一类非线性系统有限时间流形吸引的浸入与不变控制(英文)

Finite-time attractivity-based immersion and invariance control for a class of nonlinear systems

本文对一类非线性系统,提出了一种设计渐近稳定控制律的有效方法.其中,通过更新系统浸入与不变流形理论的应用方法,流形的吸引坐标可以在有限时间内收敛到平衡点.为了得到闭环系统的稳定性,增广系统的各个信号被证明是有界的.本文得出的一个重要成果是流形吸引有限时间的计算方法.此外,在施加了有限时间流形吸引控制器之后,流形对外部有界未知扰动具有不敏感性.最后利用车摆系统来论述所提出的控制方法的设计步骤,以及通过仿真验证控制器的性能.

We propose an effective approach for designing asymptotically stabilizing control laws for a class of nonlinear systems. In this approach, by modifying the application method of the immersion and invariance （I ＆ I） theorem, the off- the-manifold coordinates are ensured to converge to the equilibrium point in finite time. In order to obtain the stability of closed-loop system, all trajectories in the augmented system are proved bounded. An important result we obtained is the computation method for the finite time of the manifold attractivity. Moreover, the application of the finite-time manifold-attractivity controller makes the manifold insensitive to all external bounded unknown disturbances. The design procedures are detailed by designing a controller for a cart-pendulum system, and the controller performances are validated by simulations.