A new approach to the derivation of square root forms for fixed-point and fixed-interval smoothers is taken and schemes different from those of Kaminski and Bryson are introduced. The square-root representation of Kalman filter is known to be effective in removing the numerical instability caused by poor observability in large scale systems. Particularly the square-root fixed-point smoother derived in this paper will reduce the number of triangularizing operations significantly, enhancing the computing efficiency over that of the Kaminski-Bryson square-root smoother.

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This paper describes an optimal control for a class of nonlinear systems dx_i(t)/dt=x_i(t)F_i(x_j(t))-b_if_i(t)u(t)x_i(t), i, j=1, 2(i≠j) which represent some kinds of interactions, for example predator-prey, symbiotic or mutual, and competitive interactions.
We can classify optimal control laws into two cases by the system's global characteristics, i.e., the signs of dF_i/dx_j, df_i/dt, b_i, etc. One case is that the optimal control is a Bang-Bang one, and the other case is that the optimal control is a singular one.
The optimal control is generally a Bang-Bang one. But when each element has the control input (b_i>0, i=1, 2), and the system satisfies the following conditions, f_i'=df_i/dt>0 (i=1, 2), f_i'·f_j'<0 (i, j=1, 2, i≠j), or f_i'≤0 (i=1, 2) and some additional conditions, the optimal control may be the singular one. In that case, the performance index must be the function of input u(t) only. It is remarkable that this separation is independent on the values of the function f_i(t), and dependent on only those of f_i'(t) (in some cases, it is independent on even the values of f_i'(t)).
The function f_i(t) is not the only time variant coefficient with control input. The variation of the effect of control, which is caused by the change of the system structure brought about by the inputs, (especially it is important for the systems in nature), can be considered in this system by means of both the function f_i(t) and the results required in this paper.
Finally the optimal control of the predatorprey Volterra model including a resistance to an insecticide is shown as an example.

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This paper considers the problem of stabilizing a linear time-invariant system with delay x(t)=Ax(t)+Dx(t-h)+Bu(t), h>0 by means of a linear feedback without delay u(t)=Kx(t) to obtain a sufficient condition less restrictive than those obtained so far for such stabilization.
The result is as follows. The system is stabilizable, if (i) (A, B) is a completely controllable pair, and (ii) when (A, B) is written in a Luenberger's canonical form, D=D₁+D₂ where the columns of D₁ are linear combinations of those of B and D₂ is a lower triangular matrix.
The stabilization law stated in this paper is applicable even if the delay time h is not known precisely.

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It is a well-known fact that the whole information on the statistical property for state variables of a stochastic control system can be derived by finding firstly the multivariate joint probability density function of their variables. Nowadays the actual random data (e.g., the road traffic noise measured by a sound level meter) are measured very often in a digital form at descrete time intervals.
In this paper, we firstly give theoretical consideration on the joint probability function and its joint factorial moments suitable for an actual situation that real experimental data are taken in a form of digital level and as finite numbers. Being compared with the corresponding theories in the case of continuous level distribution, the above theoretical result is characterized by some specific features:
(1) The resulted expression has a difference form instead of differential form. Therefore, the experimental frequency distribution P_x(·) can be directly used with keeping its crude numerical form.
(2) When the difference operation is actually done in the practical application, the infinite series type expansion is exactly truncated with a finite number of terms.
(3) As a special case, let the level width tend to 0. The above theory yields the well-known expressions in the continuous level form.
Finally, we have experimentally confirmed the validity of our theory not only by means of digital simulation but also by two kinds of experimentally obtained road traffic noise data in Hiroshima City.

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This paper considers the problem of controllability and observability of a linear dynamical system with combinatorial constraints imposed on its input and output terminals; especially, matroidal-type constraints are thoroughly studied. The problems of examining the controllability and observability under constraints of matroidal type are reduced to the problem of finding a maximum common independent set of two appropriately defined matroids. Effective constructive algorithms are presented for several typical matroidal constraints and the best upper bounds of the time are given in which the controllability and the observability are to be decided.

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In this paper, the transient response characteristic of a mltivariable servo-system which tracks p-1th polynomials of time is investigated. By utilizing integral-type controllers and constant gain feedback controllers, zero steady state error can be guaranteed and the steady state values can be made insensitive to the variations of plant parameters if the resultant closed loop system remains stable. However, the transient responses are not always satisfactory in general even if the closed loop poles are assigned to desired locations by state feedback. The transient response errors, therefore, are derived as functions of the feedback gain matrix. A method which makes these errors small by adjusting the redundant parameters of the feedback gain matrix is presented. Two examples are given to verify the effectiveness of this procedure.

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The purpose of this paper is to find the suboptimal control for distributed parameter systems described by the linear partial differential equation of which the stochastic coefficients are modeled by a Markov chain with finite stages.
First, the stochastic properties of system parameters are specified by the notion of random eigenvalue problems. Secondly, based on the concept of functional analysis, the optimal control for the quadratic control performance is obtained by using the Dynamic Programming Approach.
The remainder of this paper is devoted to give an iterative algorithm for computer implementation in order to solve the basic equation for the optimal control. For the purpose of supporting the theoretical aspects developed here, results of digital simulation studies are also demonstrated.

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In this paper, an optimal control problem is considered, in which the constraint of the control variables is a parameter vector to be optimized. A practical example of this problem is an optimal system synthesis problem where the minimization of the sum of the driving cost and the equipping cost of the system is considered. The existence of the solution is shown for the problem with a nonlinear dynamics and a nonlinear cost function. The directional derivative of the cost function with respect to the constraint parameter vector is derived. Under some additional assumption such as a linear dynamics and a convex cost function, the subgradient and the gradient of the cost function are obtained. The numerical algorithm using the gradient is given.

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This paper is related to an optical measurement as a means of noncontact detection of a certain phenomenon observed in a birefringence change.
Here the matter of great concern is whether or not the measurement is eventually practical for use under given conditions.
The example presented here is the case of detecting a nerve excitation through a very small and relatively rapid change in phase-difference, say 10^-5 rad in a few milliseconds, occurring in the small area of a nerve membrane during its activity.
First, an equation was derived to give a limiting condition among such parameters as the size of phase-difference, the bandwidth, the number of iterations and the output level of photodiode.
Then, measurements were carried out on a crab nerve through the polarizing microscope. And, an investigation was made on the dependence of signal detectability on the area under measurement.

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The multiplicative comparator of spectral radiances built at the NRLM, was used to realize the International Practical Temperature Scale of 1968 (IPTS-68) above the gold point 1337.58K.
The comparator enables one to realize the condition corresponding to the equality L_x=L_y+L_z where L_x, L_y and L_z are the spectral radiances of radiation sources TL_x, TL_y and TL_z, respectively. This comparator makes it possible to multiply serially the spectral radiance 2ⁿ·L_Au, where L_Au is the spectral radiance of the blackbody of the gold point, through repetition L_x=2^n-1·L_Au+2^n-1·L_Au, which means the condition of L_y=L_z=2^n-1·L_Au. With the comparator, the temperature scale above 1337.58K is realized by this process of multiplication.
The precision of the comparator is ±7mK in transferring the spectral radiance of the gold point blackbody to that of the strip lamp and ±16mK in multiplying the spectral radiance serially by the factor of two.

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Transient characteristics of Toshiba tungsten ribbon strip lamps widely used for calibration of optical pyrometers were studied both for the initial transient (from the unlighted state to any state ready for pyrometer calibration) and for the intermediate transient (between two lighted states).
Measurements were carried out for four vacuum lamps and four fas-filled lamps under the condition of the constant current input and with the aid of a precise comparator of spectral radiances using photoelectric detection.
The results were so orderly arranged by means of the regression equation that the waiting time necessary for guaranteeing establishment of the steady state within the allowable limit can be evaluated easily and accurately for any luminance temperatures at which pyrometers are to be calibrated.

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A non-contact measuring method for testing the flatness of a mirror or a mirror-like surface by reflection of a Light beams from a group of point light sources at plane lattice points is mentioned. Forty-nine point light sources are arranged at the lattice points obtained by dividing each of the breadth and the length of an area one square meter into six equal parts, and the light beams from these point light sources are projected onto, in the first place, a liquid surface at rest, and, in the next place, a mirror surface to be measured. The reflecting beams thus obtained are focused into an image on a screen separately provided, and by measuring the co-ordinates of the spots of light on the screen in each case, the deviation compared with the ideal geometrical plane at each reflecting point on the mirror surface is calculated. In this paper, the authors propose the measuring principle, measuring errors and experimental results of the above method, and make it clear that the flatness of the mirror surface can be obtained mechanically by this method.

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In the previous paper1), the authors analyzed the elastic deformation of a single flat spring fulcrum used in scales theoretically, made it clear that the elastic curves are expressed by hyperbolic functions, and obtained the relationships between the inclination angles, φ at the upper end and ψ at the lower end, of the elastic curve.
In this paper, the authors discuss on the experimental verification of the theoretical analysis made in the previous paper1), and on practical application of the analysis in part.
It is qualitatively verified that the shape of the flat spring is expressed by hyperbolic functions from the photographs of the flat spring which is deformed by the metal blocks applied at the lower end of the spring, the shape of which depends on the position of the center of gravity of the metal blocks.
To examine the relationships between the inclination angles more quantitatively, the authors measured the values of ψ coresponding to φ which is varied from -0.1 to +0.1 rad.
The agreement between the theory and the experiment is satisfactory.

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An analog/hybrid real-time continuous signal processing system based on an analog delay line is proposed and discussed. In this system the input signal f(t) is fed to the delay line to obtain the parallel signals f(t-nΔτ)'s from its intermediate taps, and then various operations are applied to those signals by parallel analog circuits under the supervision of a digital mini-computer. The system operates on the principle of the FFT-based signal processing technique used widely at present, and shares its merit. Besides, the parallel analog circuit is capable of continuous high speed processing of an input signal.
A delay-line-based nonrecursive convoluter is actually constructed. An electric circuitry to realize an accurate analog delay line is shown. The FFT-based method of determining values of weighting coefficients of the convoluter to approximate a desired frequency response is also shown. According to this method, filters having various frequency responses are synthesized by the convolutes. Some examples of synthesis are shown. These results agreed well with theoretical computations. It is concluded that such systems are practical, and especially advantageous in picture processing, though the pilot system is designed for audio frequencies.

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The commutatorless motor with an armature induced voltage commutation has found recently many practical applications. However, it has a drawback that its commutation ability is smaller than that of a motor with forced commutation.
Examples of the most commonly used position sensor of a rotor are a device composed of proximity switches or a device composed of lamps and photo-transistors. These devices, however, have a drawback of a fixed leading angle.
The effective leading angle which determines the reverse bias period of commutating thyristor decreases with an increase of load current. If a leading angle is controlled according to the load current automatically, the commutation ability is, much increased than in the case of fixed leading angle.
Along this idea we have conducted an experiment about a new detection method of the rotor's position by detecting the armature induced voltage. This control method compensates the decrease of a leading angle due to the armature reaction by detecting the self adjusted cross point of the induced voltages and requires no mechanical position sensor such as proximity switches, photo-transistors or a sector.
Therefore, this control method enables us to control a conventional synchronous motor as a commutatorless motor only with an addition of control circuits.
According to the theoretical considerations of the criterion of the commutation ability, its maximum current becomes 3.75 times as much as that for a mechanical position sensor and its maximum torque is 3.24 times as much. The most suitable leading angle of this control method is 45∼50 degrees.
We have proposed the starting method of the commutatorless motor which is controlled by this control method and have shown that this starting method enables us to start successfully the commutatorless motor.
We have introduced theoretically the relation between the angular velocity of the motor, the power source voltage, the current and the phase angle in a state of starting and have shown a permissible range of the power source voltage for a stable starting.

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This paper describes a method for evaluating the effectiveness of the route guidance system, which provides a driver with individual information to accomplish a trip under such objectives as the travel time saving, the fuel saving, the reduced air pollution and the reduced traffic accident etc.. In this paper the travel time saving is chosen as an evaluation criterion of this system. The travel time indicates the time required from a driver's specific origin (O) to his specific destination (D). Multiple routes may be chosen with each specific O-D, owing to his route choice criteria and to his trial and error. The route choice probability is defined, based on a traffic study of a driver's comprehension of road configuration. On the other hand, the travel time along the selected route is affected by the vehicular type, the traffic flow, the traffic regulation, the traffic signal and the weather etc.. In this paper the travel time is defined in terms of a conditional probability density function. The characteristics of the function are examined by a traffic study of travel time using an improved license matching technique.
The probability density function of the travel time in the case of the specific O-D is composed of the route choice probability and the conditional probability density functions, mentioned above. Comparing the probability density function of a guided vehicle with that of a non-guided vehicle, a mathematical formula to calculate the amount of travel time saving is derived.

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