parametric solution
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Author(s):  
Weizhen Liu ◽  
Guangren Duan ◽  
Dake Gu

In this paper, a parametric feed-forward compensator and a parametric state-feedback stabilization controller are proposed for the model reference control to a class of quasi-linear systems. Quasi-linear systems are a special type of nonlinear systems whose coefficient matrices contain the state variables and also a time-varying parameter vector. The parametric state-feedback stabilization controller guarantees the stability of the closed-loop system and the parametric feed-forward compensator compensates the effect of the reference model state to the tracking error. The complete parametrization of the parametric feed-forward compensator is established based on a complete parametric solution to a class of generalized Sylvester matrix equations and solution of a coefficient matrix such that two matrix equations are satisfied. The established parametric state-feedback stabilization controller only needs a complete parametric solution to the same generalized Sylvester matrix equations but with different sets of freely designed parameters that represent the degrees of design freedom and may be further utilized to improve the system performance. A linear closed-loop form with the desired eigenstructure can be derived with the proposed parametric feed-forward compensator and parametric state-feedback stabilization controller, and a constant linear can even be obtained in certain cases. A numerical example and the application in spacecraft rendezvous are provided to illustrate the effectiveness of the proposed approach.


2021 ◽  
Vol 17 (1) ◽  
pp. 65-79
Author(s):  
Elton Cristovão da Silva Lima ◽  
Cristina Matsunaga ◽  
Leticia Teixeira Mendes

This research proposes an experimental design approach to design an ephemeral pavilion located at the Serpentine Gallery in London. The Serpentine Pavilions Programme functions as an experimentation laboratory and, at the same time, public and event spaces, enabling architects to expose their projects and work methodologies. Thus, the methods of Biomimicry and Parametric Design were combined to develop the pavilion. While the first one was used to create an ephemeral pavilion based on the Sartorius muscle, the second was responsible for generating the parametric model from a fast and intuitive manipulation code capable of exploring shape variations. This work explores the solution-based method approached by Badarnah (2012) based on a predefined problem (the pavilion project) and only after that seek some natural inspiration. Firstly, it was investigated the anatomy of the Sartorius muscle. Subsequently, with the domain of the solution, the parametric insertion of the shape was computationally performed. The anatomical study of the sartorius muscle revealed functions such as flexion, abduction, lateral rotation of the thigh, and medial rotation of the knee. Thus, the architectural choices reflect both its narrow and elongated morphology of the muscle and flexibility and rotation aspects. The pavilion also considered the previous Serpentine Pavilions regarding attributes such as area, height, and materials, which with other parameters may be changed using the code implemented in Grasshopper.


2021 ◽  
Author(s):  
Dimiter Prodanov

Abstract The SIR (Susceptible-Infected-Removed) model can be very useful in modelling epidemic outbreaks. The present paper derives the parametric solution of the model in terms of quadratures. The paper demonstrates a simple analytical asymptotic solution for the I-variable, which is valid on the entire real line. Moreover, the solution can be used successfully for parametric estimation either in stand-alone mode or as a preliminary step in the parametric estimation using numerical inversion of the parametric solution. The approach is applied to the ongoing coronavirus disease 2019 (COVID-19) pandemic in three European countries --Belgium, Italy and Sweden.


Author(s):  
V. O. Osipyan

Предложен новый подход разработки дисимметричной биграммной криптосистемы (ДБК) на основе многопараметрических решений многостепенных систем диофантовых уравнений (МСДУ), обобщающий принцип построения криптосистем с открытым ключом. Вводится новое понятие равносильности числовых наборов или параметров заданной размерности и порядка. Описанные математические модели СЗИ демонстрируют потенциал применения МСДУ для разработки СЗИ с высокой степенью надёжности


Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1775
Author(s):  
Srikanth Raghavendran ◽  
Veena Narayanan

The present study aims to develop novel parametric solutions for the Prouhet Tarry Escott problem of second degree with sizes 3, 4 and 5. During this investigation, new parametric representations for integers as the sum of three, four and five perfect squares in two distinct ways are identified. Moreover, a new proof for the non-existence of solutions of ideal Prouhet Tarry Escott problem with degree 3 and size 2 is derived. The present work also derives a three parametric solution of ideal Prouhet Tarry Escott problem of degree three and size two. The present study also aimed to discuss the Fibonacci-like pattern in the solutions and finally obtained an upper bound for this new pattern.


Computation ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 78
Author(s):  
Claudia Germoso ◽  
Giacomo Quaranta ◽  
Jean Louis Duval ◽  
Francisco Chinesta

Mesh-based solution of 3D models defined in plate or shell domains remains a challenging issue nowadays due to the fact that the needed meshes generally involve too many degrees of freedom. When the considered problem involves some parameters aiming at computing its parametric solution the difficulty is twofold. The authors proposed, in some of their former works, strategies for solving both, however they suffer from a deep intrusiveness. This paper proposes a totally novel approach that from any existing discretization is able to reduce the 3D parametric complexity to the one characteristic of a simple 2D calculation. Thus, the 3D complexity is reduced to 2D, the parameters included naturally into the solution, and the procedure applied on a discretization performed with a standard software, which taken together enable real-time engineering.


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