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4 向量场与动态系统 众所周知,现代控制理论的研究是在状态空间上,使用状态方程,但有些动态系统,特别是非线性系统,其动态演变是在微分流形上进行的,演化结果是流形上的一条曲线,描述无穷小演化的微分方程是定义在流形上的向量场,因此,研究流形上的动态系统,就要分析流形上的向量场。流形上向量场的局部坐标表示是R~n中的微分方程组。在状态空间中,向量场就是状态方程的几何解释。应用向量场来研究动态系统的方法,就是几何方法。
4 Vector Field and Dynamic System As we all know, modern control theory is state space, the use of state equations, but some dynamic systems, especially nonlinear systems, the dynamic evolution of differential manifold, the evolution of the result is manifold , A differential equation describing infinitesimal evolution is a vector field defined on the manifold. Therefore, to study the dynamic system on the manifold, it is necessary to analyze the vector field on the manifold. The local coordinate representation of the vector field on the manifold is a set of differential equations in R ~ n. In state space, the vector field is the geometric interpretation of the state equation. The application of vector field to study the dynamic system, is the geometric method.