Algorithms ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 178
Author(s):  
Sebastian Plamowski ◽  
Richard W Kephart

The paper addresses issues associated with implementing GPC controllers in systems with multiple input signals. Depending on the method of identification, the resulting models may be of a high order and when applied to a control/regulation law, may result in numerical errors due to the limitations of representing values in double-precision floating point numbers. This phenomenon is to be avoided, because even if the model is correct, the resulting numerical errors will lead to poor control performance. An effective way to identify, and at the same time eliminate, this unfavorable feature is to reduce the model order. A method of model order reduction is presented in this paper that effectively mitigates these issues. In this paper, the Generalized Predictive Control (GPC) algorithm is presented, followed by a discussion of the conditions that result in high order models. Examples are included where the discussed problem is demonstrated along with the subsequent results after the reduction. The obtained results and formulated conclusions are valuable for industry practitioners who implement a predictive control in industry.


1991 ◽  
Vol 32 (11) ◽  
pp. 3141-3147 ◽  
Author(s):  
Roman A. Maszczyk

Morphologia ◽  
2016 ◽  
Vol 10 (4) ◽  
pp. 84-87
Author(s):  
K. I. Dyagovets ◽  
D. G. Marchenko ◽  
S. B. Morozova ◽  
N. S. Petruk ◽  
L. A. Romanenko ◽  
...  

2021 ◽  
Vol 8 (4) ◽  
pp. 13-23
Author(s):  
Sherzod Abdurahmanov

A brief historical excursion into the graphics of geometry of multidimensional spaces at the paper beginning clarifies the problem – the necessary to reduce the number of geometric actions performed when depicting multidimensional objects. The problem solution is based on the properties of geometric figures called N- simplexes, whose number of vertices is equal to N + 1, where N expresses their dimensionality. The barycenter (centroid) of the N-simplex is located at the point that divides the straight-line segment connecting the centroid of the (N–1)-simplex contained in it with the opposite vertex by 1: N. This property is preserved in the parallel projection (axonometry) of the simplex on the drawing plane, that allows the solution of the problem of determining the centroid of the simplex in its axonometry to be assigned to a mechanism which is a special Assembly of pantographs (the author's invention) with similarity coefficients 1:1, 1:2, 1:3, 1:4,...1:N. Next, it is established, that the spatial location of a point in N-dimensional space coincides with the centroid of the simplex, whose vertices are located on the point’s N-fold (barycentric) coordinates. In axonometry, the ends of both first pantograph’s links and the ends of only long links of the remaining ones are inserted into points indicating the projections of its barycentric coordinates and the mechanism node, which serves as a determinator, graphically marks the axonometric location of the point defined by its coordinates along the axes х1, х2, х3 … хN.. The translational movement of the support rods independently of each other can approximate or remote the barycentric coordinates of a point relative to the origin of coordinates, thereby assigning the corresponding axonometric places to the simplex barycenter, which changes its shape in accordance with its points’ occupied places in the coordinate axes. This is an axonograph of N-dimensional space, controlled by a numerical program. The last position indicates the possibility for using the equations of multidimensional spaces’ geometric objects given in the corresponding literature for automatic drawing when compiling such programs.


Author(s):  
Terry Marks-Tarlow

This chapter describes fractal geometry as a bridge between the imaginary and the real, mind and matter, conscious and the unconscious. Fractals are multidimensional objects with self-similar detail across size and/or time scales. Jung conceived of number as the most primitive archetype of order, serving to link observers with the observed. Whereas Jung focused upon natural numbers as the foundation for order that is already conscious in the observer, I offer up the fractal geometry as the underpinnings for a dynamic unconscious destined never to become fully conscious. Throughout nature, fractals model the complex, recursively branching structures of self-organizing systems. When they serve at the edges of open systems, fractal boundaries articulate a paradoxical zone that simultaneously separates as it connects. When modeled by Spencer-Brown’s mathematical notation, full interpenetration between inside and outside edges translates to a distinction that leads to no distinction. By occupying the infinitely deep “space between” dimensions and levels of existence, fractal boundaries contribute to the notion of intersubjectivity, where self and other become most entwined. They also exemplify reentry dynamics of Varela’s autonomous systems, plus Hofstadter’s ever-elusive “tangled hierarchy” between brain and mind.


2019 ◽  
Vol 28 (2) ◽  
pp. 207-221 ◽  
Author(s):  
Thomas J. Leeper ◽  
Sara B. Hobolt ◽  
James Tilley

Conjoint analysis is a common tool for studying political preferences. The method disentangles patterns in respondents’ favorability toward complex, multidimensional objects, such as candidates or policies. Most conjoints rely upon a fully randomized design to generate average marginal component effects (AMCEs). They measure the degree to which a given value of a conjoint profile feature increases, or decreases, respondents’ support for the overall profile relative to a baseline, averaging across all respondents and other features. While the AMCE has a clear causal interpretation (about the effect of features), most published conjoint analyses also use AMCEs to describe levels of favorability. This often means comparing AMCEs among respondent subgroups. We show that using conditional AMCEs to describe the degree of subgroup agreement can be misleading as regression interactions are sensitive to the reference category used in the analysis. This leads to inferences about subgroup differences in preferences that have arbitrary sign, size, and significance. We demonstrate the problem using examples drawn from published articles and provide suggestions for improved reporting and interpretation using marginal means and an omnibus F-test. Given the accelerating use of these designs in political science, we offer advice for best practice in analysis and presentation of results.


2021 ◽  
pp. 231-250
Author(s):  
Michael J. Hautus ◽  
Neil A. Macmillan ◽  
C. Douglas Creelman

2002 ◽  
Vol 51 (5) ◽  
pp. 1133-1136 ◽  
Author(s):  
E. Pohodylo ◽  
P. Stolyarchuk ◽  
M. Chyrka

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