非线性控制系统的梯度扩张的能达性

The accessibility of gradient extension of nonlinear control systems

研究了仿射非线性控制系统的梯度扩张系统.利用非线性控制系统的微分几何理论,通过计算梯度扩张系统的输出函数沿着输入向量场和系统向量场的李导数,讨论仿射非线性控制系统的梯度扩张系统的能达性分布,研究了非线性控制系统和它的梯度扩张系统的能达性之间的关系,证明了如果梯度扩张系统是能达的,则原非线性控制系统也是能达的.

The gradient extension system of the affine nonlinear control system is studied. The accessibility distribution of the gradient extension system is discussed by using the differential theory of nonlinear control system and by calculating the Lie derivatives of output functions along the drift vector field and input vector fields.The relation between accessibility of affine nonlinear systems and accessibility of gradient extension system is studied. It is proved that if the gradient extension of nonlinear system is accessible, then the affine nonlinear system is accessible.