非线性控制系统无反馈转换为一类p-范式  

Transforming nonlinear control system to special p-normal form without feedbacK

作　　者：张端[1] 卢建刚[1] 孙优贤[1] 

机构地区：[1]浙江大学工业控制技术国家重点实验室,浙江杭州310027

出　　处：《浙江大学学报（工学版）》2004年第12期1646-1649,共4页Journal of Zhejiang University：Engineering Science

基　　金：国家自然科学基金资助项目(20206027);国家"973"重点基础研究发展规划资助项目(2002CB312200);浙江省自然科学基金资助项目(202046).

摘　　要：针对单输入解析仿射非线性系统通过状态变换等价局部转换为一类p 范式的问题,给出了充分必要条件.系统定义的向量场经过反复作李括号得到一组新的向量场,该组向量场构成了上述充要条件.在对充要条件的证明中,使用了将具有相同主要部分的拟线性偏微分方程组等价地转换为齐次线性偏微分方程组的方法,利用Frobenius定理得出最终结果.并通过一个实例,解释了如何应用这一充要条件实现从非线性系统到上述p 范式的转换.The necessary and sufficient condition under which an analytic affine nonlinear system with single-input being locally equivalent to a class of p-normal form via state transformation without feedback was presented. The presented verifiable conditions involved the vector fields obtained by some suitably chosen iterative Lie brackets of the vector fields defined in the system. The proofs were based on a new technique for applying the Frobenius theorem in a more convenient way by converting a set of quasilinear partial differential equations with the same main portion into a set of homogeneous linear partial differential equations. An example illustrated how to transform a nonlinear system into a p-normal form mentioned above without feedback using the necessary and sufficient condition.

关 键 词：控制理论 非线性控制系统 p-范式 状态变换 等价 

分 类 号：O231.2[理学—运筹学与控制论] TP271.62[理学—数学]