SANO Hideki | |

Graduate School of System Informatics / Department of System Science | |

Professor | |

Mathematics |

Last Updated :2022/04/15

#### ＜Faculty / Graduate School / Others＞

Graduate School of System Informatics / Department of System Science#### ＜Related Faculty / Graduate School / Others＞

Faculty of Engineering / Department of Computer Science and Systems Engineering, Graduate School of Engineering / Department of Electrical and Electronic Engineering, Center for Computational Social Science (CCSS)

- Office for the Promotion of International Exchange, 2021, Calculua B3
- Office for the Promotion of International Exchange, 2021, Calculua B4
- Graduate School of System Informatics, 2021, Distributed Parameter Systems Theory 1
- Graduate School of System Informatics, 2021, Distributed Parameter Systems Theory 2
- Graduate School of System Informatics / Department of System Science, 2021, Theory of System Innovation
- Graduate School of Engineering, 2021, Advanced Applied Math.I
- Faculty of Engineering, 2021, Theory of Ordinary Differential Equations
- Faculty of Engineering, 2021, Theory of Ordinary Differential Equations
- Faculty of Engineering, 2021, Discrete Mathematics
- Faculty of Engineering, 2021, Vector Analysis

- Elsevier BV, May 2021, Automatica, 127, 109540 - 109540, English
[Refereed]

Scientific journal

- Feb. 2021, 計測自動制御学会論文集, 57 (2), 78 - 85, Japanese
**分布系のカオス同期化を用いた秘匿通信システム**[Refereed]

- Feb. 2020, SIAM Journal on Control and Optimization, 58 (2), 605 - 635, English
**Event-triggered control of infinite-dimensional systems**[Refereed]

Scientific journal

- Jan. 2020, Mathematics of Control, Signals, and Systems, 32 (1), 1 - 58, English
**Sampled-data output regulation of well-posed inﬁnite-dimensional systems with constant reference and disturbance signals**[Refereed]

Scientific journal

- Sep. 2019, 計測自動制御学会論文集, 55 (9), 582 - 584, Japanese
**非局所境界条件に無駄時間を含む1階双曲型システムに対するオブザーバ：誤差システムのL2-安定性**[Refereed]

Scientific journal

- Jul. 2019, Japan Journal of Industrial and Applied Mathematics, 36 (2), 325 - 355, English
[Refereed]

Scientific journal

- Oct. 2018, IFAC-PapersOnLine 51-32 (Proceedings of the 17th IFAC Workshop on Control Applications of Optimization CAO'2018), 456 - 461, English
[Refereed]

International conference proceedings

- Sep. 2018, IEEE Transactions on Automatic Control, 63 (9), 3105 - 3111, English
[Refereed]

Scientific journal

In this paper, we study the problem of stabilizing one-dimensional parabolic systems with input delay. Especially, we consider the case of “distributed control”. The purpose is to derive the stabilizing controller of predictor type in an abstract space, by using a backstepping method combined with the semigroup theory. The use of the semigroup theory makes the proof of continuity of the inverse transformation easy. Also, it is shown that the abstract controller can be actually implemented by using a finite number of eigenvalues and eigenfunctions of the system operator. Finally, a numerical simulation result is presented to demonstrate our design method.

Springer Tokyo, 01 Jul. 2018, Japan Journal of Industrial and Applied Mathematics, 35 (2), 477 - 496, English[Refereed]

Scientific journal

This paper is concerned with reduction of the order of finite-dimensional stabilizing controllers for a class of distributed parameter systems. Since the middle of the 1980s, the design method of finite-dimensional stabilizing controllers of Sakawa type has been generalized for a wider class of parabolic distributed parameter systems with boundary control and/or boundary observation. The controller of Sakawa type consists of two kinds of observers: one is an observer of Luenberger type and the other is an estimator for residual modes. Especially, the latter is called residual mode filter (RMF), and it plays an essential role in the design of finite-dimensional stabilizing controllers when the order of RMF is “sufficiently large”. The purpose of this paper is to propose the design method containing low order RMF. An approach based on stability radius is employed.

Elsevier Ltd, 01 Jun. 2018, Automatica, 92, 49 - 55, English[Refereed]

Scientific journal

This paper is concerned with the stability analysis of a distributed parameter circuit with dynamic boundary condition. The distributed parameter circuit is written by the telegrapher's equations whose boundary condition is described by an ordinary differential equation. First of all, it is shown that, for any physical parameters of the circuit, the system operator generates an exponentially stableC0-semigroup on a Hilbert space. However, it is not clear whether the decay rate of the semigroup is the most precise one. In this paper, the spectral analysis is conducted for the system satisfying the distortionless condition, and it is shown that the semigroup satisfies the spectrum determined growthcondition.

Elsevier B.V., 01 Jan. 2018, Systems and Control Letters, 111, 34 - 39, English[Refereed]

Scientific journal

This paper concerns the H-infinity control problem of a coupled transport-diffusion system with Neumann boundary condition, related to parallel-flow heat exchange process. It is shown that, by using the previous approach for a single diffusion system, the H-infinity control problem can be solved by constructing a residual mode filter (RMF)-based controller which is of finite-dimension. A numerical simulation result is given to demonstrate the validity of the proposed method.

POLSKA AKAD NAUK, POLISH ACAD SCI, DIV IV TECHNICAL SCIENCES PAS, Feb. 2017, BULLETIN OF THE POLISH ACADEMY OF SCIENCES-TECHNICAL SCIENCES, 65 (1), 11 - 19, English[Refereed]

Scientific journal

Background: In mathematical epidemiology, age-structured epidemic models have usually been formulated as the boundary-value problems of the partial differential equations. On the other hand, in engineering, the backstepping method has recently been developed and widely studied by many authors. Methods: Using the backstepping method, we obtained a boundary feedback control which plays the role of the threshold criteria for the prediction of increase or decrease of newly infected population. Under an assumption that the period of infectiousness is same for all infected individuals (that is, the recovery rate is given by the Dirac delta function multiplied by a sufficiently large positive constant), the prediction method is simplified to the comparison of the numbers of reported cases at the current and previous time steps. Results: Our prediction method was applied to the reported cases per sentinel of influenza in Japan from 2006 to 2015 and its accuracy was 0.81 (404 correct predictions to the total 500 predictions). It was higher than that of the ARIMA models with different orders of the autoregressive part, differencing and moving-average process. In addition, a proposed method for the estimation of the number of reported cases, which is consistent with our prediction method, was better than that of the best-fitted ARIMA model ARIMA(1, 1, 0) in the sense of mean square error. Conclusions: Our prediction method based on the backstepping method can be simplified to the comparison of the numbers of reported cases of the current and previous time steps. In spite of its simplicity, it can provide a good prediction for the spread of influenza in Japan.

BIOMED CENTRAL LTD, May 2016, THEORETICAL BIOLOGY AND MEDICAL MODELLING, 13 (1), English[Refereed]

Scientific journal

This paper is concerned with the exponential stability of heat exchangers with delayed boundary feedback. Especially, heat exchangers of counter-flow type/parallel-flow type are treated, where they are respectively described by a coupled hyperbolic equations with time lag in the boundary feedback loop. When time lag does not exist, the exponential stability has been shown for counter-flow type by using the port Hamiltonian approach as well as the spectral analysis, and the conditions for the exponential stability to be assured are given. In this paper, time lag is expressed by using a transport equation, and the port Hamiltonian approach is applied to the whole system. A condition for the system with time lag to be exponentially stable is derived for counter-flow type and parallel-flow type. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

ELSEVIER SCIENCE BV, 2016, IFAC PAPERSONLINE, 49 (8), 43 - 47, English[Refereed]

International conference proceedings

In this paper, we discuss the problem of approximating stability radius appearing in the design procedure of finite-dimensional stabilizing controllers for an infinite-dimensional dynamical system. The calculation of stability radius needs the value of H-infinity-norm of a transfer function whose realization is described by infinite-dimensional operators in a Hilbert space. From the computational point of view, we need to prepare a family of approximate finite-dimensional operators and then to calculate the H-infinity-norm of their transfer functions. However, it is not assured that they converge to the value of H-infinity-norm of the original transfer function. The purpose of this study is to justify the convergence. In a numerical example, we treat parabolic distributed parameter systems with distributed control and distributed/boundary observation.

KYBERNETIKA, 2016, KYBERNETIKA, 52 (5), 824 - 835, English[Refereed]

Scientific journal

In this paper, we consider the H∞ control problem of a coupled transport-diffusion system related to parallel-flow heat exchange process. It is shown that, by using our previous result for a single diffusion system, the H∞ control problem can be solved by constructing a residual mode filter (RMF)-based controller which is of finite-dimension.

01 Oct. 2015, IFAC-PapersOnLine, 28 (25), 50 - 55, English[Refereed]

International conference proceedings

This paper is concerned with the problem of stabilizing one-dimensional parabolic systems related to formations by using finite-dimensional controllers of a modal type. The parabolic system is described by a Sturm-Liouville operator, and the boundary condition is different from any of Dirichlet type, Neumann type, and Robin type, since it contains the time derivative of boundary values. In this paper, it is shown that the system is formulated as an evolution equation with unbounded output operator in a Hilbert space, and further that it is stabilized by using an RMF (residual mode filter)-based controller which is of finite-dimension. A numerical simulation result is also given to demonstrate the validity of the finite-dimensional controller.

POLSKA AKAD NAUK, POLISH ACAD SCI, DIV IV TECHNICAL SCIENCES PAS, Mar. 2015, BULLETIN OF THE POLISH ACADEMY OF SCIENCES-TECHNICAL SCIENCES, 63 (1), 295 - 303, English[Refereed]

Scientific journal

In this paper, we consider the problem of enhancing the stability of a coupled transport-diffusion system related Ito parallel-flow heat exchange process. It is shown that the degree of stability can be enhanced by using a residual mode filter (RMF)-based controller which is of finite-dimension.

01 Feb. 2015, IFAC-PapersOnLine, 28 (1), 755 - 760, English[Refereed]

International conference proceedings

- Nov. 2014, Advances in Differential Equations and Control Processes, 14 (1), 55 - 70, English
**Modal control of linear parabolic systems with internal feedback loop**[Refereed]

Scientific journal

In this paper, we study the finite-dimensional stabilization problem of the cascade consisting of the one-dimensional transport-diffusion process and an unstable Ordinary Differential Equation ( ODE) plant, where the ODE plant is connected with the transport-diffusion process through a filter. The input to the whole system is only Dirichlet boundary input to the transportdiffusion process, and the outputs are the Dirichlet data at the boundary of process domain and the output from the ODE plant. In this paper, we use the latest method and show that the one-dimensional transport-diffusion process with such input and output can be formulated as a system with A.-bounded output operator and direct feedthrough term. It is shown that, under the assumption that the ODE plant is controllable and observable, the finite-dimensional model of the whole system becomes controllable and observable, when the filter mentioned above is a Residual Mode Filter ( RMF). This fact enables us to construct a finite-dimensional stabilizing controller by using an RMF approach.

IEEE, 2014, 2014 INTERNATIONAL CONFERENCE ON MATHEMATICS AND COMPUTERS IN SCIENCES AND IN INDUSTRY (MCSI 2014), 261 - 266, English[Refereed]

International conference proceedings

This paper is concerned with observability and the related problem for a parallel flow two-fluid heat exchanger equation with diffusive terms. The observability results are stated under two kinds of boundary observations and the eigenvalues of the observability gramians are discussed. When one considers the inverse problem of estimating the initial states under the observations, it is expected that the reconstruction of the initial states under the observation at one outlet becomes more difficult than that under the observation at two outlets, from the physical point of view. The purpose of this paper is to explain the intuitive fact by using the eigenvalues of the observability gramians. © 2012 The authors 2012. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Dec. 2013, IMA Journal of Mathematical Control and Information, 30 (4), 463 - 472, English[Refereed]

Scientific journal

This paper is concerned with observability and the related problem for a parallel flow two-fluid heat exchanger equation with diffusive terms. The observability results are stated under two kinds of boundary observations and the eigenvalues of the observability gramians are discussed. When one considers the inverse problem of estimating the initial states under the observations, it is expected that the reconstruction of the initial states under the observation at one outlet becomes more difficult than that under the observation at two outlets, from the physical point of view. The purpose of this paper is to explain the intuitive fact by using the eigenvalues of the observability gramians.

OXFORD UNIV PRESS, Dec. 2013, IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 30 (4), 463 - 472, English[Refereed]

Scientific journal

- Feb. 2013, Advances in Differential Equations and Control Processes, 11 (1), 53 - 70, English
**Modal control of a diffusion system related to linear formations**[Refereed]

Scientific journal

- Oct. 2012, JP Journal of Heat and Mass Transfer, 6 (3), 213 - 222, English
**On output tracking control of a parallel-flow heat exchanger equation with diffusive terms**[Refereed]

Scientific journal

- Jul. 2012, Proceedings of MTNS'12, Melbourne, Australia, English
**Dirichlet boundary control of an unstable ODE plant with a diffusion process in the actuation path**[Refereed]

International conference proceedings

- Apr. 2012, 計測自動制御学会論文集, 48 (4), 185 - 192, Japanese
[Refereed]

Scientific journal

We investigate the problem of enhancing the stability of a coupled transport-diffusion system with Dirichlet actuation and Dirichlet measurement. In the recent paper [H. Sano, Neumann boundary control of a coupled transport-diffusion system with boundary observation, J. Math. Anal. Appl. 377 (2011) 807-816], we treated the stabilization problem for the case with Neumann actuation and Dirichlet measurement, where the variable transformation of the state is performed by using the fractional power of an unbounded operator. However, we cannot use the similar transformation for the case with Dirichlet actuation and Dirichlet measurement, since it brings an ill-posed expression of the system. So, we use an algebraic approach for the formulation of the system. In this paper, it is shown that a reduced-order model with a finite-dimensional state variable is controllable and observable. The fact enables us to construct a finite-dimensional stability-enhancing controller for the original infinite-dimensional system by using a residual mode filter (RMF) approach. The novelty of this paper is the structure that the controller contains the dynamics with respect to the control variable. As a result, the state vector of the resulting closed-loop system includes the control variable as its entry. (C) 2011 Elsevier Inc. All rights reserved.

ACADEMIC PRESS INC ELSEVIER SCIENCE, Apr. 2012, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 388 (2), 1194 - 1204, English[Refereed]

Scientific journal

- Dec. 2011, Proceedings of EUROSIAM'11, 53-60, English
**Feedback stabilization of an unstable ODE plant with a diffusion process in the actuation path: an RMF approach**[Refereed]

Scientific journal

- Nov. 2011, Transactions of the Institute of Systems, Control and Information Engineers, 24 (11), 269 - 279, Japanese
[Refereed]

Scientific journal

In this paper, we consider an output tracking problem of a parallel-flow heat exchange process with distributed and boundary inputs. As the distributed inputs to the system, the output feedback control is first applied. Under zero boundary inputs, it is shown that the C(0) -semigroup describing the closed-loop system satisfies the spectrum determined growth condition. Next, we apply a backstepping method to the design of the boundary inputs for output tracking. Our main result shows that the output of the system reaches a reference signal in finite time under both the output feedback control and the boundary control law derived by the backstepping method. (C) 2011 Elsevier B.V. All rights reserved.

ELSEVIER SCIENCE BV, Nov. 2011, SYSTEMS & CONTROL LETTERS, 60 (11), 917 - 921, English[Refereed]

Scientific journal

- Jun. 2011, JP Journal of Applied Mathematics, 1, no.1, 19-34, English
**Output tracking control of a diffusion process with boundary inputs**[Refereed]

Scientific journal

We study the Neumann boundary stabilization problem of a coupled transport-diffusion system in the case where the observation is done at the boundary. In the recent paper of Sano and Nakagiri [H. Sano, S. Nakagiri, Stabilization of a coupled transport-diffusion system with boundary input, J. Math. Anal. Appl. 363 (2010) 57-72], we treated the stabilization problem for the case with Neumann boundary control and distributed observation. The novelty of this paper is the formulation of the boundary observation equation in a Hilbert space. We have an interesting result of its being expressed by using an A(1)(gamma)-bounded operator with gamma epsilon (1/2, 1). Moreover, it is shown that a reduced-order model with a finite-dimensional state variable is controllable and observable. This means that one can always construct a finite-dimensional stabilizing controller for the original infinite-dimensional system by using a residual mode filter (RMF) approach. (c) 2010 Elsevier Inc. All rights reserved.

ACADEMIC PRESS INC ELSEVIER SCIENCE, May 2011, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 377 (2), 807 - 816, English[Refereed]

Scientific journal

- Feb. 2011, Advances in Differential Equations and Control Processes, 7, no. 1, 1-14, English
**Neumann boundary stabilization of a coupled transport-diffusion system with boundary outputs: a backstepping approach**[Refereed]

Scientific journal

- May 2010, Advances in Dynamical Systems and Control: Proceedings of the 6th WSAES Internat. Conference on Dynamical Systems and Control, 1, 60-67
**Boundary reachability of a parallel-flow three-fluid diffusive heat exchange process**[Refereed]

Scientific journal

We consider the problem of stabilizing a coupled transport-diffusion system with boundary input. The system is described by two linear transport-diffusion equations and is not asymptotically stable. In order to stabilize the system with boundary input, sensor influence functions are assumed to be located at interior of the domain. First, we formulate the system as an evolution equation with unbounded output operators in a Hilbert space, using variable transformation. Next, we derive a reduced-order model with a finite-dimensional state variable for the infinite-dimensional system. Then, a stabilizing controller is constructed for the reduced-order model under an additional assumption. It is shown that the finite-dimensional controller together with a residual mode filter plays a role of a finite-dimensional stabilizing controller for the original infinite-dimensional system, if the order of the residual mode filter is chosen sufficiently large. Finally, the validity of the design method is demonstrated through a numerical simulation. (C) 2009 Elsevier Inc. All rights reserved.

ACADEMIC PRESS INC ELSEVIER SCIENCE, Mar. 2010, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 363 (1), 57 - 72, English[Refereed]

Scientific journal

- Jun. 2009, IMA Journal of Mathematical Control and Information, 26, 231-237, English
**Supplement to: `Boundary stabilization of hyperbolic systems related to overhead cranes' [H.Sano, IMA J. Math. Control Inf. (2008) vol.25, 353-366, doi:10.1093/imamci/dnm031]**[Refereed]

Scientific journal

- May 2009, Transactions of the Institute of Systems, Control and Information Engineers, 22 (5), 177 - 190, Japanese
[Refereed]

Scientific journal

This paper is concerned with the observability problem of a parallel-flow two-fluid heat exchanger equation with diffusion term. First, the case where two fluid temperatures are measured it the outlet is considered. It is shown that, the observed system with the measurements becomes observable oil any interval of time through a concrete series expression of the solution. Next, the two cases where each one of two fluid temperatures is measured at, the outlet, are considered. It is also shown that the observed system with the only one measurement, becomes observable on any interval of time except for the special cases of physical constant's appearing in the equation. For the exceptional cases the unobservable subspace is finite dimensional and is characterized by using the eigenfunctions of heat equation with fluid transfer term.

JAPAN ACAD, May 2009, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 85 (5), 61 - 66, English[Refereed]

Scientific journal

- Apr. 2009, RIMS Kokyuroku "Dynamics of Functional Equations and Mathematical Models", vol. 1637, 120-132, Japanese
**Stabilization of transport-diffusion equations with boundary input**International conference proceedings

- Apr. 2009, RIMS Kokyuroku "Dynamics of Functional Equations and Mathematical Models", vol. 1637, 107-119, Japanese
**Reachability and observability of a plug-flow reactor diffusion equation**International conference proceedings

**Feedback Control of Parallel-Flow Heat Exchanger Equations Using a Forwardstepping Method**In this paper, we treat feedback control of parallel-flow heat exchanger equations with distributed and boundary inputs. As the distributed inputs to the system, the output feedback control is first applied under zero boundary inputs. Then, it is shown that the C-0-semigroup describing the closed-loop system satisfies the spectrum determined growth condition. Next, we apply a forwardstepping method to the design of the boundary inputs. Our main result shows that, for any initial data belonging to a linear space, the solution of the system becomes zero in finite time under both the output feedback control and the control law derived by the forwardstepping method.

WORLD SCIENTIFIC AND ENGINEERING ACAD AND SOC, 2009, RECENT ADVANCES IN APPLIED MATHEMATICS, 1, 106-111, 106 - +, English[Refereed]

International conference proceedings

**Backstepping Boundary Control of First-order Coupled Hyperbolic Partial Integro-differential Equations**We consider a feedback control problem of first-order coupled hyperbolic partial integro-differential equations with distributed and boundary inputs. As the distributed inputs to the system, the output feedback control is first applied under zero boundary inputs. Then, we apply a backstepping method to the design of the boundary inputs. Our main result shows that, for any initial data belonging to a linear space, the solution of the system becomes zero in finite time under both the output feedback control and the control law derived by the backstepping method. Further, the exact formula of feedback solutions is presented. Two applications to the parallel-flow heat exchange equations and the reactor equations of plug-flow type are given.

WORLD SCIENTIFIC AND ENGINEERING ACAD AND SOC, 2009, RECENT ADVANCES IN APPLIED MATHEMATICS, 1, 112-119, 112 - +, English[Refereed]

International conference proceedings

- Dec. 2008, International Journal of Mathematical Models and Methods in Applied Sciences, 2 (4), 513 - 522, English
**Boundary stabilization of a string with two rigid loads: calculation of optimal feedback gain based on a finite difference approximation**[Refereed]

Scientific journal

- Oct. 2008, JP Journal of Heat and Mass Transfer, 2 (3), 327 - 338, English
**On reachability of a parallel-flow three-fluid heat exchange process with boundary inputs**[Refereed]

Scientific journal

In this paper, we treat the problem of stabilizing a flexible cable with two rigid loads which is described by two kinds of hyperbolic equations. From the engineering point of view, the model can be regarded as a distributed parameter overhead crane which conveys two loads simultaneously. In this, the mass of the cart is assumed to be not zero. After deriving a control law which does not increase an energy defined for the model, we prove the asymptotic stability of the closed-loop system by using the LaSalle's invariance principle. The stabilization problem is also discussed for the case of the system with one rigid load.

OXFORD UNIV PRESS, Sep. 2008, IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 25 (3), 353 - 366, English[Refereed]

Scientific journal

- 2008, International Journal of Factory Automation, Robotics and Soft Computing, ISSN 1828-6984, Issue 2, 132 - 137, English
**Variable structure control for a class of nonlinear systems: an approach based on piecewise linear models**[Refereed]

Scientific journal

This paper is concerned with the dynamical analysis of parallel-flow heat exchanger equations with observation at the outlet of tube/control at the inlet of tube. The parallel-flow heat exchanger equation is super-stable under zero boundary condition. The system can be described by an unbounded operator of lower triangular form through a variable transformation. By calculating a Co-semigroup generated by the operator, it is shown that the system is observable if both fluid temperatures are measured at the outlet, and that the system is observable with respect to the non-negative cone of the state space if either of them is measured at the outlet. Moreover, it is shown that the system is reachable if both fluid temperatures are controlled at the inlet, and that the system is reachable with respect to the non-negative cone of the state space if either of them is controlled at the inlet.

OXFORD UNIV PRESS, Mar. 2007, IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 24 (1), 137 - 147, English[Refereed]

Scientific journal

This paper is concerned with the problem of reachability of parallel-flow heat exchanger equations with boundary inputs. It is shown that the system with boundary inputs is formulated as a boundary control system which is well-defined in the sense of Curtain and Zwart (1995), and further that it is reachable through a concrete expression of the solution. In addition, the reachable subspace is given for the case where only one boundary input is added to the system.

JAPAN ACAD, Jan. 2007, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 83 (1), 1 - 4, English[Refereed]

Scientific journal

- 2007, システム制御情報学会論文誌, 20 (12), 457 - 464
[Refereed]

- 2007, International Journal of Factory Automation, Robotics and Soft Computing, ISSN 1828-6984, Issue 3, 158 - 163, English
**A numerical study on stabilization of distributed parameter overhead crane models**[Refereed]

Scientific journal

In this paper, we study the stabilization problem of a flexible cable with two rigid loads which is described by two kinds of hyperbolic equations. From the engineering point of view, the model can be regarded as a distributed parameter overhead crane which conveys two loads simultaneously. After deriving a control law which does not increase an energy defined for the model, we prove the asymptotic stability of the closed-loop system, using the LaSalle's invariance principle. Finally, we show that the control law works effectively through a numerical simulation.

KINOKUNIYA CO LTD, Oct. 2006, JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 23 (3), 225 - 237, English[Refereed]

Scientific journal

In this note, we treat a linear bioprocess model with recycle loop and analyze the spectrum of the closed-loop operator in order to discuss the exponential stability. It is shown that a C-0-semigroup generated by the closed-loop operator satisfies the spectrum determined growth assumption and that the recycle loop works effectively for the process through a numerical simulation.

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, Aug. 2005, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 50 (8), 1200 - 1205, English[Refereed]

Scientific journal

- 2005, システム制御情報学会論文誌, 18 (6), 222 - 228
[Refereed]

- 2005, システム制御情報学会論文誌, 18 (9), 340 - 342
[Refereed]

- 2004, 計測自動制御学会論文集, 40 (9), 915 - 924, Japanese
[Refereed]

Scientific journal

This paper is concerned with stability analysis of a mono-tubular heat exchanger equation with static output feedback. The mono-tubular heat exchanger equation is exponentially stable when the input variable is identically zero. In this paper, it is shown that the C-0-semigroup generated by the closed-loop operator consisting of the mono-tubular heat exchanger equation and the output feedback law satisfies the spectrum determined growth assumption. (C) 2003 Elsevier B.V. All rights reserved.

ELSEVIER SCIENCE BV, Dec. 2003, SYSTEMS & CONTROL LETTERS, 50 (5), 363 - 369, English[Refereed]

Scientific journal

This paper is concerned with boundary control of a linear distributed parameter bioprocess. Huang's result (Ann. Differential Equations 1(1) (1985) 43) on the spectrum determined growth assumption is applied to prove that the closed-loop system becomes exponentially stable under a certain condition with respect to the feedback gain. Moreover, it is shown that the decay rate of the open-loop system is given by letting the feedback gain tend to zero. (C) 2003 The Franklin Institute. Published by Elsevier Science Ltd. All rights reserved.

PERGAMON-ELSEVIER SCIENCE LTD, Aug. 2003, JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 340 (5), 293 - 306, English[Refereed]

Scientific journal

An H-infinity control problem with measurement feedback for infinite-dimensional discrete-time (IDDT) systems whose homogeneous parts are described by Riesz-spectra operators is considered. The aim is to construct a finite-dimensional stabilizing controller for the IDDT system that makes the H-infinity norm of the closed-loop transfer function less than a given positive number delta. For that purpose, we first formulate the IDDT system as an IDDT system in l(2) and derive a finite-dimensional reduced-order system for the IDDT system in l(2). A stabilizing controller that makes the H-infinity norm of the closed-loop transfer function less than another positive number is then constructed for the reduced-order model. The finite-dimensional controller together with a residual mode filter plays a role of a finite-dimensional stabilizing controller that makes the H-infinity norm of the closed-loop transfer function less than delta for the original IDDT system, if the order of the residual mode filter is chosen sufficiently large.

TAYLOR & FRANCIS LTD, Feb. 2003, INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 34 (3), 205 - 214, English[Refereed]

Scientific journal

In this paper, we consider H∞ control problem with measurement feedback for flexible beam equation systems. The aim is to construct a finite-dimensional H∞ controller with a given level δ for the flexible beam equation system. For that purpose, we first formulate the system as an infinite-dimensional system in l2 and derive a finite-dimensional reduced-order system for the infinite-dimensional system. Then, an H∞ controller with level d less than δ is constructed for the reduced-order model. The finite-dimensional controller together with a residual mode filter plays a role of a finite-dimensional H∞ controller with level δ for the original flexible beam equation system, if the order of the residual mode filter is chosen sufficiently large.

Dec. 2002, IMA Journal of Mathematical Control and Information, 19 (4), 477 - 491, English[Refereed]

Scientific journal

In this paper, we study H-infinity control of linear parabolic systems with unbounded output operators. Our aim is to construct a finite-dimensional stabilizing controller for the linear parabolic system that makes the H-infinity norm of the closed-loop transfer function less than a given positive number delta. To this end, we first derive a finite-dimensional reduced-order system for the linear parabolic system. Then, for the reduced-order model, we construct a stabilizing controller that makes the H-infinity norm of the closed-loop transfer function less than another positive number. It is proved that the finite-dimensional controller together with a residual mode filter plays a role of a finite-dimensional stabilizing controller that makes the H-infinity norm of the closed-loop transfer function less than delta for the original linear parabolic system, if the order of residual mode filter is chosen sufficiently large.

TAYLOR & FRANCIS LTD, Nov. 1999, INTERNATIONAL JOURNAL OF CONTROL, 72 (16), 1466 - 1479, English[Refereed]

Scientific journal

In this paper, we consider H-infinity control of linear and semilinear diffusion systems by using a finite-dimensional controller. The main aim is to construct a finite-dimensional stabilizing controller for the linear diffusion system that makes the H-infinity norm of the closed-loop transfer function less than a given positive number delta. For that purpose, we first derive a finite-dimensional reduced-order system for the linear diffusion system. Then, a stabilizing controller that makes the H-infinity norm of the closed-loop transfer function less than another positive number is constructed for the reduced-order model. It is proved that the finite-dimensional controller, together with a residual mode filter, plays a role of a finite-dimensional stabilizing controller that makes the H-infinity norm of the closed-loop transfer function less than delta for the original linear diffusion system if the order of residual mode filter is chosen sufficiently large. Moreover, it is shown that the finite-dimensional H-infinity controller constructed for the linear diffusion system also works as a finite-dimensional H-infinity controller for a semilinear diffusion system with sufficiently small nonlinear term.

SIAM PUBLICATIONS, 1999, SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 37 (2), 409 - 428, English[Refereed]

Scientific journal

The stabilization problem of infinite-dimensional systems with periodically time-varying bounded input and unbounded output operators is considered. The unboundedness of the periodically time-varying ouput operators is assumed to be A(gamma)-bounded. For example, the systems contain linear diffusion systems with boundary control and observation, where the actuator and sensor influence functions periodically vary with respect to the time variable. The aim of this paper is to show that a controller, which consists of a finite dimensional stabilizing controller constructed for the finite-dimensional reduced-order modal model and a residual mode filter, works as a finite-dimensional stabilizing controller for the original infinite-dimensional system if the order of residual mode filter is chosen to be sufficiently large.

TAYLOR & FRANCIS LTD, Jun. 1998, INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 29 (6), 643 - 651, English[Refereed]

Scientific journal

This paper investigates the exponential stability of a model of a heat exchanger of counterflow type, whose boundary conditions are governed by boundary feedbacks. A theorem by F. L. Huang is applied to prove that the system satisfies the spectrum-determined growth assumption.

Oxford University Press, 1998, IMA Journal of Mathematical Control and Information, 15 (4), 317 - 330, English[Refereed]

Scientific journal

- PERGAMON-ELSEVIER SCIENCE LTD, Dec. 1997, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 30 (4), 2197 - 2207, English
**Nonlinear model and linear robust control of overhead traveling cranes**[Refereed]

Scientific journal

rn this paper, we consider H-infinity control of infinite-dimensional linear time-varying (IDLTV) systems whose homogeneous parts are of modal type, by using a finite-dimensional controller. The aim is to construct a finite-dimensional stabilizing controller for the IDLTV system that makes the norm of the closed-loop operator less than a given positive number delta. To this end, a finite-dimensional model is firstly derived for the IDLTV system, and a stabilizing controller that makes the norm of the closed-loop operator less than another positive number gamma(<delta) is constructed for the finite-dimensional model. Then it is shown that a controller, which consists of a residual mode filter and the controller mentioned above, becomes a finite-dimensional stabilizing controller for the given IDLTV system such that the closed-loop operator has norm less than delta, if the order of the residual mode filter is chosen sufficiently large. (C) 1997 Academic Press.

ACADEMIC PRESS INC, Dec. 1997, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 216 (2), 667 - 684, English[Refereed]

Scientific journal

**AN APPLICATION OF INERTIAL MANIFOLD THEORY TO BOUNDARY STABILIZATION OF SEMILINEAR DIFFUSION-SYSTEMS**This paper deals with an application of inertial manifold theory to boundary stabilization of semilinear diffusion systems on a one-dimensional domain. It is shown that a Sakawa type of controller plays an important role in the construction of an inertial manifold for the closed-loop system with a given semilinear diffusion system. This means that the use of a Sakawa type of controller reduces the stabilization problem for the closed-loop system to the one on the inertial manifold. (C) 1995 Academic Press, Inc.

ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS, Nov. 1995, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 196 (1), 18 - 42, English[Refereed]

Scientific journal

This paper is concerned with the stabilization problem of infinite-dimensional systems with A(gamma)-bounded output operators. An operator is said to be A(gamma)-bounded if it can be written as C(A + c)(gamma) for some bounded operator C and some scalar c (see [1]). For example, the linear diffusion system with distributed (or boundary) control and boundary observation is formulated as an evolution equation with bounded input operator and A(gamma)-bounded output operator in a Hilbert space. The purpose of this paper is to show that the closed-loop system with a finite-dimensional controller containing residual mode filter, which Balas introduced for infinite-dimensional systems with bounded input and output operators, is exponentially stable if the order of residual mode filter is chosen sufficiently large.

PERGAMON-ELSEVIER SCIENCE LTD, Sep. 1994, APPLIED MATHEMATICS LETTERS, 7 (5), 17 - 22, English[Refereed]

Scientific journal

The stabilization of semi-linear parabolic distributed systems by means of boundary controls is treated, formulating the partial differential equation describing the system as an evolution equation in a Hilbert space. Here, by using the properties of an analytic semigroup, the global existence of the solution under static output feedback is shown. Moreover, in the similar way, the global existence of the solution and the stabilizability for the system which installs a finite dimensional dynamic compensator is shown.

TAYLOR & FRANCIS LTD, Aug. 1994, INTERNATIONAL JOURNAL OF CONTROL, 60 (2), 243 - 263, English[Refereed]

Scientific journal

This paper deals with the stabilization of semilinear parabolic distributed systems by means of boundary controls. The partial differential equation describing the system is formulated as a semilinear evolution equation in a Hilbert space by using a variable transformation. Here it is shown that the solution globally exists for the closed-loop system which installs a finite-dimensional dynamic compensator by using the properties of an analytic semigroup. Moreover, a sufficient condition for stabilization of the system is derived by making use of the modified Gronwall's inequality developed in this paper.

ELSEVIER SCIENCE BV, Feb. 1994, SYSTEMS & CONTROL LETTERS, 22 (2), 145 - 156, English[Refereed]

Scientific journal

An approach via inertial-manifold theory is presented as a way to study the problem of stabilizing semilinear diffusion systems using finite-dimensional controllers. It is shown that a Sakawa type of controller plays an important role in the construction of an inertial manifold for the closed-loop (controlled) semilinear diffusion system. This means that the use of a Sakawa type of controller reduces the stabilization problem for the closed-loop system to the one on the inertial manifold. © 1994 Oxford University Press.

1994, IMA Journal of Mathematical Control and Information, 11 (1), 75 - 92, English[Refereed]

Scientific journal

- Oct. 2021, IEEE Transactions on Automatic Control, 66 (10), 4982 - 4989
**State estimation of Kermack-McKendrick PDE model with latent period and observation delay**[Refereed]

- Sep. 2019, 計測自動制御学会論文集, 55 (9), 582 - 584
**非局所境界条件に無駄時間を含む1階双曲型システムに対するオブザーバ：誤差システムのL2-安定性**[Refereed]

Report scientific journal

- Nov. 2017, 計測自動制御学会論文集, 53 (11), 621 - 623, Japanese
[Refereed]

Report scientific journal

- 計測自動制御学会, Apr. 2013, 計測と制御, 52 (4), 354 - 360, Japanese
**分布パラメータ・むだ時間と制御**[Invited]

Introduction scientific journal

- Oct. 2012, 計測自動制御学会論文集, 48 (10), 683 - 685, Japanese
[Refereed]

Report scientific journal

- Apr. 2012, システム制御情報学会論文誌, 25 (4), 101 - 103, Japanese
[Refereed]

Report scientific journal

- Mar. 2009, システム制御情報学会論文誌, 22 (3), 123 - 125, Japanese
[Refereed]

Report scientific journal

- 2009, 京都大学数理解析研究所講究録1637「関数方程式のダイナミクスと数理モデル」, 120 - 132
**境界入力をもつ移流拡散方程式系の安定化** - 2009, 京都大学数理解析研究所講究録1637「関数方程式のダイナミクスと数理モデル」, 107 - 119
**プラグフロー反応拡散方程式の可到達性と可観測性** - 2002, 計測自動制御学会論文集, 38 (11), 1003 - 1005, Japanese
[Refereed]

Report scientific journal

- 1999, 鹿児島大学理学部紀要, 32, 21 - 25
**安定半径を考慮したワーキングヘッドの切り替え制御** - Aug. 2021, システム/制御/情報, 65 (8), 336 - 339
**双曲型システムの展望 ― 境界制御／境界観測系の新しい定式化** - Aug. 2021, システム/制御/情報, 65 (8), 305 - 310
**分布定数系のカオスとその応用について**

- 第64回システム制御情報学会研究発表講演会, 22 May 2020, Japanese
**潜伏期間と観測遅れを伴うKermack-McKendrickモデルに対する状態推定** - 第64回システム制御情報学会研究発表講演会, 22 May 2020, Japanese
**無限次元系に対する自己駆動制御** - 2019年度 応用数学合同研究集会, Dec. 2019, 大津
**無限次元系のイベント駆動制御について**Oral presentation

- 2019年度 応用数学合同研究集会, Dec. 2019, 大津
**観測遅れを伴うKermack-McKendrickモデルに対する状態推定**Oral presentation

- 日本応用数理学会2019年 年会, Sep. 2019, 東京
**境界フィードバックループに無駄時間要素を含む1階双曲型システムの安定性解析**Oral presentation

- 第6回計測自動制御学会制御部門マルチシンポジウム, Mar. 2019, Japanese, Domestic conference
**非局所境界条件にむだ時間を含む1階双曲型システムに対するオブザーバ設計と誤差システムのL2-安定性**Poster presentation

- 2018年度 応用数学合同研究集会, Dec. 2018, Japanese, Domestic conference
**無限次元システムのサンプル値サーボ問題について**Oral presentation

- 2018年度 応用数学合同研究集会, Dec. 2018, Japanese, 大津, Domestic conference
**境界入力に無駄時間要素を含む1階双曲型システムの安定化について**Oral presentation

- 日本応用数理学会2018年 年会, Sep. 2018, Japanese, 名古屋, Domestic conference
**非局所境界条件にむだ時間を含む双曲型システムに対する状態推定**Oral presentation

- Workshop on evolution equations and related topics, Sep. 2017, Japanese, 大阪大学待兼山会館（豊中キャンパス）, Domestic conference
**入力に無駄時間要素を含む放物型システムの安定化について**Oral presentation

- 第4回計測自動制御学会制御部門マルチシンポジウム, Mar. 2017, Japanese, 岡山, Domestic conference
**入力無駄時間要素をもつ熱拡散系のディリクレ境界安定化**Oral presentation

- 2016年度 応用数学合同研究集会, Dec. 2016, Japanese, 大津, Domestic conference
**境界入力に無駄時間要素を含む熱拡散系の安定化について**Oral presentation

- 第59回自動制御連合講演会, Nov. 2016, Japanese, 北九州市, Domestic conference
**無限次元フィードバック系における安定半径の近似について**Oral presentation

- 第59回自動制御連合講演会, Nov. 2016, Japanese, 北九州市, Domestic conference
**入力むだ時間を有する熱拡散系の安定化**Oral presentation

- 非線形現象の特徴化に基づく制御理論調査研究会 第2回研究会, Nov. 2016, Japanese, 大阪, Domestic conference
**境界入力に無駄時間要素を含む熱拡散系の安定化について**[Invited]

Invited oral presentation

- 第3回計測自動制御学会制御部門マルチシンポジウム, Mar. 2016, Japanese, 名古屋, Domestic conference
**動的境界条件をもつ分布定数回路の安定性について**Oral presentation

- 数理人口学・数理生物学セミナー, Jan. 2016, Japanese, 東京, Domestic conference
**無限次元制御系に対する安定半径の近似について**Oral presentation

- 第58回自動制御連合講演会, Nov. 2015, Japanese, Domestic conference
**バックステッピング法に基づく感染症の初期流行予防のための人口制御**Oral presentation

- 日本応用数理学会2015年度年会, Sep. 2015, Japanese, Domestic conference
**バックステッピング法に基づく感染症の初期流行予防のための人口制御**Oral presentation

- 第1回制御部門マルチシンポジウム, Mar. 2014, Japanese, 計測自動制御学会制御部門, 東京, Domestic conference
**並流型熱交換プロセスに関連した移流拡散系の境界制御**Oral presentation

- 環瀬戸内応用数理研究部会 第17回シンポジウム, Jan. 2014, Japanese, 日本応用数理学会, 松山市, Domestic conference
**内部にフィードバックループを有する線形放物型システムのモード制御**Oral presentation

- 岡山理科大学における微分方程式セミナー（微分方程式セミナー通算第36回）, Sep. 2013, Japanese, 岡山市, Domestic conference
**Stabilization of linear parabolic systems with internal feedback loop**Oral presentation

- 第38回発展方程式研究会, Dec. 2012, Japanese, 東京, Domestic conference
**フォーメーションに関連した放物型システムの制御について**Oral presentation

- 第61回理論応用力学講演会, Mar. 2012, Japanese, Tokyo, Domestic conference
**Output tracking control of a parallel-flow heat exchanger equation with diffusive terms**Oral presentation

- 第37回発展方程式研究会, Dec. 2011, Japanese, Gifu, Domestic conference
**拡散プロセスを通して駆動される集中定数プラントの安定化**Oral presentation

- 第54回自動制御連合講演会, Nov. 2011, Japanese, Toyohashi, Domestic conference
**On estimation of the initial value of a parallel-flow heat exchange process**Oral presentation

- The 40th SICE Symposium on Control Theory, Sep. 2011, Japanese, 計測自動制御学会制御部門, Osaka, Domestic conference
**On stabilization of an unstable mixed parameter system**Oral presentation

- The 9th WSEAS International Conference on System Science and Simulation in Engineering, Oct. 2010, English, WSEAS, Iwate, Japan, International conference
**Switching control of parallel-flow heat exchange processes**Oral presentation

- The 39th SICE Symposium on Control Theory, Sep. 2010, Japanese, 計測自動制御学会制御部門, Osaka, Domestic conference
**Stabilization of the one-dimensional diffusion equation with boundary control and boundary observation**Oral presentation

- The 6th WSAES International Conference on Dynamical Systems and Control, May 2010, English, WSAES, Kantauri, Sousse, Tunisia, International conference
**Boundary reachability of a parallel-flow three-fluid diffusive heat exchange process**Oral presentation

- Japan Mathematical Society Annual Meeting 2010 March, Mar. 2010, Japanese, 日本数学会, Keio University, Domestic conference
**Feedback control of parallel-flow heat exchanger equations using a forwardstepping method**Oral presentation

- Japan Mathematical Society Annual Meeting 2010 March, Mar. 2010, Japanese, 日本数学会, Keio University, Domestic conference
**Backstepping boundary control of first-order coupled hyperbolic partial integro-differential equations**Oral presentation

- Workshop on Mathematical Control Theory in Kobe, Jan. 2010, Japanese, Takigawa Memorial Hall, Kobe University, Domestic conference
**Stabilization of a coupled transport-diffusion system: a case with boundary control and boundary observation**Oral presentation

- The 14th WSAES International Conference on Applied Mathematics, Dec. 2009, English, WSAES, Puerto De La Cruz, Tenerife, Canary Island, Spain, International conference
**Feedback control of parallel-flow heat exchanger equations using a forwardstepping method**Oral presentation

- The 14th WSAES International Conference on Applied Mathematics, Dec. 2009, English, WSAES, Puerto De La Cruz, Tenerife, Canary Island, Spain, International conference
Oral presentation

- Kobe Analysis Seminar, Oct. 2009, Japanese, Graduate School of Science, Kobe University, Domestic conference
**天井クレーンの分布定数モデルと安定化について**Oral presentation

- Japan Mathematical Society Annual Meeting 2009 September, Sep. 2009, Japanese, 日本数学会, Osaka University, Domestic conference
**Boundary stabilization of a parallel-flow three-fluid heat exchange process considering diffusive effect**Oral presentation

- Japan Mathematical Society Annual Meeting 2009 September, Sep. 2009, Japanese, 日本数学会, Osaka University, Domestic conference
**Boundary stabilization of a parallel-flow three-fluid heat exchange**Oral presentation

- Japan Mathematical Society Annual Meeting 2009 September, Sep. 2009, Japanese, 日本数学会, Osaka University, Domestic conference
**Boundary reachability of a parallel-flow three-fluid diffusive heat exchange process**Oral presentation

- Japan Mathematical Society Annual Meeting 2009 September, Sep. 2009, Japanese, 日本数学会, Osaka University, Domestic conference
**Boundary reachability of a parallel-flow three-fluid diffusive heat exchange process**Oral presentation

- Summer PDE Seminar 2009, Aug. 2009, Japanese, Ryukoku University Seminar House "Tomoikiso", Domestic conference
**Stabilization of a parallel-flow three-fluid diffusive heat exchange process with boundary input**Oral presentation

The Institute of Systems, Control and Information Engineers

The Society of Instrument and Control Engineers

The Mathematical Society of Japan

The Japan Society for Industrial and Applied Mathematics

システム制御情報学会

日本数学会

計測自動制御学会

日本応用数理学会

- Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Kobe University, Apr. 2021 - Mar. 2025
**ファン・デル・ポール境界条件をもつ双曲型方程式の同期化制御とその秘匿通信への応用** - 学術研究助成基金助成金／基盤研究(C), Apr. 2015 - Mar. 2019, Principal investigator
Competitive research funding

- 学術研究助成基金助成金／基盤研究(C), Apr. 2013 - Mar. 2016
Competitive research funding

- 学術研究助成基金助成金／基盤研究(C), 2011, Principal investigator
Competitive research funding

- 科学研究費補助金／基盤研究(C), 2010
Competitive research funding

- 科学研究費補助金／基盤研究(C), 2009, Principal investigator
Competitive research funding

- 科学研究費 基盤研究(C)(2), Apr. 2004 - Mar. 2006, Principal investigator
**放物型偏微分方程式系のサンプル値制御に関する理論的・数値実験的研究**Competitive research funding

- 科学研究費 若手研究(B), Apr. 2002 - Mar. 2004, Principal investigator
**慣性多様体と無限次元システムのロバスト安定化**Competitive research funding

- 科学研究費 奨励研究(A), Apr. 1999 - Mar. 2001, Principal investigator
**放物型偏微分方程式系のロバスト制御**Competitive research funding