Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression
Reexamination Certificate
1998-07-02
2001-10-30
Teska, Kevin J. (Department: 2763)
Data processing: structural design, modeling, simulation, and em
Modeling by mathematical expression
C703S013000, C700S028000
Reexamination Certificate
active
06311143
ABSTRACT:
TECHNICAL FIELD OF THE INVENTION
The present invention relates to an apparatus and a method which can be utilized for a design of, for example, a digital filter and so on, and which gives robustness to a function that may be used for such a design.
BACKGROUND OF THE INVENTION
The “robustness” is defined as a robustness of a behavior of a system against deviations. Since an actual system involves various kinds of deviations, a guarantee of the robustness is a very important issue in engineering. For example, when a behavior of a feedback loop system is not practically influenced by the introduction of a certain level of external disturbances thereinto, it is said that the system has a “robustness”. As for the deviations, there are not only such external disturbances, but also internal variations of some parameter values caused by characteristic changes due to time passing of parts of the system.
The present inventor has already proposed a suiting method, in which a suiting region is previously set with respect to a physical characteristic, and functions (i.e. suiting functions) contained in the suiting region are found as a family of functions with parameters (cf. Unexamined Japanese Patent Publication (HEI) 7-226656)). According to the previous suiting method, a spread solution region is obtained, and, by using the spread solution region, a parameter design could be performed for a family of functions with a robustness against variations of parameter values.
In the parameter design according to a conventional method of optimizing method, for example, by minimizing a target function, only one optimized set of parameter values is obtained. Due to the obtained optimized parameter values being only one set without any spread, in the parameter design, it is impossible to take a quantitative robustness into consideration with respect to a change of a system behavior which is caused by the introduction of deviations of parameter values thereinto.
Also, in the aforementioned previous suiting method, in order to implement a suiting function, corresponding to the obtained parameter values, to a signal-processing device or the like, it is necessary to select only one set of parameter values from the solution region of the parameter values. Nevertheless, in the aforementioned previous suiting method, a general selection method for promoting a robustness of the suiting function is not especially prepared.
Further, in the aforementioned previous suiting method, there is a case where only one solution is calculated rather than a solution region. In order to obtain a solution uniquely, it is necessary to select how solution is calculated by using additional conditions because a solution of the suiting method ordinarily obtains a solution region. Nevertheless, in the past, the setting of uniformizing-conditions was not performed for promoting the robustness of the suiting function. Thus, generally, the obtained parameter values did not have the desired desired robustness.
Accordingly, in view of the above-mentioned problems, the present invention is directed to an improvement of the above-mentioned suiting method, such that solutions with robustness, and therefore robustly-stable physical systems, can be obtained when a solution region or a unique solution is needed.
DISCLOSURE OF THE INVENTION
In spite of a deviation being introduced into parameter values corresponding to the suiting function, when the parameter values still remain in a suiting region, this deviation is defined as an allowable deviation of this parameter values. In a suiting method according to the present invention, a robust parameter value stands for a parameter value which has large allowable deviations, and a most robust parameter value stands for a parameter value which has the largest allowable deviation.
A suiting apparatus according to the present invention at least comprises means for setting a suiting region corresponding to an allowable range of a physical characteristic, and a suiting function determination means for finding at least one suiting function at least approximately contained in a range of the suiting region, by solving simultaneous inequalities. The suiting apparatus is characterized in that the suiting function determination means sets the suiting function as a family of functions with certain parameters, sets a distance from a boundary of a solution region corresponding to a boundary of the suiting region, and finds a suiting function with robust parameter values by solving the simultaneous inequalities under a condition that the distance becomes larger than a beforehand given level or is maximized.
Also, a suiting method according to the present invention at least comprises a first step of setting a suiting region corresponding to an allowable range of a physical characteristic, and a second step of finding at least one suiting function at least approximately contained in a range of the suiting region. The suiting method is characterized in that the second step sets the suiting function as a family of functions with certain parameters, sets a distance from a boundary of the solution region corresponding to a boundary of the suiting region, and finds a suiting function with robust parameter values by solving the simultaneous inequalities under a condition that the distance becomes larger than a beforehand given level or is maximized.
In this specification, “a physical characteristic” stands for a desired characteristic, desired form, measurement value, communication signal, pattern signal, etc. Also, “a suiting” stands for a method of deriving a function (hereinafter referred to as a suiting function) at least approximately within a region corresponding to a spread of an input (hereinafter referred to as a suiting region), and more concretely a method of deriving a set of parameter values of the suiting function.
This suiting method involves an enormous amount of operations even in a case where the suiting function is expressed in a simple form. Accordingly, it is impossible to find the solution by manual calculation, and it only becomes possible by using a digital computer etc. Also, “a suiting method” stands for a method of executing the suiting, and “suiting apparatus” stands for an apparatus for executing the suiting method. Namely, the suiting apparatus stands for a digital computer or the like by which the suiting method is executed.
A typical suiting method will be explained below using a vector notation.
A representative example of a suiting method is expressed as the procedure of setting an appropriate function with parameters as f(x) and finding parameter values satisfying:
M
−
(x)<f(x)<M
+
(x)(∀×&egr;D) (1)
Herein: D indicates a domain in a multidimensional space. The inequality system (1) is called a determinating inequality system for the suiting, and the f(x) satisfying inequality system (1) is called a suiting function. Also, M
+
(x), which determines the upper bound of the suiting function f(x), is called an upper bound function, and M
−
(x), which determines the lower bound of the suiting function f(x), is called a lower bound function. The entire range determined by upper bound function M
+
(x) and lower bound function M
−
(x) is called a suiting region T(={(x, y)|×&egr;D, M
−
(x)<y<M
+
(x)}). Upper bound function M
+
(x) and lower bound function M
−
(x) may be set as values of +∞ and −∞, respectively. Also, a suiting region may be set by a center value and an allowable width with respect to the center value.
The inequality system (1) is expressed by a finite number of simultaneous inequalities. A range of the parameter values of f(x) which satisfy all of the finite numbers of inequalities is the solution region. This solution region is obtained by transforming the suiting region to a parameter space. Accordingly, one point in the solution region corresponds to a suiting function which attains a value within the suiting region.
When a suiti
Broda Samuel
Greenblum & Bernstein P.L.C.
Teska Kevin J.
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