论文标题
在无法观察到的目标方面的新观点
New perspectives on output feedback stabilization at an unobservable target
论文作者
论文摘要
我们解决了在无法观察的目标点处动态输出反馈稳定的问题。挑战在于根据目标和系统特性的拮抗性质：当系统接近目标时，系统往往不太明显。我们说明了两个主要思想：国家反馈定律的精心扰动可以产生闭环系统的新可观察性属性，并将系统嵌入到双线性系统中，使具有耗散错误系统的观察者允许可观察到性问题。我们将它们应用于具有线性动力学和非线性观察图的系统案例，并使用临时有限维嵌入。更普遍地，我们引入了一种基于无限维统一嵌入的新策略。为此，我们扩展了动态输出反馈稳定的常规定义，以便允许输出输出的无限二维观察者。我们展示了如何基于表示理论的该技术来实现在不可观察的目标下实现输出反馈稳定。
We address the problem of dynamic output feedback stabilization at an unobservable target point. The challenge lies in according the antagonistic nature of the objective and the properties of the system: the system tends to be less observable as it approaches the target. We illustrate two main ideas: well chosen perturbations of a state feedback law can yield new observability properties of the closed-loop system, and embedding systems into bilinear systems admitting observers with dissipative error systems allows to mitigate the observability issues. We apply them on a case of systems with linear dynamics and nonlinear observation map and make use of an ad hoc finite-dimensional embedding. More generally, we introduce a new strategy based on infinite-dimensional unitary embeddings. To do so, we extend the usual definition of dynamic output feedback stabilization in order to allow infinite-dimensional observers fed by the output. We show how this technique, based on representation theory, may be applied to achieve output feedback stabilization at an unobservable target.
