The problem is studied in this paper of designing a decoupling system by a state feedback control law with or without dynamic compensator.
It is shown that the precompensator presented by Silverman is of a minimum dimension, and a simple method for obtaining the order of the precompensator is presented. The extension of the concept to the multivariable system with r-output/m-input leads to an algorithm of designing a lower order precompensator for decoupling. It is easily shown that if a constraint is incorporated in the control law in such a way that the resulting decoupling problem is linear, then the algorithm presented here gives the precompensator of a minimum dimension.

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This paper delas with the synthesis problems of the minimal time control of n-th order linear, systems, x=Ax+bu, with bounded control amplitude, |u(t)|≤1.
When the initial value of the adjoint vector satisfies φ^T(0)b=0, it is shown that the reachable subset Ω_s, by using the control u(t)=sgn (φ^T(t)b), constitutes the switching hyper surface. And how to determine the optimal control u^*(x) with the usege of Ω_s is shown. Applying the GMDH (Group Method of Data Handling), the method of identifying the switching hyper surface is discussed. Also discussed in the paper is the method of reducing the bad effects such as hunting of the state vector arround its equilibrium point or chattering of the manipulated variable caused by an error in the identification.
Several numerical results are shown to demonstrate the possibility of constructing the minimal time feedback control system by using the switching hyper surface.

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This paper deals with a method of synthesizing optimal control for a class of multivariable linear stochastic discrete-time systems with parameter variations. As is well known, for this type of control problem, the “self-tuning regulator” is proposed. The regulator recursively identifies and corrects the model, which is used to derive the control law, until the model matches the controlled object. The self-tuning regulator becomes effective, however, only when the parameters of the controlled object are unknown constants or very slow variables. In the other case, namely, when a variable which represents the cause of parameter variations varies around its nominal value, the concept of sensitivities seems to be applicable. In this paper, the closed-loop control law which minimizes a quadratic performance index containing sensitivity variable is derived. The optimal control becomes a linear dynamical system. All the equations to be solved are linear, but there are equations having no unique solution. Therefore, it is shown that every solution yields the same control law, and any solution might as well be used to synthesize an optimal control system.

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In this paper, a new procedure for selecting weighting matrices in linear quadratic optimal control problems (LQ-problems) is proposed. In usual LQ-problems, the quadratic weights are decided on trial and error in order to get a good response. But using the proposed method to select the quadratic weights, all poles of the closed loop system are located in such an area that is desired for a good response as well as for the stability of the system. As the closed loop systems constructed by this method have merits for LQ-problems as well as for pole assignment problems, this procedure will be useful in constructing linear feedback systems. Taking into consideration that little is known about the relationship between the quadratic weights and the poles of a closed loop system, this procedure is also interesting from the theoretic point of view.

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The fuzzy transitive relation is very essential for a fuzzy ordering relation in fuzzy decision problems and also for a fuzzy equivalence relation in fuzzy clustering problems. But data of binary relation given by questionnaires do not usually satisfy the transitivity condition. Then the transitive closures of binary relation are used to be transitive. This paper deals with a heuristic method for finding a fuzzy transitive relation which is a good approximation to a given relation. The fuzzy transitive relation obtained by this method is closer to the relation in the system under consideration than the transitive closure is in the sense of the error sum of squares.

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We treat discrete-time systems in this paper. The purpose of this paper is to establish the relation between the canonical dynamical system, the canonical linear representation system and the canonical affine dynamical system which have the same behaviors.
We have already established the realization theorems of dynamical systems, linear representation systems and affine, dynamical systems; that is, we obtained the definite canonical systems which realize any given input response map a: U^*→Y, and proved that these canonical systems are unique up to isomorphisms in each category.
The linear representation systems are the dynamical systems whose state spaces are the linear representations of concatenation monoid U^*, i. e., LINEAR U^*-MODULES. The class of linear representation systems contains homogenous bilinear systems and K-∑-automaton as subclasses.
On the other hand, the affine dynamical systems are defined as the dynamical systems whose state spaces are affine representations of U^*, i. e., AFFINE U^*-MODULES. This class containes linear systems and inhomogenous bilinear systems as subclasses.
Linear representation systems and affine dynamical systems are canonical iff they are quasi-reachable and distinguishable.
Canonical linear representation systems and canonical affiine dyndamical systems are not necessarily reachable as dynamical systems, their state spaces are defined to be the linear hulls and the affine hulls of really reachable sets, respectively.
In this paper, we present the procedures to obtain a linear representation system from an affine dynamical system having the same behaviors, and vise versa. Then, we give the necessary and sufficient conditions for the systems obtained by the procedures to be canonical.
The procedure to construct the homogenous bilinear system from a biaffine system having the same behaviors has been already presented in the paper 8). But the homogenous bilinear systems constructed by this procedure are not necessarily canonical. Hence, their existence condition for the realization problem is not correct and we point out an error in the proof of the uniqueness theorem.
Our results establish the definite relation between the canonical homogenous bilinear system and the canonical inhomogenous bilinear system which have the same behaviors.

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In recent years, the complex behaviours of some very simple mathematical models attract much attention in various fields of science and engineering. In this paper the dynamics of a popular discrete time model for two-species competition is discussed. Domains of existence and stability of 2ⁿ-cycles are shown in the parameter space of this model, and a condition for coexistence of two species is obtained. Finally, the existence of chaotic behaviour and the structure of so-called “strange attractor” are demonstrated by computer simulation.

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The mode of oscillation resulting from the instability of a system in self-oscillatory, as exemplified by limit cycling.
This paper presents a method for predicting whether or not certin kinds of nonlinear sampled-data feedback systems can oscillate, and verifying the existence of the predicted oscillation.
Mainly the existence of quantizer-induced limit cycles is investigated. The describing function is obtained for the nonlinear block containing a quantizer, a sampler and a zero-order hold circuit.
For the sub-harmonics of the sampler frequency, a systemtic method is developed to determine the smallest region of the complex plane in which the describing function can be asserted to lie.
Drawing the inverse Nyquist diagram of the linear part in the same plane, the sequence of limit cycle is predicted by the well-known graphical method.
Verifying the result, a numerical method is used. The D.F. procedure is most suitable for prediction and a numerical method is more advantegeous for verifying.
For a setter nonlinearity, with or without memory, the smallest region in which the D.F. can be asserted to line is also shown. It seems to have some deeper significance.
No report of this type of study has been published to date.

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In the previous paper, we presented a sufficient condition for the stability of large-scale interconnected systems with the help of comparison functions to describe the dynamical behaviors of subsystems.
In this paper, a development of the above result to more general interconnected systems, in which the inputs of subsystems are no more linear functions of the outputs of the other subsystems and some of the subsystems are no more expotentially stable is considered. The stability analysis of such systems is reduced to the study of nonlinear differential equations with off-diagonally increasing right hand sides. For this problem the concept of M-functions plays an important role and on the basis of these results, conditions for the staility of interconnected systems are studied.

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This paper deals with a methodology and a system of the profile pattern recognition of a motorcar. The pattern is assumed to be a polygon constructed by simplifying a complicated shape pattern. In the methodology of the motorcar shape recognition, six kinds of parameters of feature extraction are adopted such as the numcer of corners, the number of separated concave corners, the number of continuous concave corners, the aspect ratio, the maximum edge ratio and the size of the pattern.
Furthermore, it is proposed to apply the operation of simplifying the pattern when the complicated shape pattern such as a motorcar shape is subjected to the pattern recognition. An analysis of human being in the complicated shape pattern recognition has been executed and the experimental results showed two characteristic features of simplification. One is a character which simplifies a corner with respect to a corner angle. Another is a character with respect to a distance between adjacent corners. The stress of each corner is defined from these two characteristic features. If the stress of each corner is smaller than the given threshold stress value, the corner is simplified and neglected.
Seven kinds of grouping patterns which are symbolized referring to the sectional profile pattern of a motorcar commonly encountered in the road are considered. The sectional profile pattern is selected as a side pattern of the motorcar. The grouping patterns are a bus, a micro-bus, a large-truck, a truck, a motorcar, a wagon-car and a mini-motorcar. The total number memorized in the minicomputer is 432 kinds of motorcar shapes. The number of the matching patterns as a truck is 36. These are similar and generated by neglecting the convex corners. The concave portion is not neglected, because this portion is a specific feature of the shape.
The developed system is featured by the capability of recognizing in less than 3 seconds per one pattern and classifying the patterns into 7 kinds of grouping patterns.

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This paper deals with intransitive ordering problems which appear in some evaluation involving paired comparison. The main path diagram, the fundamental pattern, the extended fundamental pattern and the pseudo-interval ordering are defined to analyze the set of objects intransitively ordered. From those definitions and their basic meaning this paper obtains an algorithm to decompose the intransitively ordered set into subsets satisfying the property of the pseudo-interval ordering.

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The length of a linear figure drawn on a plane, such as an urban road map or a river, is usually measured by tracing the figure with a curvimeter. But when the length of a complex figure is measured, the result often varies widely. One of the reasons for this error is that some part of the figure has been traced more than once or not traced at all.
On the other hand, an alternative method based on integral geometry was proposed by Steinhaus⁵⁾ which is to count the number of intersection points between the figure and parallel lines superposed on it. The counting is done several times changing the orientation of the parallel lines. By this method, the length can be determined with high accuracy by decreasing the interval d of parallel lines and/or increasing the number of directions m, and when only a rough estimate is needed the time necessary for measuring can be reduced.
In this paper, we derive an estimate of the error in measuring the length of a complex figure by Steinhaus' method by theoretical analysis as well as by numerical experiments. Based on this estimate, we show how to choose the appropriate values of d and m in order to achieve the required accuracy. In addition, we propose several conditions in order to minimize the human error in counting the number of intersection points.
The experimental results show that the method based on integral geometry is better than the method using a curvimeter both in accuracy and in time for some complex figures that are likely to appear in practice.

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This paper describes the method of decreasing the inherent error, the so-called step error, in a conventional FM-CW radar. In this method the microwave antenna is driven to the amount of nλ/4. in order to modulate the phase of microwave, where λ is the wavelength of the carrier wave and n is an integer. During the modulation, the step error is averaged and then decreased.
The maximum phase deviation in this method is always equal to nπ, independent of the distance to be measured, which is the condition that minimizes the step error. First, the properties of the residual error is analized for the case when a stroke of the antenna deviates from nλ/4.
Next, a distance is experimentally measured with the radar in order to confirm the decrease in the step error. As a result of these experiments, it is found that when the maximum frequency deviation is 100MHz, the standard deviation of residual error is less than 30mm, though the step error in a conventional FM radar would be 37.5cm.
Moreover it is found that this radar can be used to measure from such a short distance as 0.5m.
Taking advantage of these merits, this method can be adapted to the level meter of coke or ore in the blast furnace, to the level meter of molten steel in the converter and to some other cases of industrial use.

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The output of radiation detectors such as a GM tube or a scintilation detector is a pulse train. It is known that the random time occurence of the pulses follows a Poisson distribution.
In this paper a new pulse generator is presented, the output is similar to that of these radiation detectors. The method for generating the pulse train is based on the mathematical transformaion of the uniformly distributed random numbers to random time intervals of pulses using the exponential function.
The theoretical analyses and the experimental results using the practical generator show that the statistical properties of the pulse train generated by this method are satisfactorily similar to those of random time pulses having a Poisson distribution.
The generator has also several featurs such as the high stability, the high repeatability and the capability of changing the mean pulse rate value in proportion to an external signal, and is very usuful for testing and studying of various measuring or control systems using radioisotopes.

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The temporal change of thermal environment caused by weather conditions or by waste heat is one important index of environmental information. A temporal change of temperature is formally given by the difference between the thermal infrared images collected at the times t₁ and t₂. However, objects having different thermal infrared emissivities and temperatures are taken simultaneously into a pixel of remotely sensed multispectral and multitemporal images, and the proportions of different objects in the pixel change with time. Therefore, for two temporal thermal infrared images, one cannot distinguish between the true temporal change of the surface temperature and the apparent change of it caused by the temporal change of the proportions of the objects in the pixels.
The exterior product image processing by using the image information of the visible channels removes the apparent temporal change of surface temperature caused by the changes of the proportions on the two thermal infrared images. Consequently, the temperature change on the processed image gives the true temporal temperature difference pattern which is independent of the proportions of the various objects on the earth's surface.

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In failure detection, we have two incompatible demands: One is the high reliability for detection, the other is the short mean detection time. That is, if the mean detection time is long, the loss due to delays of detection will be large. On the other hand, if the mean detection time is short, the loss due to false alarms will be large. In this paper, we consider an optimization problem of a failure detection system that balances the two incompatible demands described above.
Here, as a detection method, the modified Wald's SPRT is used. This method, which works well for detection of failures or parameter changes, uses a likelihood ratio computed from a sequence of observation data with noise.
A proposed problem is as follows: find the optimal mean time T between two false alarms to minimize the mean performance deterioration of the given system, when the performance deterioration ratios for the false alarm and the miss alarm are known. A solution for this problem is given and finally a simple numerical example is given.

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In developing the control system for the shoulder arm prosthesis, we have tried to answer the following fundamental question: How can we control the prosthesis to produce the intended movement by a natural physiological signal-giving motion?
First we define the intended movement to be a synergical movement to position the wrist. And in order to connect this movement with the physiological signal-giving motion of the shoulder, the analogue processing technique is adopted to detect the signal-giving motion. And the control-by-intention technique is newly proposed on the basis of the end point control technique in order to control the wrist positioning synergically. In the end point control technique, the control variable is the end point (an important position of the wrist in ADL), while in the control-by-intention it is an arbitrary direction vector. In order to obtain the synergical control of the prosthesis by the vector, the end point control technique is extended and the control-by-intention technique by the grid point vector has been introduced. Moreover the elbow declination control is introduced to make the movement more flexible by a tentative change of the content of grid points. As the result it is possible to make the prosthesis motion much more similar to the natural human movement in ADL.

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The conductivity of a solid-state electrochemical cell with LaF₃ vapor deposited film as electrolyte varies with the concentration of oxygen in the ambient atmosphere at room temperature. Some fundamental experiments have been carried out in order to realize a solid-state oxygen sensor with LaF₃ vapor deposited film. The merits of the sensor are that it can be used at room temperature withouth eating, not like a ZrO₂ oxygen sensor, and that it can be easily made small because it makes use of a solid-state cell.
Oxygen sensors with Au as a cathode, La or Cu as an anode, and LaF₃ vapor deposited film or single crystal as a solid electrolyte have been fabricated, and their characteristics such as the current sensitivity to the oxygen concentration and the current responce to the change of oxygen concentration have been measured. It has been observed that the cell current is proportional to the logarithm of the oxygen concentration and the responce time is about 3 minutes for the vapore deposited film cells and about 20 minutes for the single crystal cell.
The structure of LaF₃ vapor deposited film has been studied by means of reflection high energy electron diffraction. The LaF₃ vapor deposited film has a polycrystalline structure and its grain orientation depends on the deposition conditions.
The material transport through the film has been studied by means of Auger electron spectroscopy in conjunction with Argon ion sputtering. Some oxygen deposition have been observed at the anode interface of the sensor, after a few days operation.
These experimental results indicate that the LaF₃ oxygen sensor responds to oxygen by the following sequence: reduction of oxygen at the cathode, oxygen ion transport through the LaF₃ film, and oxidation of the anode metal.

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Most pneumatic resistors have non-linear flow characteristics, though a linear one is desirable for easy design of pneumatic circuits. A capillary is a linear pneumatic resistor, but its linearity is limited within a small pressure difference.
The flow rate of a non-linear resistor such as an orifice or a nozzle is proportional to the product of the opening area and the square root of the pressure difference. Therefore, if the opening area can be changed proportional to the square root of the pressure difference, the flow rate must become proportional to the pressure difference. The linear pneumatic resistor reported here is based on this principle. The resistor consists of a bendable diaphragm and a fixed partition with a port. The diaphragm, overlapped on the port, forms an opening slit along the fixed partition, when it bends. The negative pressure developed in the slit grows with the overlap, and controls the opening area of the slit to produce the linearity. The resistor with an appropriate overlap shows a good linearity in the wide range of the pressure difference. A guide for desining the linear resistor is shown based on experiments and analysis.

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