非线性大系统的弱能控性的一个判别条件

将非线性系统的弱能控性的方法应用于非线性大系统,提出了非线性大系统的弱能控性的定义及非线性大系统的弱能控性的条件·由非线性子系统的弱能控性得到了非线性大系统的弱能控性,非线性大系统的弱能控的充要条件是它的各个子系统弱能控·研究发现非线性系统是否弱能控可以考察它的能控性李代数是否满秩,非线性大系统是否弱能控可以考察它的各个子系统是否弱能控,即各个子系统的能控性李代数是否满秩,而无需考察大系统的能控性李代数是否满秩·

Discriminatory Condition for Weak Controllability of Nonlinear Large-Scale System

The controllability of large-scale nonlinear system is discussed by virtue of the weak controllability of common nonlinear system to define the weak controllability of large-scale nonlinear system with its conditions also obtained, i.e., the large-scale nonlinear system is weakly controllable since the nonlinear subsystems are the same. The necessary and sufficient condition of a weakly controllable large-scale nonlinear system is that each and every subsystem of the large-scale nonlinear system is weak controllable. It is proved that a large-scale nonlinear system is weak controllable if only each and every Lie Algebraic expression of controllability of subsystem can satisfy its controllability rank condition, regardless of the controllability of the large-scale nonlinear system, as well as a nonlinear system that is weak controllable if its Lie Algebraic expression of controllability can satisfy its controllability rank condition.