Minimization of the L∞-Induced Norm for Sampled-Data Systems
Minimization of the L∞-Induced Norm for Sampled-Data Systems
复制标题
采样数据系统 L∞ 诱导范数的最小化
DOI：
10.23919/acc.1992.4792167
复制
发表时间：
1992
期刊：
影响因子：
--
通讯作者：
J. Pearson
中科院分区：
文献类型：
--
作者：
Bassam Bamieh;M. Dahleh;J. Pearson
本文给出了任意对象的l1采样问题的完整解。l1采样数据问题描述如下：给定一个连续时间对象，具有连续时间性能目标，设计一个数字控制器，提供此性能。该问题与标准离散时间方法的不同之处在于，它考虑了闭环系统的互采样行为。由此产生的闭环系统动态包括连续时间和离散时间动态，因此这样的系统被称为混合系统。它示出，给定任何程度的准确性，存在一个标准的离散时间l1问题，它可以被确定的先验，这样，对于任何控制器，实现了一个水平的性能的离散时间问题，相同的控制器实现相同的性能在规定的精度水平，如果作为一个采样数据控制器。这是通过首先使用连续时间中的提升技术将混合系统转换为等效的无限维离散时间系统，然后逼近系统中模拟样本间动态的无限维部分来实现的。这种近似是独立的控制器，并获得明确的界限的程度的近似。证明了这种近似的收敛性至少为1/n。
In this paper, a complete solution for the l1 sampled-data problem is furnished for arbitrary plants. The l1 sampled-data problem is described as follows: Given a continuous-time plant, with continuous-time performance objectives, design a digital controller that delivers this performance. This problem differs from the standard discrete-time methods in that it takes into consideration the inter-sampling behavior of the closed loop system. The resulting closed loop system dynamics consist of both continuous-time and discrete-time dynamics and thus such systems are known as hybrid systems. It is shown that given any degree of accuracy, there exists a standard discrete-time l1 problem, which can be determined apriori, such that for any controller that achieves a level of performance for the discrete-time problem, the same controller achieves the same performance within the prescribed level of accuracy if implemented as a sampled-data controller. This is accomplished by first converting the the hybrid system into an equivalent infinite dimensional discrete-time system using the lifting technique in continuous time, then the infinite dimensional parts of the system which model the inter-sample dynamics are approximated. This approximation is done independently of the controller, and explicit bounds are obtained for the degree of approximation. It is shown that the convergence of this approximation is at least as 1/n.