Closed-form solution for seismic response of adjacent buildings with linear quadratic Gaussian controllers

2001 ◽  
Vol 31 (2) ◽  
pp. 235-259 ◽  
Author(s):  
Y. L. Xu ◽  
W. S. Zhang
Keyword(s):  
Closed Form ◽  
Seismic Response ◽  
Closed Form Solution ◽  
Form Solution ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Adjacent Buildings

A Closed Form Solution for Discrete-Time Linear-Quadratic Nash Games

1987 ◽  
Vol 20 (9) ◽  
pp. 425-429
Author(s):  
H. Abou-kandil ◽  
P. Bertrand ◽  
M. Drouin
Keyword(s):  
Closed Form ◽  
Discrete Time ◽  
Closed Form Solution ◽  
Form Solution ◽  
Linear Quadratic ◽  
Nash Games ◽  
Time Linear

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

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