Hideki Sano

Output tracking control of a parallel-flow heat exchange process

Abstract 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.

Stability analysis of the telegrapher’s equations with dynamic boundary condition

Abstract 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 stable C 0 -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.

On observability gramian of a parallel flow heat exchanger equation with diffusive terms

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.

Low order stabilizing controllers for a class of distributed parameter systems

Abstract 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.

Application of the backstepping method to the prediction of increase or decrease of infected population.

BackgroundIn 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.MethodsUsing 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.ResultsOur 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.ConclusionsOur 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.

Dirichlet Boundary Stabilization of Unstable Mixed Parameter Systems

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 transport diffusion 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 Aγ-bounded output operator and direct feed through 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.