The problem considered in this paper is the identification of states and parameters in noisy nonlinear dynamic systems. It is a well-known fact that the identification problem for nonlinear systems results in the problem of solving the nonlinear two-point boundary value problem (T. P.B.V.P). The methods of quasilinearization and invariant imbedding are often used as computational algorithms for solving this type of nonlinear T.P.B.V.P.
From the point of view of the computational aspect, the quasilinearization method is a nonsequential or off-line algorithm, namely, a batch one. On the other hand, the invariant imbedding is a sequential or on-line algorithm.
A computational algorithm by the combined use of quasilinearization and invariant imbedding was already given as the optimization technique in order to solve nonlinear T.P.B.V. P in the optimal control problem and the system identification problem. The algorithm is a predictor-corrector formula in which the invariant imbedding predicts the missing initial condition and the quasilinearization procedure corrects this predicted value.
In this paper, a new computational algorithm which differs from the predictor-corrector algorithm is proposed as the optimization technique. The algorithm presented involves a batch-sequential computational process in which the states and parameters are estimated by invariant imbedding at a sub-time interval in a forward sweep after processing the data by the quasilinearization method at the interval. For this reason, this algorithm will be called a batch-sequential identification algorithm. The algorithm requires less computational effort than the predictor-corrector formula and also has better convergence properties and identification accuracy than the filter algorithm via invariant imbedding, taking an appropriate choice of initial conditions and sub-time intervals.
Experimental results from an example of a simple identification problem indicate that the proposed batch-sequential identification scheme is feasible for the nonlinear system identification problem.

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An improved horizontal cross capacitor was designed and constructed to achieve higher accuracy in the determination of absolute capacitance value, following the former cross capacitor with an accuracy of 1 ppm.
To eliminate some major causes of error, four main electrodes were finished more precisely and new mechanisms were adopted for alignment of the electrodes. The alignment is inspected with an auto-collimator and a special inspecting tool. The four-main-electrodes system has about O.5μm of the irregularity in the inner space formed by the electrodes.
The length of the electrodes system is determined from observation on the fringe of a Fabry-Perot interferometer system. Its light source is a ³He-²⁰Ne laser.
A precise capacitance beidge with an inductive ratio arm to be used for measurements of the capacitor was built. After discussing the inductive ratio, a ratio transformer of the bridge with a ratio of 10/1 was designed. Its ratio error is less than 0.2ppm.The sensitivity of the transformer bridge whose output capacitance especially tuned by a high Q coil is also presented. The sensitivity attained is 0.01aF at 150Vand 1592Hz.
Uncertainty in absolute determination of 0.1pF by the cross capacitor is estimated at 0.25ppm.

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Some of the properties of extremum functions and their applications to Bayesian decision problems are discussed. Suppose that a conditional probability P (|y) over state space X, given some information y, is specified. Let f (x, u) be the performance index, where u is the decision variable. It turns out that the minimum of the conditional expectation Ex|y {f(x, u)} with respect to u is measurable so that the expectation E_y minu E_x|y {f(x, u)} can be taken. It is also shown that a measurable functionn u(y) can be chosen in such a way that u(y) minimizes E_x|y {f(x, u)} A class of min-max decision problems is also discussed.

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To obtain reliable information from data under the limitations of measuring interval and/or sampling number, it becomes necessary to take the dynamic characteristics into account and fully utilize the transient output of a measuring instrument.
This paper studies, from the above viewpoint, a new measuring method of data processing method for the case of certain measuring process contaminated with correlated noises. And the error theory is extended for evaluating the measured values obtained by that measuring process, and for giving some suggestions on the measurement programming.
As computational examples for the measuring instrument described as a first order system, the relations are illustrated between the variance of error of the measured value and certain parameters, such as the time constant of measuring instrument, sampling number, measuring interval, and sampling times.
With correlated noises, the variance of error of the measured value does not decrease to zero for a finite measuring interval and/or sampling number.
It is recommended that the dynamic characteristics of the measuring instrument and sampling times should be determined based on the nature of the noise sources.

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Hoping to develop a future primary standard of length to use for precision interferometric length measurement, a frequency-stabilized He-Ne laser has been made. The frequency of the 0.633μm output is locked to one of the hyperfine components of an absorption line of moleculer iodine ¹²⁷I₂ by the method of saturated absorption.
The laser cavity in which the absorption cell of iodine is placed, is servo-controlled by dual feedback loops; one is for proportional control by a piezoelectric transducer, and the other is for on-off control driving a specially designed fine tuning apparatus with a parallel spring system until the servo error is reduced to less than a set value.
The stability of the frequency is evaluated by Allan variance and standard deviation measurements of the beat frequency between two stabilized lasers. Results of the measurement for five hours and a half give an Allan variance of 8kHz for a 10 second averaging period and a standard deviation of 96kHz. From these data, long term stabilities of 1.2×10^-11 from the Allan variance and 1.4×10^-10 from the standard deviation are evaluated for the individual laser.
The relations between the temperatures of molecular iodine in the absorption cell and of the laser output, between the maximum frequency deviation of the modulated laser output and the first and third derivative signals of inverse Lamb dip produced by saturated absorption in iodine vapour are obtained. And systems for measuring the beat frequency by analogue and digital methods are described.

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For the purpose of using parallel capillaries as transmission lines in analogue fluidic circuit systems, the power transmission characteristics are theoretically and experimentally investigated. The effects of the dimensions of parallel capillaries, the internal impedance of the signal source, and the load impedance are studied over the frequency range of 0∼300Hz. It is shown that the parallel capillaries are useful as low-pass transmission lines between fluidic amplifiers, but it is difficult to obtain good characteristics at the attenuation band. The experimental results agree well with predictions from a distributed parameter theory over the total frequency range. For a lumped parameter theory, the differences are within 10 percent at Ω≤40. (Ω=2πfa²/ν)
Finally the theoretical method of design for a parallel capillaries transmission line is described with an example.

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This paper deals with a biomechanical study on the adaptive posture of a gliding snake. The “principle of α adaptation” is proposed, describing that a snake moves by adapting its wriggling angle α to the ratio of frictional coefficients between the ventral and the ground surface. Zoological experiments with the snake Elaphe Quadrivirgata show good agreement with the theoretical results derived from the author's kinematics of serpentine locomotion.

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In this paper, a mathematical model of white Gaussian processes distributed in a bounded spatial domain is established in the framework of generalized function theory.First, both the spatially distributed white Gaussian process and the spatially distributed Wiener process are defined by introducing the concept of generalized random fields. It is also shown that the derivative of spatially distributed Wiener process with respect to time is the spatially distributed white Gaussian process in the sense of distributions.Secondly, the regularized distributed Wiener process with respect to spatial variables whose sample function is sufficiently smooth in the spatial domain defined is mathematically established. It is also verified that the regularized distributed Wiener process defined here satisfies the conditions of abstract Wiener processes defined by Curtain and Falb.Finally, a mathematical model of system noise distributed in a bounded spatial domain is approximately represented by the abstract Wiener integral.

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Let z(t) denote a random signal process, its observation process y(t) be given by y(t)_??_z(t)+v(t), and z(t) denote the linear least squares estimate of z(t) based on {y(τ);τ≤t}, where v(t) is a white process which is uncorrelated with z(t). It was first shown by Kailath in a heuristic manner that the innovation process ν(t) of y(t) defined by ν(t)_??_y(t)-z(t) is a white process with the same correlation operator as that of v and has the same information as the original observation process y as far as linear estimates are concerned. The complete proofs of these properties requires a rigorous treatment of the white process because v(t) appearing in the observation process is not an ordinary random process. One way to treat the white process is to employ a stochastic integral, which enables one to discuss a problem involving a white process without defining the white process explicitly. Another way is to define it in the framework of generalized random processes.
In 1972, Kailath gave a rigorous proof of the properties of the innovation process using stochastic integrals. In the same year, the proof using generalized random processes was given by H. Inaba. In this paper, we discuss the linear filtering problem for random fields and show that even for the case of random fields the corresponding innovation process has the same properties as those of the innovation process for stochastic processes.

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The adder, the multiplier and the integrator of the Stochastic Computer, in which the computer variables are expressed by the frequency of ON or OFF random pulses, have already been reported. However, as a general purpose analog computer, the stochastic computer needs a function generator. In this paper we propose a new type stochastic function generator which generates the arbitrary function f (t) providing 0<f(t)<1 by a sequence of pulses. The function generator is composed of extremely simple circuits using the adders and multipliers of the stochastic computer, although its principle is the weighted sum of Walsh orthogonal function. An analog output is available by the use of a simple low pass filter. As its application, a time invariant function generator, a digital to stochastic converter and a correlation function generator are described.

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Seeking the maximum point of an unknown multi-modal function is one of the most important problems for solving an optimal decision in the case where the criterion may have many local maxima. However, no useful method to find the global maximum point has been available yet.This paper presents a powerful method for multi-dimensional criterion functions. This is an extension of the method formerly developed for the one-dimensional case by authors.
The search procedure consists of three main steps: (i) to fit local models according to observed data, (ii) to essimate the location of the maximum point considering the peaks of the model and the uncertainty of the models due to lack of enough data, (iii) to search an area where the estimated maximum point exists.
Simulation studies on two 1-dimensional and four 2-dimensional test functions randomly selected provided fairly good results.
The correct maxima are detected with less than 0.5% errors. Number of observations in this method was almost the same as that of ramdom search in 1-dimensional case and about one-eighth times in 2-dimensional case.

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It is important to find the system of minimal complexity among equivalent systems, that is, systems with the same input-output relation.
As for finite dimensional linear time-invariant systems, minimal complexity is considered as minimal dimension. The algorithm for obtaining irreducible realization is given. And the close relation between controllability, observability and irreducibility is presented.
As for linear time-invariant systems with delay, a few concepts of controllability are defined and necessary and sufficient conditions for them are given. Also the relation between controllability, observability and irreducibility is investigated.
This paper is concerned with time-invariant linear systems with delay. The number of integrators or the number of delay lines needed to construct the system is used to demonstrate the complexity of the system. Two irreducibilities, one for minimal integrator and one for minimal delay line, are considered, and an algorithm for obtaining systems with such properties is introduced. Two kinds of controllability and observability, ones for integrators and ones for delay lines, are defined, and the necessary and sufficient conditions for these properties are given. Close relations among these controllabilities, observabilities and irreducibilities mentioned above are presented.

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Knowledge of the type of feedback system that will follow a desired input with zero steady state error is useful for designers. In this paper any m-input m-output feedback system (r-input m-output transfer element) is shown to be classified as a type [l₁, ……, l_m] system, depending on the controllability characteristics of the error system in servo problems. The definition of the type-[l₁, ……, l_m] system, of course, includes one for the 1-input 1-output system, and this definition is widely known in classical servo-theory. The type of system can be decided by using the criterion matrix M which is defined by an expansion of the open loop transfer function matrix of the system. Knowledge of the type of the transfer element enables us to design a type-[l₁, ……, l_m] output feedback system having a dynamic compensator of lower order than was necessary in earlier design technique.

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This study has been performed to clarify the behavior of the fluidic sonic oscillator. First we reconsider the propagation of pressure waves in the connecting tube during oscillation. Then we experimentally investigate the switching characteristics of wall reattachment fluidic devices and the mechanism of generation of pressure wave at the switching.
The results obtained can be summarized as follows:
1) In a sonic oscillator, the difference of pressure in two control ports just before the jet switching is at most zero. Therefore it is necessary that the switching pressure difference of the device for a sonic oscillator is less than or equal to zero.
2) When the mean pressure in two control ports is less than a certain value, the switching pressure difference of the device becomes less than or equal to zero. And the connection of the control ports by a tube can generate the sonic oscillation, if the mean pressure in the tube becomes lower than the value mentioned above.

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This paper deals with the techniques of reproducing input waveforms of linear dynamic systems, which are the application of the theory of input observability by the author, and those of constructing quasi-invariant control systems using reproduced load or disturbance waveforms. Three methods of reproducing input waveforms are discussed, viz., analog and digital inverse circuit methods and a polynomial method. The last one does not include a difference operation and is applicable to systems whose input terminals are more than output terminals. We apply these three techniques to the measurement of the motor torque and the load torque waveforms of an induction motor system (0.2kw, 4 poles, 50hz).
This paper also shows the realizability of the quasi-invariant condition between a pair of input and output terminals with only one path. The approximation of the control circuit is enough for practical use, which is verified by the examination of a thyristor-leonard system and analog simulations.

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We consider a control system which is described by a special but important class of timehomogeneous stochastic differential equations. The drift coefficients in the equations are considered controlled and the control policy is a measurable functioi of the present state of the system. A long-term average cost is associated with the system, and our problem is to choose a control which minimizes this cost. In this paper an extension of Ito's differentation rule to functions belonging to a Sobolev space is given, and this result is used to derive a sufficient condition for optimal controls which is analogous to that given by Wonham. A theorem on the existence of optimal stochastic controls is also given under some sufficiently strong assumption

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This paper presents a fundamental consideration for the solution sets of linear optimal problems with a vector-valued performance index. A unified definition of three solution sets, which are efficient, proper and optimal, is given in terms of polar cones. Certain characteristics shared by the solution sets are investigated. The relationships between the solutions of the linear programming problems reduced from the vector-valued problem and the solution sets are established. The conditions which the solution sets should satisfy are derived by examining whether the intersection of two convex cones is empty or not. The conditions are useful for establishing an algorithm to find the solution sets. In order to facilitate understanding of the characteristics and the conditions obtained in this paper, a simple example is solved. A direction for further research of this problem and an application of the study are mentioned.

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