In this paper, a unified theory of the statistical treatment for the output probability distribution is newly proposed by introducing a statistical Lagrange series expansion method. In the development of the theory, the assumed situation is that a general random process of arbitrary distribution type is passed through a non-stationary stochastic system of memory type with an arbitrary non-linear feedback element.
For the purpose of finding the effect of an arbitrary non-linear feedback element on the output probability distribution, the explicit expressions of the probability distributions are derived in general forms of non-orthogonal expansion series, reflecting the various effects of the forward linear element of the system into the first term.
Further, in view of the arbitrariness of the input characteristics, the possible variety of non-linear element and fluctuation forms of system parameters, and the complexity of the statistical treatment involved, the validity of theoretical expressions is experimentally confirmed by the method of digital simulation.

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The control problem of a stochastic system including distributed parameter subsystems of transportation type is discussed. The system discussed in this paper is a mixed parameter system which is described by a system of ordinary differential equations and hyperbolic partial differential equations both perturbed by Gaussian white noise. The stochastic mathematical model of the system is formulated as stochastic integral equations, and a sufficient condition, under which the model has a unique solution, is derived. The optimal control problem of the linear system for a quadratic cost performance is discussed, and a sufficient condition for the optimal control is obtained. Applying this condition, the optimal control can be realized by linear feedback of the state {x(t), ξ(t, )}, and the optimal feedback gain is obtained as the solution of the Riccati type differential equation.

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Recently, many researchers attempted to consider the optimal estimation problems for a stochastic system with noisy observation from the viewpoint of the information theory. But their studies were mainly limited to the investigation on linear systems.
In this paper, we determine the optimal filter for a non-linear system from the information-theoretical viewpoint by considering the influence of non-linear elements.
As a result, it is derived that the optimal filter for the non-linear system coincides with the well-known Kushner filter.
Moreover, we treat the two-dimensional dynamical system as a numerical example, and show that it is possible to effectively evaluate the accuracy of estimation by using the entropy of the estimation error studied here.

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The purpose of this paper is to treat the problem of controllability of the distributed-parameter systems described by the linear wave equation. We consider both finite dimensional distributed control functions appearing in the differential equation and boundary control functions appearing in the boundary condition. When the controllers appear in the differential equation, it is desirable from an engineering viewpoint that the support of the controllers is “small”. For this reason, the idealized case, where the controllers are expressed by Dirac's δ-measures, is also treated. In each case, the necessary and sufficient condition for controllability is obtained.

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This paper describes an optimal design of automatic steering system of automobiles. In this study, an automatic control equipment which can control an automobile along a guidance cable is used. This equipment is fabricated with fully electric components.
First, the dynamics of the automobile is measured by the frequency response method. Secondly, an optimal design method of an automatic steering control system is proposed. This method is based on the Kalman filter and the optimal control theory. Thirdly, the performance index of the control system is determined as the solution of the inverse problem of the optimal control theory. These second and third parts are special features of this study. Furthermore, it is confirmed both by simulations and by field experiments that the theory mentioned above is effective in the design of automatic steering control system.

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In this paper, we deal with a new searching method algorithm. Previously we suggested new searching method SCAM (Sequence Coordinate Additive Method), and this algorithm is giving good results. But in this method a time-consuming linear searching is necessary. Here, we propose the Preliminary Searching SCAM.
This method has the following properties. (1) Linear searching isn't necessary. (2) This method has second order convergence. (3) If the object function is of a quadratic form, by only the same number of trials as the number of coordinates, we can arrive at the optimal point.
In this paper, we describe this new algorithm and the comparison of the calculating time and the convergence.

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Recently, several methods of synthesis for decoupled control by state feedback or output feedback have been developed by Falb, Wolovich, Gilbert, Pearson and others. Concering these methods, it can be pointed out that although much stress is laid on treating the problem of decoupling controlled objects, relatively little attention is given to the other problems such as those of compensation which are equally important in automatic control systems.
In this paper, we tried to treat these relevant problems simultaneously and derived a new synthesis method of decoupled control systems. By using this method, we can get a decoupled control system in which each decoupled subsystem has the following properties at the same time:
(1) No steady state error exists for both the arbitrary reference inputs and the disturbances. Here these inputs and disturbances, are assumed to be of the type described, by a p-th order polynomial of time at t≥0 and to be zero at t<0.
(2) Property (1) remains unchanged in spite of the change of parameters in the controlled objects.
(3) Every pole of the system can be set equal to arbitrarily designated real or conjugate complex numbers by adjusting the free parameters.
(4) The order of Pearson's dynamic compensator is L. Then the zeros of (L+1), which is derived by adding the dynamic compensator, can be set equal to arbitrarily designated real or conjugate complex numbers.

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This paper is concerned with the fundamental properties of the response of relay-type scalar stochastic systems. The system considered here is described by scalar Ito's stochastic differential equation, in which the diffusion coefficient is assumed to be twice continuously differentialable, and the drift coefficient is assumed to have negative jumps in some points and to be twice continuously differentialable in other points. It is well-known fact that the Fokker-Planck equation for the probability density function for the response does not hold on the whole domain of the state space, but its equation holds on each domain of the state space in which the drift coefficients are differentialable.
Firstly, the existence, uniqueness, Markov nature and continuity of the solution for the relay-type scalar stochastic differential equation are discussed, and secondly the boundary conditions to solve the Fokker-Planck equations on each domain of the state space are obtained.

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This paper presents consideration on the mean square stability of a linear continuous time system perturbed by a Gaussian white noise linearly dependent on the state variables. A necessary and sufficient condition is given for the system's stability, and some sufficient conditions which are easier to use are also given. Similar stability conditions are presented for the linear discrete time systems with a state dependent noise.
The results obtained here are generalizations of earlier results given by Willems, Kleinman, McLane, etc.

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The pedestrian flow in a network of evacuation routes is considered as a lumped parameter system. The state variable equations are formulated to describe the pedestrian density, the pedestrian flux and such like being functions of space and time. In the formulation the retardation of flow is also taken into consideration.
On the retardation of pedestrial flow, assuming that it is caused by the flow becoming incompressible in an area in which the density reaches a maximum, the “coefficient of retardation” representing a degree of retardation is derived.
Employing the relationship between density and velocity and the maximum density obtained by an observation of actual flow, an assumed pedestrian flow in an actual urban area is simulated.

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In this paper, a binary picture is partitioned into regions on the basis of geometrical properties. The definition of a region unit is induced from the basic geometrical property of regions. A region is defined as a union of the region units, and it is equivalently represented by its contours and covers, which are arranged in the form of indexed picture planes. This form is convenient for examining sequential as well as planer properties of regions. Furthermore, the local vertex is defined from the concept of digital lines, and a contour can be divided into line segments. A set of planar operators is given for those picture processings.

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In this paper, is discussed a new method of electronic measurement of water content in plants by means of high sensitive impedance meter. The impedance meter was designed to measure stem-water in plants with a low impedance (capacitance; 10pF∼40pF, resistance; 2kΩ∼15kΩ). The water content is measured by capacitance and the concentration of solution in water is measured by resistance. The most important qualities required of the impedance meter are the sensitivity to capacitance and resistance changes, the stability during a continuous operation for long hours and the insensitivity to any other change in the plant. In the equipment, the capacitance output is insensitive to a resistance change and the resistance output is insensitive to a capacitance change. The measuring range of capacitance is about 0∼100pF and the measuring range of resistance is about 1kΩ∼∞. The maximum resolution of capacitance is 10^-3pF and the maximum resolution of resistance is 10^-2μ_??_. The stability was observed to be within less than 4mV in terms of zero drift during 24 hours' continuous operation. In order to apply the equipment to plant physiological research, responses of tobacco plant to light inputs, humidity inputs and temperature inputs were examined in a computer controlled growth cabinet. As a result.
(1) By a step input of light (30, 000lux) at the air temperature of 25°C and humidity of 60% R.H., the change of water content in stem was about 1pF in capacitance. (2) By a step input of humidity (60% R.H._??_80% R.H.) at the same temperature and light on, the change of water content in stem was about 1pF in capacitance. (3) By a step input of temperature (25°C_??_30°C) at the air humidity of 60% R.H. and light on, the change of water content in stem was about 0.5pF in capacitance.
The reliability of the relation between the capacitance determined by these results and the transpiration from a usual method was examined by digital simulation. It was made clear that the equipment was a useful instrument in measuring water contents in plants.

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The statics of complex lever systems was treated theoretically in the previous paper. In this paper, the experimental data for such systems are presented.
A scale is constructed with three levers and has a capacity of one kilogram, and “lever coefficients” κ₁=1 (standard), κ₂=-1 and κ₃=1. If it is adjusted appropriately, its accuracy remains better than 1/2500 while the base is tilted up to 0.25rad from the level. This value of accuracy is comparable to that of Roberval balance (upper dish type) which is used on the horizontal plane.
The “slopeproof conditions” are examined by waiving them one by one to see how they influence weighing.
The experimental results agree well with the theory.

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In this paper, we propose our idea to open up a new field in seismology. Many practical seismometers developed up to now do not perform satisfactorily enough to record long period movements (1∼60sec) in the case of great earthquakes.
In more recent times gyroscopic instruments have been used for various purposes where limited accuracy is required.
We pay attention to the essential properties of a gyroscope such as the precession and the gyroscopic reaction moment, and propose a new instrument as a precise seismometer with a dynamic long period pendulum (proper period 2, 10, 20min) using gyroscope.
In this observation system, we utilize a vertical gyro-pendulum (transducer). The horizontal seismological movements transferred to the torque cause the gyro-axis to precess about the mutually perpendicular axes, and the precessional velocities are measured by rate-gyroscopes (measuring instruments) as amplifiers.
We examine the various dynamical characteristics as a seismometer for practical use and present technical considerations for the future development. The results obtained by the above considerations suggest that the accuracy of measurement is further improved by our new instrument.

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The effects of distributed sampling periods on hybrid data processing are studied theoretically. It is assumed that the difference Δτ of each sampling period deviates from its mean according to a probability density function, p(Δτ). Firstly, it is shown that the characteristic function P(ω) of p(Δτ) behaves as a frequency window if the exact sampling times are used. Then the effects of neglecting the randomness are examined and statistics of errors of resultant spectra are discussed. It is clarified that the effects are essentially equivalent to those which appear when a signal is sampled with an exactly equal period after pre-filtered by a filter, whose transfer function is P(ω). Some applications of a sampler with distributed sampling periods and results of computer simulation are also presented.

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In this paper, we deal with the contacting-both-walls switching by considering the dynamic of reattached jet.
We discuss the motion of jet in the neighbourhood of statical equilibrium state. By assuming a small change of state, a linearized equation of motion is deduced to investigate the stability of static equilibrium state. Then a condition for switching is suggested.
This condition is phenomenologically discussed, and it is made sure that the condition has no incompatibility with our experimental facts.
Finally, the results calculated for switching control flow rates are compared with the experimental results to demonstrate the propriety of this switching analysis.

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This paper presents a method of numerical integration for Stieltjes integration, a construction of a High Accuracy Digital Differential Analyzer based on the method and a few experimental results which show a high computation accuracy and flexibility of the HADDA.
A formula of numerical Stieltjes integration is obtained from Adams method of numerical integration and a formula of numerical differentiation which comes from differentiation of the Newton backward interpolation polynomial. A digital integrator based on this formula is designed and constructed by a minicomputer. A few differential equations are solved by the constructed HADDA and the accuracy of these solutions are investigated.
The experimental results show that (1) the computation error of the HADDA is of order of Δt² while that of the existing DDA's is of order of Δt, where Δt is the incremental size of a independent variable t, (2) the computation speed of the HADDA is about 1/2 of that of the DDA's (3) furthermore, the extension of highly accurate integration from time integral to a more general Stieltjes integration makes the flexibility of the HADDA much higher. For example, it becomes possible to solve nonlinear differential equations much more accurately.

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With the increase of the share held by thermal power plants in the total electric power system, a sudden big load variation and a rapid start-up and shut-down of a power plant are becoming very important. It is necessary to develop a control system that is able to respond quickly to a load demand change by using a control computer.
The paper deals with the development of a computer control system for boiler startup, which is very difficult to control accuratery the boiler outlet fluid temperature, because not only the boiler time constant is very large, but also the time constant and the gain vary very much during the boiler startup. The steps and results are as follows;
(1) The characteristics of a boiler outlet fluid temperature during the boiler startup were analyzed, and the control problems were extracted.
(2) The adaptive computer control system which predicts the change of the boiler outlet fluid temperature and automatically requlates control parameters according to the change of boiler characteristics.
(3) The control characteristics of the systems at various operational conditions of a plant were analyzed by using a hybrid simulator and an actual power plant.
As a result, the stable control characteristics over the whole range of the boiler startup process were demonstrated. Even with the temperature rise from 370 to 400°C, which is said to be the most difficult part in controlling the rise of fluid temperature because the boiler water is transformed into vapor, the deviation of temperature was controlled within 5°C.

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This paper relates to the design of control systems for unstable mechanical systems. For demonstrating the applicability of control theory to practical real systems, a controller is designed and manufactured for a cart-pendulum system which has been studied by many control engineers as an “inverted pendulum” problem.
The control system presented in this paper is a hybrid controller which is constructed by an analogue stabilizing controller and a digital micro computer. The control system is designed to swing up into the inverted position the pendulum which stays initially in the natural pendent position and to stabilize the pendulum about the inverted position.

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