研究者詳細 - 伊藤　博

論文 - 伊藤　博

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Vaccination with Input-to-State Stability for SIR Model of Epidemics 査読有り

Hiroshi Ito

Proceedings of the IEEE Conference on Decision and Control 2021-December 2812 - 2817 2021年12月

担当区分：筆頭著者,　責任著者記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）

2021年12月13日 - 2021年12月17日

Vaccination control for SIR models of epidemics is studied in the framework of input-to-state stability. Two types of feedback controllers are proposed for mass vaccination of immigrants and inhabitants. In addition to asymptotic stability which is global in the state space, this paper demonstrates guarantees of input-to-state stability with respect to variation of flow rate of immigrants and newborns. One type of the proposed control laws uses ISS Lyapunov functions. The other modifies the control laws by focusing the reduction of peaks of infected population within the ISS guarantees.

DOI： 10.1109/CDC45484.2021.9683439

Scopus

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A construction of strict Lyapunov functions for a bilinear balancing model 査読有り国際誌

Hiroshi Ito

IFAC-PapersOnLine for The 3rd IFAC Conf. Modelling, Identification and Control of Nonlinear Systems ( IFAC ) 54 ( 14 ) 161 - 166 2021年10月

担当区分：筆頭著者,　責任著者記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）

Japan 2022年09月15日 - 2022年09月17日

This paper focuses on a two-dimensional compartmental model which is linear except for bilinear terms of balancing kinetics. It is an equation of Lotka-Volterra type, but its structure is not symmetric like the predator-prey equation. This paper elucidates fundamental challenges in non-local stability analysis of the model. In particular, obstacles in constructing strict Lyapunov functions are discussed. A method consisting of tilting and semi-global construction is presented to overcome the challenges. Its benefit is highlighted from the viewpoint of input-to-state stability with respect to inflow perturbation.

DOI： 10.1016/j.ifacol.2021.10.346

Scopus

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Input-to-state stability and Lyapunov functions with explicit domains for SIR model of infectious diseases 査読有り国際誌

Ito H.

Discrete and Continuous Dynamical Systems - Series B ( American Institute of Mathematical Sciences ) 26 ( 9 ) 5171 - 5196 2021年09月

担当区分：筆頭著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

This paper demonstrates input-to-state stability (ISS) of the SIR model of infectious diseases with respect to the disease-free equilibrium and the endemic equilibrium. Lyapunov functions are constructed to verify that both equilibria are individually robust with respect to perturbation of newborn/ immigration rate which determines the eventual state of populations in epidemics. The construction and analysis are geometric and global in the space of the populations. In addition to the establishment of ISS, this paper shows how explicitly the constructed level sets reect the ow of trajectories. Essential obstacles and keys for the construction of Lyapunov functions are elucidated. The proposed Lyapunov functions which have strictly negative derivative allow us to not only establish ISS, but also get rid of the use of LaSalle's invariance principle and popular simplifying assumptions.

DOI： 10.3934/dcdsb.2020338

Scopus

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Preface for Special issue on SICE Annual Conference 2020 招待有り査読有り国際誌

Noboru Sakamoto, Shigemasa Takai, Hiroshi Ito

SICE Journal of Control, Measurement, and System Integration ( SICE ) 14 ( 2 ) 1 - 1 2021年06月

A Strict Smooth Lyapunov Function and Input-to-State Stability of SIR Model 査読有り

Hiroshi Ito

Proceedings of the American Control Conference ( IEEE ) 2021-May 4811 - 4816 2021年05月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）

アメリカ 2021年05月25日 - 2021年05月28日

This paper shows that the SIR model of infectious diseases is input-to-state stable (ISS) with respect to the net flow of susceptible individuals into the region in both disease-free and epidemic situations. The key development is the construction of a continuously differentiable strict Lyapunov function. Firstly, for asymptotic stability, this paper clarifies that a continuously differentiable Lyapunov function can deduce the stability on the whole state space even if its derivative is not strictly negative. Secondly, it is demonstrated that a new idea of modifying the Lyapunov function to render its derivative strictly negative allows one to detect an appropriate margin to prove ISS of the SIR model. The accomplishment is based on the pursuit of a Lyapunov function which is not entirely separable into components. It contrasts with previously studied and popular Lyapunov functions which are incapable of assessing robustness properties such as ISS.

DOI： 10.23919/ACC50511.2021.9482900

Scopus

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Signed Small-Gain Criteria Amenable to Asymmetry with Respect to Equilibria in Establishing iISS of Networks 査読有り

Ito H.

Proceedings of the IEEE Conference on Decision and Control 2020-December 6278 - 6284 2020年12月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）

This paper proposes a framework of signed small-gain criteria which are automatically amenable to asymmetry of gain-type dissipation with respect to equilibria. In theory and practice, the asymmetry has been avoided via over-bounding by symmetrization, which often results in unreasonably demanding or negative answers in stability, stabilization, robustness and robustification of dynamical systems. Natural systems are composed in accordance with the principle of conservation, and employ mechanisms which are more versatile than linearity. Exact energy balance is exhibited through nonlinear mechanisms, but it is not symmetric with respect to equilibria, due to the nonlinearity. Stability and robustness embedded in such energy balance cannot be detected after symmetrization. The signed small-gain methodology proposed in this paper provides powerful tools that absorb the asymmetry automatically in establishing integral input-to-stability of dynamical networks.

DOI： 10.1109/CDC42340.2020.9304236

Scopus

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Strong Integral Input-to-State Stability of Nonlinear Networks through Balancing Kinetics 招待有り査読有り

Ito H.

Proceedings of the IEEE Conference on Decision and Control 2020-December 482 - 487 2020年12月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）

This paper proposes a methodology for establishing stability of nonlinear dynamical networks through balancing mechanisms that appear in system models explicitly. In addition to global asymptotic stability of equilibria, the notion of strong integral input-to-state stability (Strong iISS) is employed to address robustness of the networks with respect to disturbances and noises in the presence of saturation nonlinearities forming balancing relations. Conservation is covered as the exact balance. Unlike network small-gain criteria known in the literature of iISS, the developed criteria do not lump the balancing relations. The formulation covers positive networks and networks of iISS systems.

DOI： 10.1109/CDC42340.2020.9304155

Scopus

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Interpreting models of infectious diseases in terms of integral input-to-state stability 査読有り

Ito H.

Mathematics of Control, Signals, and Systems 32 ( 4 ) 611 - 631 2020年12月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（学術雑誌）

© 2020, The Author(s), under exclusive licence to Springer-Verlag London Ltd. part of Springer Nature. This paper aims to develop a system-theoretic approach to ordinary differential equations which deterministically describe dynamics of prevalence of epidemics. The equations are treated as interconnections in which component systems are connected by signals. The notions of integral input-to-state stability (iISS) and input-to-state stability (ISS) have been effective in addressing nonlinearities globally without domain restrictions in analysis and design of control systems. They provide useful tools of module-based methods integrating characteristics of component systems. This paper expresses fundamental properties of models of infectious diseases and vaccination through the language of iISS and ISS of components and whole systems. The systematic treatment is expected to facilitate development of effective schemes of controlling the disease spread via non-conventional Lyapunov functions.

DOI： 10.1007/s00498-020-00272-w

Scopus

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Max- and Sum-Separable Lyapunov Functions for Monotone Networks with Balancing Kinetics 査読有り

Ito H.

2020 59th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2020 742 - 747 2020年09月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）

© 2020 The Society of Instrument and Control Engineers - SICE. This paper investigates max- and sum-separable Lyapunov functions for monotone networks exhibiting balancing kinematics. Input-to-state stability is sought for internal stability and disturbance attenuation generalizing operator-norms nonlinearly. For linear networks it is known that max- and sum-separable Lyapunov functions can be expressed analytically with right- and left-eigenvectors. This paper discusses extensions of the formulas to nonlinear networks. The main target is non-identical balancing kinematics for which analytical solutions have not been available. It is shown that max- and sum-separable construction is no more given by eigenvectors, but it still accepts closed-form expressions.

Scopus

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Feedback control on immigration to reduce spread of infectious diseases with an ISS guarantee 査読有り

Ito H.

2020 59th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2020 736 - 741 2020年09月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）

© 2020 The Society of Instrument and Control Engineers - SICE. The capability of non-medical strategies to reduce spread of infectious diseases is limited, but evidently quarantining and isolation methods have been effective to slow the transmission. This paper studies regulations on immigration which manipulates the number of individuals entering the area. The immigration including newborns cannot be zero to maintain human societies or ecological systems, but a decision can be made to slow or delay the entering individuals when it is effective to reduce the spread peaks. This paper proposes a feedback control strategy with theoretical guarantees of non-local convergence to the steady state which the society targets. It is proved that small errors in the manipulation of immigration cause only small deviations and they never result in tragedies in terms of input-to-state stability.

Scopus

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Feedback balancing between vaccination and quarantine for disease control: a simulation for COVID-19 in Japan 査読有り

Hajime Nakata, Hiroshi Ito.

60th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2020 ( SICE ) 1252 - 1257 2020年09月

担当区分：責任著者記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）

Japan 2020年09月08日 - 2020年09月10日

Smaller and negative exponents in Lyapunov functions for interconnected iISS systems 査読有り国際誌

Hiroshi Ito

The 21st IFAC World Congress 1 6365 - 6370 2020年07月

Asymptotic and tracking guarantees in interval observer design for systems with unmeasured polytopic nonlinearitiess 査読有り国際誌

Hiroshi Ito, Thach Ngoc Dinh

The 21st IFAC World Congress 1 5084 - 5089 2020年07月

A complete characterization of integral input-to-state stability and its small-gain theorem for stochastic systems 査読有り国際誌

Hiroshi Ito

IEEE Transactions on Automatic Control 65 ( 7 ) 3039 - 3052 14 pages 2020年07月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（学術雑誌）

For stochastic systems, this article develops a Lyapunov-type characterization of integral input-to-state stability (iISS), which is truly parallel to the deterministic one. In contrast to preceding results, this article allows stochastic noise to be active globally in the state space. Deriving pathwise bounds of stochastic processes is the original key idea and it leads to new techniques to unify Lyapunov-type characterization of iISS with that of input-to-state stability (ISS). The ISS test becomes a special case of the iISS test completely, which forms a stochastic counterpart of the popular iISS/ISS framework for deterministic nonlinear systems analysis and design. The usefulness of the developed iISS/ISS characterizations is substantiated by utilizing them to consolidate stochastic versions of small-gain criteria to establish stability of interconnected systems without restricting noise effects to bounded domains. The framework of integral noise-to-state stability is also made useful by allowing the global stochastic noise.

DOI： 10.1109/TAC.2019.2946203

Scopus

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Preface for Special issue on SICE Annual Conference 2019 招待有り査読有り国際誌

Tanaka Hideyuki, Hiroshi Ito

SICE Journal of Control, Measurement, and System Integration ( SICE ) 13 ( 3 ) 49 - 49 2020年05月

Technical committee on nonlinear systems and control 招待有り査読有り国際誌

Ito H.

IEEE Control Systems 40 ( 2 ) 15 - 18 2020年04月

Interval observer of minimal error dynamics 査読有り

Ito H.

Automatica 113 2020年03月

担当区分：責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

© 2019 Elsevier Ltd This paper proposes a simple interval observer which can generate tighter interval estimates of variables in transient states than the standard interval observer. The simple nonlinear dynamics shrinks the estimated intervals to true state variables at the maximum velocity in the absence of disturbances. In the presence of bounded disturbances, ultimate bounds of the interval estimates are given under the standard assumption for interval observer design.

DOI： 10.1016/j.automatica.2019.108794

Scopus

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Asymptotic and tracking guarantees in interval observer design for systems with unmeasured polytopic nonlinearities 招待有り査読有り

Ito H., Dinh T.N.

IFAC-PapersOnLine 53 ( 2 ) 5010 - 5015 2020年01月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）

For a class of nonlinear systems subject to disturbances, an observer is proposed to estimate time-varying intervals in which their state variables are guaranteed to stay all the time. The objective is to effectively deal with nonlinearities depending on unmeasured variables which have been usually treated as uncertainty in observer design. Focusing on nonlinearities in a polytopic form, this paper shows how an interval observer can replace nonlinearities in unmeasured variables by nonlinearities in estimated intervals. Theoretical guarantees and simulation comparisons are presented to demonstrate that the use of interval-dependent nonlinearities gives better estimates than the use of an overbounding observer.

DOI： 10.1016/j.ifacol.2020.12.1099

Scopus

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Smaller and negative exponents in Lyapunov functions for interconnected iISS systems 査読有り

Ito H.

IFAC-PapersOnLine 53 6287 - 6292 2020年01月

担当区分：筆頭著者記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）

For integral input-to-state stable (iISS) systems, stability of their interconnections can be established through a small-gain condition. Unlike input-to-state stable (ISS) systems, iISS systems admit gain functions only in limited ranges. Thus, composing a Lyapunov function which is valid globally is instrumental for addressing iISS. A Lyapunov function which is popular in the iISS framework proves the stability of interconnected systems whenever the small-gain condition is satisfied. However, it is hardly practical since its nonlinearities are often artificial and involve astonishingly large exponents. This paper drastically reduces the exponents analytically and numerically. This paper also extends the exponents to negative numbers, and demonstrates that two-sided exponents allow one to avoid unnecessary complicated Lyapunov functions.

DOI： 10.1016/j.ifacol.2020.12.1747

Scopus

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SIR感染モデルに基づく流入個体数規制の不確かさに対するISS保証の一解析

伊藤博

自動制御連合講演会講演論文集 ( 自動制御連合講演会 ) 63 ( 0 ) 389 - 392 2020年01月

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