Adjoint and Hamiltonian input-output differential equations

Crouch P.E.; Lamnabhi-Lagarrigue F.; van der Schaft A.J.

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Adjoint and Hamiltonian input-output differential equations

机译：伴随和哈密顿输入输出微分方程

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Based on developments in the theory of variational and Hamiltonian control systems by Crouch and van der Schaft (1987), this paper answers two questions: given an input-output differential equation description of a nonlinear system, what is the adjoint variational system in input-output differential form and what are the conditions for the system to be Hamiltonian, i.e., such that the variational and the adjoint variational systems coincide? This resulting set of conditions is then used to generalize classical conditions such as the well-known Helmholtz conditions for the inverse problem in classical mechanics

机译：基于Crouch和van der Schaft（1987）对变分和哈密顿控制系统理论的发展，本文回答了两个问题：给定非线性系统的输入输出微分方程描述，输入-输入中的伴随变分系统是什么？输出微分形式以及该系统成为哈密顿量的条件是什么，即使得变分系统和伴随变分系统重合？然后，将所得的一组条件用于概括经典条件，例如众所周知的经典力学逆问题的亥姆霍兹条件

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来源
《IEEE Transactions on Automatic Control》 |1995年第4期|p.603-615|共13页
作者
Crouch P.E.; Lamnabhi-Lagarrigue F.; van der Schaft A.J.;
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正文语种 eng
中图分类自动化系统;
关键词
Helmholtz equations; differential equations; nonlinear control systems; Hamiltonian control systems; Hamiltonian input-output differential equations; Helmholtz conditions; I/O differential equations; adjoint variational system; nonlinear system; variational contr;

机译：Helmholtz方程;微分方程;非线性控制系统;Hamiltonian控制系统;Hamiltonian输入输出微分方程;Helmholtz条件;I / O微分方程;伴随变分系统;非线性系统;变分控制;

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专利

1. Adjoint and Hamiltonian input-output differential equations [J] . Crouch P.E., Lamnabhi-Lagarrigue F. IEEE Transactions on Automatic Control . 1995,第4期

机译：伴随和哈密顿输入输出微分方程
2. A family of integrable differential–difference equations, its bi-Hamiltonian structure and binary nonlinearization of the Lax pairs and adjoint Lax pairs [J] . Xi-Xiang Xu Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2012,第4期

机译：一个可积微分方程组，其双哈密尔顿结构以及Lax对和伴随Lax对的二进制非线性化
3. A modification of one method for solving nonlinear self-adjoint eigenvalue problems for Hamiltonian systems of ordinary differential equations [J] . Abramov A.A. Computational mathematics and mathematical physics . 2011,第1期

机译：一种求解常微分方程哈密顿系统非线性自伴特征值问题的方法的改进
4. On the characterization of Hamiltonian systems via differential input-output equations [C] . Crouch, P.E., Lamnabhi-Lagarrigue, . 1992

机译：用微分输入输出方程表征哈密顿系统
5. Self-adjoint representations of a certain sequence of spectral differential equations. [D] . Wellman, Richard. 1995

机译：频谱微分方程的某些序列的自伴表示。
6. On Self-Adjoint Differential Equations of Second Order [O] . Walter Leighton 1949

机译：关于二阶自伴微分方程
7. Adjoint and Hamiltonian input-output differential equations [O] . Crouch, Peter E., Lamnabhi-Lagarrigue, Francoise, van der Schaft, Arjan 1995

机译：伴随和哈密顿输入输出微分方程
8. Adjoint and Hamiltonian Input-Output Differential Equations (Revised Version December 1993) [R] . Crouch, P. E., Lamnabhi-Lagarrigue, F., van der Schaft, A. J. 1994

机译：伴随和哈密顿输入输出微分方程（修订版1993年12月）

Adjoint and Hamiltonian input-output differential equations

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