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Volume 8 (1972)
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Volume 8, Issue 6
Displaying 1-15 of 15 articles from this issue
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Approach by Means of Interior Penalty MethodMikio KOBAYASHI, Yasujiro OSHIMA1972 Volume 8 Issue 6 Pages 629-634
Published: December 30, 1972
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSA necessary and sufficient condition for an optimal solution of the constrained optimal control problem in Banach space has been derived by means of an exterior penalty by the authors.
The purpose of this paper is to derive the similar condition by means of an interior penalty method.
It is shown that a series of the approximate solutions converges to the optimal one weakly and a series of the values of the cost functional generated from those approximate solutions converges to the optimal value. Using those results, the necessary and sufficient condition is derived by considering the minimization problem of a new functional.
In the main problem considered here, the control and state variables are defined in Lp (1<p≤∞) or Euclidean space. The constraints are described by equalities and inequalities, where the equality constraints are defined in Lp or Euclidean space and the inequality constraints are defined in L∞ or Euclidean space.View full abstractDownload PDF (777K) -
Yoshikazu SAWARAGI, Toshihiro KOBAYASHI1972 Volume 8 Issue 6 Pages 635-643
Published: December 30, 1972
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSIn this paper the sensitivity synthesis of optimal control is extended to distributed parameter systems.
Sensitivity functions and sensitivity equations are, at first, defined and derived for the three types of system parameter variations, that is, the ordinary system parameter variation, the variation of initial conditions and the variation of time delay parameter.
Next it is pointed out that the concept of the combined system which consists of a model system and its parameter sensitivity equation plays an important role in the sensitivity synthesis of optimal control.
After the definition and the explicit condition of controllability of the systems governed by simultaneous linear partial differential equations are discussed, the controllability and the uncontrollability of the combined system are analyzed.
At last the sensitivity synthesis of optimal control is introduced into the problem of terminal control in order that the terminal constraints are satisfied in spite of the parameter variations. Comparing with the conventional synthesis, the effectiveness of the sensitivity synthesis is demonstrated by giving simple examples.View full abstractDownload PDF (1151K) -
Setsuzo TSUJI, Teruo ITOH1972 Volume 8 Issue 6 Pages 644-651
Published: December 30, 1972
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThe problem considered in this paper is the minimum-time problem of nonlinear discrete systems with state and control constrained. In the first half of this paper, the algorithm is given, which solves the minimum-time problem by solving the sequence of the fixed endpoint optimal control problem by the penalty function method. The convergence proof of the algorithm is given. In the latter half of this paper, another algorithm is given, which minimizes the penalty functions which appear in the above fixed endpoint optimal control problems and necessarily contain Heaviside's step functions. This algorithm is especially interesting in the case where the system and the constraints are linear. An illustrative example is given.View full abstractDownload PDF (1088K) -
Yuzo YAMANE1972 Volume 8 Issue 6 Pages 652-659
Published: December 30, 1972
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSIt is well known that the optimal control in a linear quadratic problem calls for feedback of all the state variables in the plant.
In many practical situations, however, not all the state variables are accessible for direct measurement and observation. Moreover, the designer may not wish to use a state reconstructor such as an observer proposed by Luenberger, because combining a state reconstructor with the plant means an increase in the performance index, the problem's complexity and the expense of the combined system. Rather, one may want to generate the control variable via a linear feedback from the output variables. In this case, one is interested in determining an optimal set of feedback gains, viz., “specific optimal control”. Such an optimal solution, in general, depends upon all the initial states.
This paper presents an approach to this class of problems where one is void of a priori knowledge concerning all or some of initial states.View full abstractDownload PDF (946K) -
Yukichi YONEMURA, Masami ITO1972 Volume 8 Issue 6 Pages 660-666
Published: December 30, 1972
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSIn this paper, the controllability and observability of tandem connection of two linear time invariant systems each having the Jordan form representation are considered. The criteria for the composite system to become controllable and/or observable are given for the general cases. The method of proof employed in this paper is more straightforward and simpler than that in Panda's paper [4].View full abstractDownload PDF (523K) -
Kinji MORI, Etsujiro SHIMEMURA1972 Volume 8 Issue 6 Pages 667-675
Published: December 30, 1972
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSA pursuit game of a stationary linear system with time-delay is considered here. The state of this system is infinite dimensional but the target set is finite dimensional. The mathematical model of the system is formulated here as a coupling of a lumped parameter subsystem and a distributed parameter subsystem, and the target set is defined as a subset in the state space of the lumped parameter subsystem.
In this pursuit game three different types of information patterns are defined. They are, respectively, (i) the open loop information pattern for the pursuer, (ii) the closed loop information pattern for the pursuer and (iii) the open loop information pattern for the evader. In (i) and (ii), one of the sufficient conditions for completion of the game and the pursuer's closed loop control are obtained. This pursuer's closed loop control u is constructed by the state x(t) of the lumped parameter subsystem, his opponent's control v(t) and the histories of x, u and v. It is shown that, in (iii), the evader can choose his feedback control for the game not to be completed in some finite time.View full abstractDownload PDF (1036K) -
An Approach to Extremum Seeking Method for Multimodal ProblemsNorio OKINO, Yasuo SASAKI1972 Volume 8 Issue 6 Pages 676-683
Published: December 30, 1972
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSConsidering the progress in the maximum seeking method for multi-dimensional non-linear programing, recently the studies on the unimodal problem have developed rapidly and steadily to yield results. The multimodal problem, however, has remained unsolved in spite of its importance in the industry.
In this paper, a new method is proposed to contribute to solving the latter problem.
A noticeable feature of this method is to separate every peak which has a meaningful extremum from the wide n-dimensional surface using Monte Carlo integration skillfully. After the trial search is repeated a set number of times around the search points which are given by random arrangement, the several points whose values of the function are relatively high are selected and the spreading area (defined specially) of the peak is calculated. Whether to register it as an independent peak separated or not is decided on the basis of the position and the spreading area of every peak.
In this procedure, the criterion for the separation is given theoretically and also the necessary number of trials can be estimated by the theory which incorporates a statistical contemplation. In addition to theoretical consideration, a few experiments on the three kinds of test functions are made to confirm the performance separating the independent peaks. Experimental values agreed well with the thoretical results.
This method has such merits as being applicable to all functions without restriction, even discontinuous and to multi-n-dimensional problems even if n is considerably large. These are merits of the random method in general, and of course, this method has a weak point, in that the accuracy of results can not be given by anything except statistical values.
In order to reach a maximum point on the multimodal surface, the techniques in case of unimodal problems can be used after some independent peaks have been separated by this method.View full abstractDownload PDF (927K) -
Hiroshi KUBO1972 Volume 8 Issue 6 Pages 684-689
Published: December 30, 1972
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSAt present, there are a few methods of multimodal optimization technique, which are used in order to find a solution case by case. The global search techniques which are used in all of these methods are usually nonsequential ones. In this paper, we make an attempt at using only a sequential technique in this global search.
As is commonly known, a necessary condition for the differentiable scalar function to become optimal is that its first derivative is equal to zero. When the function is defined over on n-dimensional space, the first derivatives generate hypersurfaces. A point which is any intersection of n hypersurfaces of derivatives is defined as a pole. The intersection of n-1 hypersurfaces, taking off any one from these n hypersurfaces, forms a curve, which is defined as a pole line. A curve evidently links a pole with another. The principle of the method proposed in this paper is to search sequentially these poles using the network of these pole lines. The existence and uniqueness of the pole line, the relation between the pole line and the pole, and the selecting of a resolution from poles are proved.
This method needs that the performance measure is of the class C2 because of the existence of continuous hypersurfaces, and furthermore that some unequality constraints are of the class C1 and close the feasible domain because of closing the network of pole lines. Otherwise, it may occur that an optimal solution is not found in this method, for all of extremums found in this method are connected with a certain network of pole lines. In particular, it is impossible to find the solution which exists on the boundary of unequality constraints, but in this case the method finding it using Lagrange multiplier is briefly described. Furthermore, the convergence of solutions in this method under certain conditions and two simple experimentations are reported.View full abstractDownload PDF (813K) -
Tsutomu FUJITA, Hiroshi SUGIYAMA1972 Volume 8 Issue 6 Pages 690-696
Published: December 30, 1972
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThe purpose of the present paper is to show an approach to the suboptimal control policy for controlling the nonlinear stochastic control system.
Specifically, the so-called continuous-discrete nonlinear stochastic control system is treated in this paper, because this type of control system seems to be important in practical situation. In this stochastic control system, the nonlinear system dynamics operate continuously and the non-linear observations are taken at the preassigned discrete time points.
First, applying the quasilinearization technique, the state estimation algorithm is proposed.
Then, using this estimation algorithm, a suboptimal control policy is proposed with the discrete type criterion function, instead of the criterion function of the continuous type, because of the discrete observations.
Then, a selection procedure is proposed for determining the unknown parameter included in this suboptimal control policy and, using this procedure, our suboptimal control policy is established.
Finally, the computer simulational experiments are shown, using our suboptimal control policy, in case of the several exemplary control systems.
Our policy and algorithm seem to be useful for the practical applications, so far as our experimental results are concerned.View full abstractDownload PDF (932K) -
Minoru HIGASHIGUCHI1972 Volume 8 Issue 6 Pages 697-703
Published: December 30, 1972
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThe Energy-Angular-Momentum Diagram is proposed in this paper to clarify the orbit transfer problem of a space vehicle. With the use of this diagram, some properties of parameter variations in the orbit transfer can be represented in a more intuitive manner.
On this diagram, the orbit is shown by the point (orbit point) x=2c/μ, y=h2/μ where c=energy, h=angular momentum, μ=gravitational parameter (3.98604×105km3/s2 for the earth).
The Energy-Angular-Momentum Diagram has properties as follows:
1. The orbit having the eccentricity e is shown by the point on the hyperbola 1+xy=e2
2. No orbit point appears in the domain 1+xy<0. Let the boundary hyperbola (1+xy=0) be H.
3. The ordinates of two points of contact on H where the tangential lines from the orbit point touch the hyperbola H, are the apoapsis radius rap and the periapsis radius rpg, respectively.
4. We consider two parallel straight lines on the diagram. The tangential line of the hyperbola H that passes the point (-2/r, 0) is designated as T. And the line L is the line that is parallel to T and that passes the orbit point (x, y). We assume that this line L crosses X-axis at the point (xl, 0). Then the axial velocity component va and the transversal velocity component vt of the space vehicle are related to this diagram by:
xl+(2/r)=va2/μ, x-xl=vt2/μ where r=radius from the focus to the space vehicle.
5. The orbit transfer of the space vehicle due to some velocity change can be explained by the nonlinear transformation.
That is, velocity components which are expressed in orthogonal coordinate are transformed to coordinates of the orbit point expressed in the skew coordinate whose axes are the x-axis and the straight line T and whose scale is proportional to the squared value of velocity, in the Energy-Angular-Momentum Diagram.View full abstractDownload PDF (753K) -
Tatsuo HIGUCHI1972 Volume 8 Issue 6 Pages 704-708
Published: December 30, 1972
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSIn a single core magnetic amplifier proposed by Darling, it has been found that the voltage drop of the pair diode plays an important role in order to increase the amplifier gain and the DC load power. Therefore, it is anticipated that the design method for the circuit will become complicated as compared with the one for conventional magnetic amplifiers.
The first step in amplifier design is to select a single core and a pair diode to be used. Taking into account the DC load power required by the specification, a criterion may be given to determine the core size and the threshold voltage of the pair diode. Then, on the basis of the given core and pair diode, the circuit constants which satisfy the specification can be decided.
In the last part of this paper, the Darling's circuit is designed to show the design steps. The required DC load power is expressed as a parameter. A double anode connection of zenor diodes is used as the pair diode. Thus, a pair diode with the required threshold voltage can be realized. The output power obtained in practice is compared with the designed one. As a result it is clarified that this design method is useful.View full abstractDownload PDF (653K) -
Iwao YAMAMOTO, Tadaharu YOKOGAWA1972 Volume 8 Issue 6 Pages 709-716
Published: December 30, 1972
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSA testing method for the elasticity of thin metal plate with thickness less than 0.3mm is described. A specimen is held as a cantilever of which free end is centered between two symmetrically set nozzles. The specimen oscillates by the push-pull air jet pressure from the nozzles. The pressure forces are obtained from a two-phase pneumatic oscillator consisting of a motor driven rotary disk having its surface inclined to the rotating plane and two nozzles which are put on the same plane near the surface of the disk. By changing the angular velocity of the disk, the specimen is made to resonate. The Young's modulus of the specimen can be estimated by observing the resonant frequency. The testing method is also applicable to fatigue test of thin plates. Compared with the conventional method, this testing method has the merit that neither attachment nor special machining is needed on the specimen regardless of specimen materials. The testing method would be also applicable to such non-metalic soft materials as paper and plastics.View full abstractDownload PDF (1148K) -
Susumu HATTORI, Tetsuo FUJIWARA1972 Volume 8 Issue 6 Pages 717-723
Published: December 30, 1972
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSA new precise comparator was manufactured on trial in order to compare the spectral radiances of two tungsten strip lamps which are used as pyrometric standards. The comparator is composed of two objective lenses, two right-angled prisms, a light chopper and a light detecting system.
The beam of light from the filament of one of the two lamps which are to be compared, being converged by the setup of a lens and a prism arranged on the one arm of the comparator, makes a real image of the filament on the chopper, which receiving also the other beam, changes the cross-sectional area of the two beams reciprocally. The beams, thus chopped reciprocally, enter the detecting system through an aperture. The system, composed of an interference filter (λmax=0.648μm), a photomultiplier and a phase discriminator, detects the periodical change of the incident monochromatic radiant power at the wavelength of 0.648μm, discriminates the phase difference between the periodical change of the radiant power and that of the vibration of the chopper and judges whether the spectral radiances of the lamps are equal or not.
It is confirmed experimentally that in this comparator systematic errors and drift are negligibly small and the precision of comparison is about ±0.05°C at luminance temperature of 1065°C.View full abstractDownload PDF (1071K) -
Mechanical Analysis and Zoological Experiment for the Stationary Straightforward MovementYoji UMETANI, Shigeo HIROSE1972 Volume 8 Issue 6 Pages 724-731
Published: December 30, 1972
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSA biomechanical study on the serpentine locomotion of snakes is presented including both mechanical analysis and its experimental verification with respect to Elaphe quadrivirgata. The mechanical analysis is based on an active linear linkage model, and the theoretical relations of forces induced by antagonistic muscles in straight-forward undulatory movement are obtained. A peculiar mode of snake's movement, which the authors define as the “vertex-lifting locomotion” (as shown Fig. 1), is shown to be optimal for rapid movement. The zoological experiments show good agreement with the theoretical results as well as some assumptions. Thus the authors conclude that this paper will be the first from the biomechanical point of view on snake's locomotion.View full abstractDownload PDF (2797K) -
Osamu KATAI, Sousuke IWAI1972 Volume 8 Issue 6 Pages 732-739
Published: December 30, 1972
Released on J-STAGE: March 27, 2009
JOURNAL FREE ACCESSThis paper discusses an information theoretic approach for Bayesian dichotomization of patterns.
In the first section, we introduce a new measure which is closely related to the recognition rate of Bayesian pattern recognizer and is easy for practical use. This measure is defined as the correlation between the teacher's response and Bayesian discriminant function.
Further, it is shown that the measure is composed of three non-negative parts well known in information theory and statistics. These parts are analyzed in connection with Bayesian pattern recognition.
In the second section, the relation between the recognition rate and the measure is discussed by the aid of central limit theorem. This relation assures the usefulness of the measure in the synthesis of pattern recognizer and the quantization of patterns.
Experimental computer simulation ascertains the above discussions and results.View full abstractDownload PDF (968K)
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