S. Hara’s research while affiliated with The University of Tokyo and other places

The backstepping method is a systematic design tool for boundary control of various types of partial differential equations (PDEs). There has been no attempt to apply it to PDEs whose input is not at the boundary. In this paper, we consider a problem of feedback stabilization of 1-dimensional parabolic (unstable) PDEs with internal actuation based on the backstepping method. Since such a PDE can not be converted to a stable PDE by state feedback and the state transformation used in backstepping, an additional transformation is introduced. Under a certain condition, the newly proposed transformation moves the input from the interior of the domain to the boundary. This enables us to cancel the residual term that causes the open-loop instability by using the input. Furthermore, this transformation is continuously invertible. Therefore, a stabilizing state feedback for the original PDE is derived through the inverse transformation. The results are demonstrated by a numerical simulation.

Quorum-sensing is one of cell-to-cell communication mechanisms for bacteria, and it essentially involves in biological dynamics such as gene expression. In this paper, we derive analytical expressions for local stability/instability conditions for a class of quorum-sensing networks with cyclic gene regulatory networks. The conditions lead to two biological facts on local stability of the quorum-sensing network. First, we clarify that there exists three parameters which play essential roles in local stability of the quorum-sensing network. Second, we show a relationship between gene networks and quorum-sensing network for achieving the local instability.

In this paper, we deal with a problem to capture a target by linear multi-agent systems where the agents behave autonomously, whereas the target escapes with a reasonable strategy. We give necessary and sufficient conditions or sufficient conditions for the success of the capturing for several cases. The conditions clarify the performance competition between the target and the agents and we propose preferable strategy for the target and the agents, respectively. We consider the problem in the case of simple or general dynamics of the target and the agents. We also demonstrate the results by using numerical simulation.

In this paper, we derive an existence condition of periodic oscillations in cyclic gene regulatory networks, of which the dynamical behavior is described by nonlinear differential equations. For this purpose, we first point out that change of the equilibrium point with respect to biochemical parameters is important for comprehensive analysis, and show the properties which the equilibrium point should satisfy. Then, by employing these properties, we derive an analytic condition for the existence of periodic oscillations in cyclic gene regulatory networks where genes have homogeneous dynamics. Compared to preceding studies, our condition has the following distinctive features: (i)it is analytically written only in terms of the system parameters, (ii)it is applicable for cyclic gene regulatory networks consisting of any number of genes. Thus, biological interpretation of the result is easily obtained, and, in fact, it is concluded that cyclic gene regulatory networks with homogeneous gene dynamics tend to have periodic oscillations as the number of genes gets large. Finally, we discuss the case of cyclic gene regulatory networks with heterogeneous gene dynamics.

In this paper, we propose a hierarchical modeling of the systems described by conservation laws. A conservation law on a hierarchically parted domain can be considered as a subsystem which interacts with neighbor elements through fluxes. Therefore, we regard the system as a networked system of each subsystem. The important idea is to weaken the interconnection in the sense of a rank. For detailed analysis of our method, we apply the proposed method to a diffusion equation. The hierarchical model is described by a non-circulant block Toeplitz matrix. Because the resulting system is symmetrically-networked system, we can show that the eigenvalues of the system consist of those of related uniform models. We also show that our method relaxes the stability condition of the fully discretized model. Finally we examine the performance of the hierarchical model by numerical simulations.

A linear system with a generalized frequency variable denoted by G(s) is a system which is given by replacing transfer function's 's' variable in the original system G₀(s) with a rational function 'Phi(s)', i.e., G(s) is defined by Go(Phi(s)). A class of large-scale systems with decentralized information structures such as multi-agent systems can be represented by this form. In this paper, we investigate fundamental properties of such a system in terms of controllability, observability, and stability. Specifically, we first derive necessary and sufficient conditions that guarantee controllability and observability of the system Q(s) based on those of subsystems Go(s) and 1/Phi(s). Then we present Nyquist-type stability criterion which can be reduced to a linear matrix inequality (LMI) feasibility problem. Finally, we apply the results to stability analysis of a class of formation control and confirm the effectiveness of the approach as a general framework which can unify variety of results in the field.

We consider a networked control system that utilizes unreliable channels where packets may be lost. By modeling the losses as stochastic processes, we propose a mixed H₂/H_∞ control approach for synthesis of a controller that depends on the information regarding the losses. The approach is applied to a bilateral teleoperating system. Numerical results show that the proposed control achieves desired performance.

This paper considers a control synthesis problem for linear systems to meet design specifications in terms of multiple frequency domain inequalities in (semi)finite ranges. Our approach is based on the generalized Kalman–Yakubovich–Popov (GKYP) lemma, and dynamic output feedback controllers of order equal to the plant are considered. A new multiplier expansion is proposed to convert the synthesis condition to a linear matrix inequality (LMI) condition through a standard linearizing change of variables. In a single objective setting, the LMI condition may or may not be conservative, depending on the choice of the basis for the multiplier expansion. We provide a qualification for the basis matrix to yield non-conservative LMI conditions. It is difficult to determine the basis matrix meeting such a qualification in general. However, it is shown that qualified bases can be found for some cases, and that the qualification condition can be used to find reasonable choices of the basis for other cases. The synthesis method is then extended to the multiple objective case where a sufficient condition is given for the existence of a controller to meet all the prescribed specifications. Finally, design examples for an active magnetic bearing are given to illustrate the effectiveness of the proposed design method. Copyright © 2006 John Wiley & Sons, Ltd.

This paper proposes a new method of parameter space design for robust control synthesis which guarantees the real stability radius constraint, accomplished by using Quantifier Elimination (QE). We aim at practicality by employing the scheme to combine the Sign Definite Condition (SDC) and a special QE algorithm using the Sturm-Habicht sequence. The validity of our approach is confirmed by several design examples.

In this paper, we deal with congestion control of one bottleneck type for TCP/AQM network systems and investigate the H 2 control performance limitation. To this end, we first represent the dynamics of the congestion window size at source nodes and the queue length at the bottleneck link by a discrete time model. We then prove the stability of the plant and provide the Youla parametrization of all stabilizing controllers. With this parametrization, we consider an H 2 optimization problem of the queue length at the bottleneck link. We derive an explicit form of the best achievable H 2 norm and discuss the control performance limitation with respect to the ratio of the transmission time of the packets from source nodes to the link and the round trip time.