微分-代数系统的向量相对度与漏斗控制
Vector relative degree and funnel control for differential-algebraic systems
摘要：
研究多输入多输出微分代数系统的跟踪控制问题。首先，将向量相对度的概念推广到线性系，得到了“截断向量相对度”的新概念，并导出了一个新的规范形。之后，我们考虑一类非线性泛函微分-代数系统，它包括具有截断向量相对度的线性系。对于这个类，我们引入了一个反馈控制器，它实现了，对于一个给定的足够平滑的参考信号，跟踪误差在一个预先指定的性能漏斗。我们说明我们的结果的机器人机械手的一个例子。
英文摘要：
We consider tracking control for multi-input multi-output differential-algebraic systems. First, the concept of vector relative degree is generalized for linear systems and we arrive at the novel concept of "truncated vector relative degree", and we derive a new normal form. Thereafter, we consider a class of nonlinear functional differential-algebraic systems which comprises linear systems with truncated vector relative degree. For this class we introduce a feedback controller which achieves that, for a given sufficiently smooth reference signal, the tracking error evolves within a prespecified performance funnel. We illustrate our results by an example of a robotic manipulator.
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