浸入与不变方法原理及其在非线性自适应控制中的应用

非线性系统理论的实际工程需求和复杂性使其成为控制学科中最具吸引力和挑战性的研究领域，为此介绍了一种新的非线性控制律设计方法——浸入与不变（I&I）理论.该方法首先选择一个比被控系统维数低的（局部）渐近稳定的目标系统，然后设计浸入映射和控制律，使得原系统在控制律作用下的动态轨迹都是目标系统在浸入映射下的像，并且该控制律能够保持目标系统的像为不变吸引流形，且使闭环轨迹有界.针对未知点质量模型，设计了一种新的非线性浸入与不变自适应控制律，实现了对参考指令的精确跟踪.将其与基于确定等价原则的自适应控制律相比较，仿真结果表明，所设计的浸入与不变控制律能够更好地处理带有未知参数的系统.

Immersion and invariance theory and its application in nonlinear adaptive control

The actual engineering demands and the complexities of the nonlinear system theory have led it to become the most attractive and challenging research field in control subjects, therefore, a new nonlinear control law design method—immersion and invariance (I&I) theory has been introduced. With this method, a (partially) asymptotically stable system with a dimension less than that of the controlled system is firstly selected as the target system, then the immersion mapping and control law are designed to make the controlled dynamics of the original system is an immersion image of the target system. In addition, the control law can keep the image of the target system as an invariant and attractive manifold, and render the trajectory of the closed-loop system bounded. Focusing on the unknown point mass model, a new nonlinear immersion and invariance adaptive control law is designed for realizing the precise tracking of a reference command. Compared with the adaptive control law based on the certainty-equivalent principle, the simulation results show that the proposed I&I adaptive control law is quite effective for processing a system with unknown parameters.