For a stochastic delay differential equation, a stability condition is derived in the sense of mean square stability. The condition substantiates the fact that noise with an appropriate power can reduce the influence of time delay in the differential equations. It is also illustrated by a numerical example. To derive the stability condition, the so-called domain subdivision method and Ito's formula are adopted.
Recently, the concept of transfer functions for meromorphic control systems has been proposed. These transfer functions have many similar properties to the transfer functions of linear systems. This paper shows that an input-affine meromorphic system is input-output linearizable with static state feedback if and only if its transfer function is not identically zero.
In order to construct a rational framework of designing discrete event control systems, it is necessary to develop the method of modeling concurrent systems, describing control objectives, and synthesizing controllers based on the plant models and control objectives. If the control of discrete events is viewed as the manipulation of event occurrences, the role of a controller is to enable and inhibit the occurrences of events. This paper presents a framework for control of discrete event systems so as to achieve the desired behavior specified as a control objective. For this purpose, by using condition/event nets (C/E nets) as a modeling tool for discrete event systems and partial languages as a behavioral description tool for C/E nets, we formulate a control problem to synthesize a controller which guarantees that all and only the desired behaviors described by a partial language is possible. We then present the solvability and solution techniques of the formulated problem, together with the discussion about the design of discrete event control systems with uncontrollable and unobservable events.
Further results on sufficient LMI conditions for H∞ static output feedback (SOF) control of discrete-time systems are presented in this paper, which provide some new insights into this issue. First, by introducing a slack variable with block-triangular structure and choosing the coordinate transformation matrix properly, the conservativeness of one kind of existing sufficient LMI condition is further reduced. Then, by introducing a slack variable with linear matrix equality constraint, another kind of sufficient LMI condition is proposed. Furthermore, the relation of these two kinds of LMI conditions are revealed for the first time through analyzing the effect of different choices of coordinate transformation matrices. Finally, a numerical example is provided to demonstrate the effectiveness and merits of the proposed methods.
In recent years, frequency control and impedance control systems have been studied to realize efficient wireless transmission systems using magnetic resonance coupling. However, the frequency control system has a problem that the usable frequency is bounded by the Industry-Science-Medical (ISM) band, and the impedance control system has a problem that the flexibly controllable impedance converting circuits are difficult to realize. Therefore, this paper proposes an efficient wireless power transmission system which operates at fixed frequency and impedance. In the proposed system, the relative position of the transmitter to the target antenna was measured and controlled to achieve high transmission efficiency. The relative position was measured based on a novel position sensing method also using magnetic resonance coupling. As a result, the transmission efficiency increases from 45.0% to 62.4% where the target value was 70.0%, and the effectiveness of the system on improving the transmission efficiency is experimentally verified.
This paper proposes a simple controller parameter tuning method that can compensate for hysteresis. The proposed method is based on the so-called fictitious reference iterative tuning (FRIT) technique which can easily tune controller parameters such as proportional-integral-derivative gains using a one-shot closed-loop experimental data. In the proposed framework, a simple hysteresis model is introduced to a control system, and its inverse is used as a hysteresis compensator. Since the hysteresis model is characterized with only three parameters, the related computational burden is moderate in the parameter tuning process. Also, the proposed FRIT method needs an only one-shot experiment as in the standard FRIT one, which implies that the feature of FRIT is well-maintained. In the optimization process, the so-called covariance matrix adaptation evolution strategy is used for simultaneously searching hysteresis parameters as well as controller parameters. The proposed FRIT method is applied to an experimental control system that comprises a shape memory alloy actuator, and its effectiveness is verified.
This paper is concerned with the well-posedness (in the classical sense) and robust stability analysis of linear time-invariant (LTI) systems. Among approaches to robust stability analysis of LTI systems is the one based on the separator-type robust stability theorem derived through the topological separation notion. This paper first shows that the well-posedness assumption underlying this theorem, which has been considered to be essential in the discrete-time case, can actually be removed completely. Some arguments and an example are further provided, suggesting that removing such an assumption is indeed a nontrivial task. Relevant aspects are also discussed about well-posedness of uncertain systems through the systematic arguments underlying the construction of such an example, both in the discrete-time and continuous-time cases.
This paper considers stabilization of linear time-invariant descriptor systems by dynamic output feedback controllers. We deal with general descriptor systems including those being irregular or impulsive, and derive state-space stabilizing controllers. On the derivation process of the state-space controllers, we first consider descriptor-type controllers. We present a necessary and sufficient condition for the existence of a descriptor-type controller which makes the closed-loop descriptor system regular, impulse-free, and stable. The condition is expressed in terms of linear matrix inequalities (LMIs), and we show that coefficient matrices of any descriptor-type stabilizing controller of the same size as the given descriptor system can be represented by the solution of the LMIs. Then, we present a necessary and sufficient condition for the descriptor-type controller to be transformable to an input-output equivalent state-space controller with the dimension of the dynamic order (the rank of the coefficient matrix for the time-derivative of the descriptor variable) of the given descriptor system, that is, a state-space stabilizing controller. The transformability condition is mild and almost always satisfied by the obtained descriptor-type controller. Furthermore, even if the transformability condition is not satisfied, a slightly modified solution of the LMIs, which always exists, gives a descriptor-type controller being transformable to a state-space controller. The transformation is carried out analytically, thus the coefficient matrices of any such state-space stabilizing controller can be expressed by the solution of the LMIs. We also reveal that if we restrict the classes of descriptor systems or descriptor-type controllers such that their transfer functions are strictly proper, the descriptor-type controllers obtained by the LMI condition are always transformable to state-space controllers.
In this paper, sampled-data control of piecewise affine (PWA) systems with parameter uncertainty is addressed based on both the interval method and the authors' previously proposed method. First, the optimal sampled-data control problem of continuous-time PWA systems with parameter uncertainty is rewritten as an optimal control problem of discrete-time PWA systems with parameter uncertainty. Since in the obtained problem weighting matrices of the cost function are also uncertain, this problem is a min-max mixed integer programming (MIP) problem. Then, by using the interval method and the authors' previously proposed method, this problem is approximated by an MIP problem. Finally, the effectiveness of the proposed method is shown by a numerical example.