scholarly journals Construction of invariant whiskered tori by a parameterization method. Part I: Maps and flows in finite dimensions

2009 ◽  
Vol 246 (8) ◽  
pp. 3136-3213 ◽  
Author(s):  
Ernest Fontich ◽  
Rafael de la Llave ◽  
Yannick Sire
Keyword(s):  
Parameterization Method ◽  
Whiskered Tori

scholarly journals A Symbolic Computation Approach to Parameterizing Controller for Polynomial Hamiltonian Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Cao ◽  
Xiaorong Hou
Keyword(s):  
Nonlinear Systems ◽  
Hamiltonian Systems ◽  
Symbolic Computation ◽  
External Disturbance ◽  
Disturbance Attenuation ◽  
Internal Stability ◽  
Parameterization Method ◽  
Numerical Example ◽  
Isaacs Equations ◽  
Controller Parameterization

This paper considers controller parameterization method ofH∞control for polynomial Hamiltonian systems (PHSs), which involves internal stability and external disturbance attenuation. The aims of this paper are to design a controller with parameters to insure that the systems areH∞stable and propose an algorithm for solving parameters of the controller with symbolic computation. The proposed parameterization method avoids solving Hamilton-Jacobi-Isaacs equations, and thus the obtained controllers with parameters are relatively simple in form and easy in operation. Simulation with a numerical example shows that the controller is effective as it can optimizeH∞control by adjusting parameters. All these results are expected to be of use in the study ofH∞control for nonlinear systems with perturbations.

Path planning of free-floating space robot based on control variable parameterization method

2019 ◽  
Vol 27 (2) ◽  
pp. 372-378
Author(s):  
张 旭 ZHANG Xu ◽  
曾祥鑫 ZENG Xiang-xin ◽  
郎 博 LANG Bo
Keyword(s):  
Path Planning ◽  
Control Variable ◽  
Space Robot ◽  
Parameterization Method

Study of Penrose Tiling Using Parameterization Method

2019 ◽  
Vol 64 (3) ◽  
pp. 376-385 ◽  
Author(s):  
A. V. Shutov ◽  
A. V. Maleev
Keyword(s):  
Penrose Tiling ◽  
Parameterization Method
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