对称非线性系统的结构简化

The Structural Simplification of Symmetric Nonlinear Systems

文献[1]对于对称非线性控制系统作了结构上的简化分解,本文在此基础上,利用李代数的半直和分解及其Cartan子代数的概念,对一般李群作用下的对称非线性控制系统作了进一步的降低变量个数的简化分解。这一分解是较为深入和彻底的,更进一步简化了系统的结构。

Simplified structural decompositions of nonlinear control systems possessing symmetries have been given in the reference[1].Based on this,the paper provides further simplified structural decompositions for nonlinear systems with general symmetric Lie groups in terms of the semi-direct sum decomposition of Lie algebras and the concept of Cartan subalgebras of Lic algebras.The result here is better than that in [1].