In this paper, a sequential filter algorithm is derived for the Distributed-Delay Model (multidimensional linear difference equation of high-order) in which the subsystems are serially inter-connected. Taking advantage of the serial structure of the system, the computational burden for a state estimation is enormously reduced. A mathematical model for the pollution dynamics of a river is described by the Distributed-Delay Model with the serially connected structure, and the sequential filter obtained in this paper is applied to the state estimation of water quality in the Yomo River near Osaka. It is shown that, among the various state estimation algorithms, the sequential filter developed in this paper is a powerful one for the Distributed-Delay Model with a serially connected structure.

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This paper deals with optimum information processing problems in the general setting of decision problems. Information structures are described by σ-fields generated by data and structures of transition probability. From the intrinsic standpoint of decision problems, the information value induced by the optimum objective cost functional is defined. From the standard information theory, an information measure such as Shannon's mutual information is introduced. Relations among information structures, the information value and the information measure are clarified. Using these results, optimum design problems of information structures with respect to the information value are discussed. Further, a new design method is proposed, which is not directly based on the information value, namely the objective cost functional, but on the information measure. It is however shown that this method is not inconsistent with the information value and has a simple form.

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The input-output structures of linear, time-invariant, discrete-time systems are investigated. The newly defined perfect reachability and the perfect (null) controllability are discussed together with the perfect observability and the perfect reconstructibility which have been studied by other authors. First the definition is given of those subspaces in the state space which characterize those structural properties, and then it is shown that the subspaces are invariant to the state feedback and the output injection. Making use of this invariance property, the general systems with the direct transmission are reduced to those without the direct transmission.
With the aid of the newly defined subspaces, some formulae related to the perfect observability are rederived, the proof of perfect observability being much simpler than that of other authors. The duality between the perfect observability and the perfect reachability and so forth is also clarified. The perfect observability is equivalent to the conservation of the observability for any state feedback, while the perfect reachability is equivalent to the conservation of the reachability for any output injection. There is no such equivalence relation for the perfect reconstructibility and the perfect controllability. The perfect observability does not necessarily imply the perfect reconstructibility and vice versa. These points are made clear by presenting counterexamples.
The newly defined structural properties are examined with relation to the input observability and the output reproducibility, and to the solution of the Ricatti difference equations.

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This paper describes a method for identification of nonlinear systems characterized by the cascade connection of a linear element and a zero-memory nonlinear element. The dynamics of the linear element is represented by the weighting coefficients derived from the impulse response and the characteristics of the zero-memory nonlinear element is approximated by the polynomial equation.
The identification method proposed in this paper is a kind of sequential approximation method and the procedure of the estimation takes the following two steps. As the first step, the approximate solutions of the parameters of linear element are obtained by the nonparametric training procedure of the threshold logic learning machines, and then the approximate solutions of the parameters of zeromemory nonlinear element are obtained by the gradient method. As the second step, the accuracy of the approximate solutions derived in the first step is improved by the modified gradient method.
In this paper, the authors explain the algorithm of this method and discuss the convergence problems of the estimated parameters and show some results of the digital simulation which support the described theory.

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An artificial hand with many joints should be able to move avoiding obstacles under the operator's command. Some reports have been presented on the route finding method of the machine and its simulation but they have dealt with only two dimensional movements. Moreover, the movement of a hand must be considered not as that of a point but as that of the space occupied by the finger and the arm parts. Hence, the existing methods cannot be applied immediately to control the hand to move without hitting obstracles in the space.
At first, three methods are presented to evaluate the controlled variables of joints working in the space without any obstacle. The two are the application of nonlinear programming technique, the SUMT and the gradient projection. According to the simulation, both are better than the previous methods to date but the gradient projection is much superior to the SUMT. The third method, utilizing the geometrical characteristics of the artificial hand, has proved to be the best.
Then an algorithm for route finding in the space having many obstacles are presented. Segmenting the space into blocks, the problem is transformed to the one finding the sequence of blocks through which the arm and finger pass. It is ascertained by calculation and experiment that the method is effective for the control to drive the hand to any point in the working space, avoiding obstacles, and is also practical in point of computer time and memory.

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This paper considers the least square approximation with the data given at the lattice points in the multidimensional hypercube. Since the solution is obtained as the sum of a prohibitively large number of terms, usual termwise calculation of the solution requires a great deal of computational labour. So, we obtained an algorithm which regards these large number of terms as a population and evaluates the solution based on a relatively small number of terms sampled at random from the population. In order to make the scattering due to the random sampling as small as possible, the algorithm is designed to sample the pairs of similar terms in such a way that the terms cancel each other, based on the idea of the control variate method. The control variate, which is a linear apporximation of the data, is constructed by performing a preliminary random sampling. The results of the calculation of a twenty-dimensional example show that the proposed algorithm is very efficient. A considerable reduction of on-line computational labour is expected by using the proposed algorithm together with the algorithm without the control variate method. The proposed algorithm is considered especially effective for the problem with the data with a relatively large linear part.

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Seeking the min-max point of an unknown function which has several saddle points is one of the most important problems to obtain the optimal mixed strategy in a general game. However, no useful method is available for the problem.
This paper presents a powerful method for obtaining multi-dimensional, multi-saddle payoff functions. The search procedure consists of six main steps: i) to fit local models according to the observed data, ii) to estimate the model's uncertainty due to the lack of data, iii) to estimate the upper limit function and the lower limit function of the unknown function, iv) to estimate a point which is thought to be min-max with a maximum possibillity, v) to ovserve the unknown function at the estimated point, vi) to check if the observed point is the true min-max point.
Simulation studies on unintentionally sellected four test functions of two scalar variables produced fairly good results. The correct min-max points are detected with less than 0.3% error after about 100 observations. The number of the observation is about one-thousandth of that which would be required in applying a uniform lattice search.

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It is shown that the two-dimensional potential distribution of a region involving different dielectrics is successfully measured with the conducting paper method. In place of the electrostatic field, the current field of the conducting paper is measured, but the portion of the conducting paper corresponding to the different dielectric is replaced with the specific conducting paint whose conductivity is proportional to the permittivity of the dielectric.
As an example, measurements of the equipotential distributions in various special electrodes with one dielectric have been taken and the experimental field plots of interest are presented. The advantages of this method are that the equipotential plot is directly drawn on the conducting sheet, and that there are no polarization effects, so either a.c. or d.c. may be used. This method is very useful for optimizing the location and shape of electrodes with various dielectrics.

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The authors have developed a new type of channel electron multipliers (CEM's) which are made of the caramic semiconductors of barium titanate family or zinc oxide-titanium oxide family. The ceramic CEM's have a gain of 10⁸ at the applied voltage of 3∼4kV, and have a typical value of resistance 10⁹Ω. The CEM's of barium titanate family have positive resistivity-temperature characteristics unlike those of the conventional type using a semiconductor thin film on the inner wall of a glass tube. This ensures a protection against a “thermal run away” and the selection of the value of resistance of tube materials is not unduly limited.
It was also expected that the ceramic CEM's were durable and stable both mechanically and chemically. Experiments using mainly those of barium titanate family were performed to clarify the upper limit of the operation temperature and the allowable baking condition. The ceramic CEM's used in the experiment were able to work at temperature above about 250°C, whereas a decrease of gain took place when the CEM's of a conventional type were operated at temperatures above about 150°C. The baking condition allowable for the ceramic CEM's was higher in temperature and longer in time than those for the conventional CEM's.
The initial value of electron gain of 10⁸ fell to 10⁷ after the accumulated counts of 10⁹, somewhat less than 10¹⁰ counts for the conventional CEM's. However, the ceramic CEM's exhibited an almost constant gain over the first 10⁸ counts followed by an irregular gain decrease, while in the case of the conventional CEM's the gain exhibited a linear decrease during the operation. The CEM's which suffered a gain fatigue during the life test completely recovered their initial gain following a reexposure to the atmosphere. They are also sensitive to ions and soft X-rays. Besides the characteristics mentioned above, the ceramic CEM's have an advantage that they can be manufactured easily and economically. In the industrial applications, the CEM's may be used as a β-ray detector or a photomultiplier in a vacuum sealed structure. In this case, more reliable performance can be expected for the ceremic CEM's than for the conventional CEM's because the CEM's allow a higher temperature for baking during the sealing process.

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A method for pneumatically generating an arbitrary function is described. The system manufactured on trial consists of a pneumatic sensor, a rotating disk with fan-shaped blocks and a mechanism to drive the disk. The blocks are arranged on the periphery of the disk surface to form an annular ring as a whole, and each level of the upper surface of the blocks on the disk surface can be adjusted separately with a spring and screw assembly, in accordance with the required posisitioning related to the desired functional curve. The pneumatic sensor is a fixed nozzle which is perpendicular to the block upper surfaces, and it is a part of an pneumatic micrometer circuit with other pneumatic components. By rotating the disk at a constant speed, the gap between the nozzle and its counter-face changes, and thus a continuous pressure change analogous to the required function curve generats at the output of the pneumatic circuit. A discussion is given on the generated waveform which depends on the successive gap width, the nozzle size, and on the dynamic characteristics. Based on the similar principle, a pneumatic transducer has been made to generated an arbitrary function pneumatic pressuer by a linear displacement. The paper describes this transducer which employs many rectangular blocks arranged like keys of a piano.

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This paper investigates the problem of designing a feedback compensator to stabilize a linear system with delays.
The compensator is constructed by delay elements, and a sufficient condition for the linear system with delays to be stabilized by this compensator is obtained in the terms of the system parameters. The rate with which the state of the system decreases to zero using this compensator is also discussed.
The sufficient condition and the compensator design method are both suitable for practical use.
These results are obtained by a kind of generalization of a canonical form for ordinary differential systems.

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The behavior of confined water jet under free surface has been examined.
The jet does not flow straight. The water above the upper part of the jet is surrounded by a free surface, two cover plates, the nozzle block, and the jet, while the water below the lower part of the jet is not confined. A water bubble region generates in the upper part because of the entrainment effect of the jet. The pressure in this region will be lower than the static pressure. Therefore, the jet deflects towards the free surface, but its condition is not always stable. When the jet velocity becomes larger than a critical value, the whole water in the upper part of the jet is entrained into the jet and the fluid in this area turns into air. Then the jet deflects in a stable manner towards the free surface. The phenomenon in this case is similar to Coanda effect.
The critical velocity of the jet increases as the distance from the free surface to the nozzle exit becomes longer, while it decreases as the nozzle width becomes larger. The attachment length of the jet becomes longer with the increase of the jet velocity.

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Sufficient conditions for non-oscillating responses of a relay-controlled composite system are studied. We find a typical example in the VQ control of an electric power system, where non-oscillating responses of the controlling switches are desired. The realys considered have dead regions, multi-inputs and the following properties: The space of the input variables to the relay is devided into a finite number of regions, while the output of the relay is constant for the inputs which belong to the same region. The non-oscillating trajectory is defined to be a trajectory which does not pass a pair of regions defined as opposite. Assume that every trajectory of isolated subsystems which starts from an initial point belonging to some area is non-oscillating. The trajectories of the composite system may be supposed also nonoscillating if the subsystems are weakely coupled. Evaluating the upper bound of interference that a subsystem receives from other subsystems, the conditions for non-oscillating responses are obtained. The results may also applicable as stability criteria for the systems of which Lyapounov functions are difficult to find.

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A multivariable feedback system y(s)=G(s)x(s), x(s)=u(s)-F(s)y(s) is treated where G(s) is the transfer function matrix of a plant and F(s)=diag(f₁(s), …, f_n(s)) is that of a controller. A new bound for the transfer function h_k(s) that relates y_k(s) to u_k(s) when the k-th loop is open but the other loops are closed is given. The main result reads: |h_k(s)-g_kk(s)|<a_k(s)if|f_j(s)^-1+g_jj(s)|>a_j(s)(j=1, …, n;j≠k). Here, A=diag(a₁(s), …, a_n(s)) is such a matrix that A-B is a semi-M-matrix and B=(b_jl) is given by b_jj=0, b_jl=|g_j(s)|(j≠l). A method to determine A when B is given is also presented. The result is useful for the design of multivariable systems.

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In order to study convective heat transfer and flow in a model water way, it is strongly desirable to measure local flow velocities in the range as wide as 10^-2 to 10¹cm/s, using weak electrolyte.
A new method has been developed for this purpose, in which an electrolyzed boundary is produced in the weak electrolyte by a DC current along the single probe and is used as a mark which moves together with the liquid flow.
The applicable ranges of this method are: flow velocity range; 0.02∼12.5cm/s, liquid temperature range; 20∼57°C, and resistivity range of electrolyte; 1>×104∼2×10⁵Ω·cm.
In the measurement of the velocity profile in a vertical channel, the measured and pre-set mean velocities agreed with the accuracy better than±10%.

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A new method of vehicular speed measurement is presented. The principle is to determine the transit time, whicn is required for two points on a motor vehicle to pass over a point on a road surface. Two optical detectors are mounted on a moter vehicle in line, in the vehicle direction. Random signals are obtained from the road surface by the detectors. The relative delay between the signals is determined from their coincidence, by shifting one of them, or from the peak of their cross-correlation function.
The measurement is capable of very high accuracy.
Errors of the speed measurements are studied in detail: The resolution of the delay determination from a single cross-correlation function depends on the sampling interval of the random signals. Statistical error of the measured speed depends on (1) the aperture diameters of the detecters, (2) SNR of the signals and (3) the averaging length required to obtain the crosscorrelation functions. The vehicular speed can be determined to an accuracy of 0.7%, for instance, using rectangular apertures of 6×30mm and an averaging length of 2.20m.
Advantages over the conventional methods and shortcomings of the new method are described.

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The optimal control of linear time-invariant systems relative to time-multiplied quadratic performance indices is discussed. The problem is to design a dynamic compensator by using the degree of optimality which quantitatively measures the total performance of the control system.
The necessary condition for the optimal dynamic compensator is derived.
The dynamic compensators for the second, third and fourth order plants are designed as example. It is shown in Example 1 that the 1st order dynamic compensator is sufficient to control the plants under consideration because there is little difference in the degree of optimality between the 1st order dynamic comensator and the 2nd or the 3rd order dynamic compensator. Example 2 shows that the timemutiplied quadratic performance is excellent in estimating the control schemes.

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A single-phase bridge inverter with series diodes has a simple construction, but it is impossible to apply a pulsewidth control method to it. In order to make up for this weak point, one device, which is similar to this type and has an adjustable pulsewidth of voltage, is proposed. Its commutating inductance can be reduced by half the value of the single-phase bridge inverter with series diodes.
In this device, the couple of diodes connected to a commutating capacitor are replaced with a couple of thyristors so that each of the two branches has two thyristors. When these two thyristors on the branch are fired by gate signals with a phase difference, the output voltage can be kept at zero during the phase difference between the two thyristors. The time duration adjustment of this interval provides the device with the function of the output control.
The operation of this inverter with some inductive loads is illustrated. The approximate solutions of the reversebiased time and the peak currents of the thyristors at the commutation interval are given. Using these solutions, it is easy to decide the optimum values of commutating capacitors and inductors.

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The velocity distribution of the attached jet in a liquid fluid amplifier has been investigated by means of a constant temperature hot-film anemometer. The dimensions of the fluidic element used are; main nozzle width b_m: 10∼25mm (variable), offset D: (2.0∼6.1) b_m (variable) and side wall angle α: 0∼22.5° (variable).
Using water of about 20°C as the operating fluid, the studies were performed in the conditions of main jet velocity υ₀=2.5∼4.0m/s and various forms of the element. The data were analyzed referring to Goertler's model of turbulent jet.
The following results of the experimental studies are obtained: (1) The velocity distribution of any attached jet is closely approximated by Goertler's model in which a reasonable spread parameter is evaluated separately on the attached and unattached sides of the jet. (2) The effect of element in the conditions of various side wall angles, offsets and nozzle widths on the spread parameter was studied. (3) Empirical formulas for the spread parameter were obtained as functions of radius of curvature of jets. (4) In any attached jet, the momentum conservation holds good in the upstream region of the vortex.

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