School of Electrical and Electronic Engineering, Shiraz University of Technology, Modares Blvd., P.O. Box 71555/313, Shiraz, Iran.
ISA Trans. 2012 Mar;51(2):298-303. doi: 10.1016/j.isatra.2011.10.010. Epub 2011 Nov 5.
In this paper, the problem of robust partial stabilization is considered and two approaches for partial stabilization of uncertain nonlinear systems are presented. In these approaches, the nonlinear dynamical system is divided into two subsystems, which are called the first and the second subsystems. This division is done based on the required stability properties of the system's states. The reduced input vector (the vector that includes components of the input vector appearing in the first subsystem) is designed to asymptotically stabilize the first subsystem. In the first approach, a new partial stabilization technique, based on the first order sliding mode control idea is proposed. In the proposed method, hereafter called the partial sliding mode, a sliding surface is designed such that restricting the motion on this surface guarantees the stability of only the first part of the system's state. In the second approach, a Lyapunov-based controller is proposed for partial stabilization and then an additional feedback control is designed so that the overall feedback law guarantees a robust manner in the presence of uncertainties.
本文研究了鲁棒部分镇定问题，提出了两种不确定非线性系统的部分镇定方法。在这些方法中，将非线性动力系统分为两个子系统，分别称为第一子系统和第二子系统。这种划分是基于系统状态所需的稳定性特性进行的。设计简化输入向量（包含出现在第一子系统中的输入向量分量的向量）以使第一子系统渐近稳定。在第一种方法中，提出了一种新的基于一阶滑模控制思想的部分镇定技术。在所提出的方法中，以下称为部分滑模，设计了一个滑动面，使得限制在该表面上的运动仅保证系统状态的第一部分的稳定性。在第二种方法中，提出了一种基于李雅普诺夫的控制器用于部分镇定，然后设计了一个附加的反馈控制，使得整体反馈律在存在不确定性的情况下以鲁棒的方式保证。
