Synthesis for Constrained Nonlinear Systems Using Hybridization and Robust Controllers on Simplices
Synthesis for Constrained Nonlinear Systems Using Hybridization and Robust Controllers on Simplices
复制标题
在单纯形上使用混合和鲁棒控制器综合约束非线性系统
DOI：
--
复制
发表时间：
2011
影响因子：
6.8
通讯作者：
Samuel Martin
中科院分区：
文献类型：
--
作者：
A. Girard;Samuel Martin
在这个技术笔记中，我们提出了一类约束非线性系统的控制器综合方法。它是基于使用一种杂交，即混合抽象的非线性动力学。这种抽象是在状态空间的三角剖分上定义的，在三角剖分的每个单纯形上，非线性动力学被一个受干扰的仿射系统保守地近似。除了干扰外，这种杂化可以看作是简单体上的分段仿射杂化系统，在过去的十年中，已经开发出了吸引人的控制合成技术。我们扩展这些技术来处理系统受到干扰，通过合成和协调局部鲁棒仿射控制器定义在简单的三角测量。结果表明，所得到的混合控制器可以成功地控制原约束非线性系统。我们的方法虽然保守，但可以完全自动化，并且在计算上易于处理。为了证明该方法在实际应用中的有效性，我们将该方法应用于小车上的摆锤控制。
In this technical note, we propose an approach to controller synthesis for a class of constrained nonlinear systems. It is based on the use of a hybridization, that is a hybrid abstraction of the nonlinear dynamics. This abstraction is defined on a triangulation of the state-space where on each simplex of the triangulation, the nonlinear dynamics is conservatively approximated by an affine system subject to disturbances. Except for the disturbances, this hybridization can be seen as a piecewise affine hybrid system on simplices for which appealing control synthesis techniques have been developed in the past decade. We extend these techniques to handle systems subject to disturbances by synthesizing and coordinating local robust affine controllers defined on the simplices of the triangulation. We show that the resulting hybrid controller can be used to control successfully the original constrained nonlinear system. Our approach, though conservative, can be fully automated and is computationally tractable. To show its effectiveness in practical applications, we apply our method to control a pendulum mounted on a cart.