the problem of optimal sensor placement for detecting cyber-attacks in networked control systems. The problem is formulated as a zero-sum game with two players, namely a malicious adversary and a detector. Given a protected target vertex, the detector places a sensor at a single vertex to monitor the system and detect the presence of the adversary. On the other hand, the adversary selects a single vertex through which to conduct a cyber-attack that maximally disrupts the target vertex while remaining undetected by the detector. As our first contribution, for a given pair of attack and monitor vertices and a known target vertex, the game payoff function is defined as the output-to-output gain of the respective system. Then, the paper characterizes the set of feasible actions by the detector that ensures bounded values of the game payoff. Finally, an algebraic sufficient condition is proposed to examine whether a given vertex belongs to the set of feasible monitor vertices. The optimal sensor placement is then determined by computing the mixed-strategy Nash equilibrium of the zero-sum game through linear programming. The approach is illustrated via a numerical example of a 10-vertex networked control system with a given target vertex.

Place, publisher, year, edition, pages
Elsevier, 2022
Keywords
Cyber-physical security, networked control systems, game theory
National Category
Computer Sciences
Identifiers
urn:nbn:se:uu:diva-485955 (URN)10.1016/j.ifacol.2022.07.234 (DOI)000852734000009 ()
Conference
9th IFAC Conference on Networked Systems (NECSYS), JUL 05-07, 2022, Zurich, Switzerland
Funder
Swedish Research Council, 2018-04396Swedish Research Council, 2021-06316Swedish Foundation for Strategic Research
Available from: 2022-09-30 Created: 2022-09-30 Last updated: 2023-12-28Bibliographically approved
Runvik, H. & Medvedev, A. (2022). Impulsive time series modeling with application to luteinizing hormone data. Frontiers in Endocrinology, 13, Article ID 957993.
Open this publication in new window or tab >>Impulsive time series modeling with application to luteinizing hormone data
2022 (English)In: Frontiers in Endocrinology, E-ISSN 1664-2392, Vol. 13, article id 957993Article in journal (Refereed) Published
Abstract [en]

This work considers the estimation of impulsive time series pertaining to biomedical systems and, in particular, to endocrine ones. We assume a signal model in the form of the output of a continuous linear time-invariant system driven by a sequence of instantaneous impulses, which concept is utilized here, in particular, for modeling of the male reproductive hormone axis. An estimation method to identify the impulsive sequence and the continuous system dynamics from sampled measurements of the output is proposed. Hinging on thorough mathematical analysis, the method improves upon a previously developed least-squares algorithm by resolving the trade-off between model fit and input sparsity, thus removing the need for manual tuning of user-defined estimation algorithm parameters. Experiments with synthetic data and Markov chain Monte-Carlo estimation demonstrate the viability of the proposed method, but also indicate that measurement noise renders the estimation problem ill-posed, as multiple estimates along a curve in the parameter space yield similar fits to data. The method is furthermore applied to clinical luteinizing hormone data collected from healthy males and, for comparability, one female, with similar results. Comparison between the estimated and theoretical elimination rates, as well as simulation of the estimated models, demonstrate the efficacy of the method. The sensitivity of the impulse distribution to the estimated elimination rates is investigated on a subject-specific data subset, revealing that the input sequence and elimination rate estimates can be interdependent. The dose-dependent effect of a selective gonadotropin releasing hormone receptor antagonist on the frequency and weights of the estimated impulses is also analyzed; a significant impact of the medication on the impulse weights is confirmed. To demonstrate the feasibility of the estimation approach for other hormones with pulsatile secretion, the modeling of cortisol data sets collected from three female adolescents was performed.

Place, publisher, year, edition, pages
Frontiers Media S.A., 2022
Keywords
endocrine regulation, impulsive hormone secretion, mathematical modeling, luteinizing hormone, gonadotropin-releasing hormone, ganirelix, cortisol, adrenocorticotropic hormone
National Category
Endocrinology and Diabetes
Identifiers
urn:nbn:se:uu:diva-488930 (URN)10.3389/fendo.2022.957993 (DOI)000885199200001 ()36387902 (PubMedID)
Funder
Swedish Research Council, 2019-04451
Available from: 2022-11-25 Created: 2022-11-25 Last updated: 2024-01-17Bibliographically approved
Projects
Mathematical modeling,analysis and estimation in endocrine systems with pulse-modulated feedback [2012-03153_VR]; Uppsala UniversityControl of the impulsive Goodwin´s oscillator [2015-05256_VR]; Uppsala UniversitySynchronization and entrainment in the impulsive Goodwin´s oscillator [2019-04451_VR]; Uppsala University; Publications
Abdalmoaty, M. & Medvedev, A. (2023). Continuous Time-Delay Estimation From Sampled Measurements. Paper presented at 22nd World Congress of the International Federation of Automatic Control (IFAC), July 9-14, 2023, Yokohama, Japan. IFAC-PapersOnLine, 56(2), 6982-6987Medvedev, A., Proskurnikov, A. V. & Zhusubaliyev, Z. T. (2023). Design of the Impulsive Goodwin's Oscillator in 1-cycle. Paper presented at 22nd World Congress of the International Federation of Automatic Control (IFAC), July 9-14, 2023, Yokohama, Japan. IFAC-PapersOnLine, 56(2), 6660-6665
Patient-specific dynamical modeling and optimization of Deep Brain Stimulation [2020-02901_VR]; Uppsala University
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-6608-250x

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