论文标题
基于内核的系统标识的解决方案的存在和独特性
The Existence and Uniqueness of Solutions for Kernel-Based System Identification
论文作者
论文摘要
在过去的十年中，在系统识别中出现了繁殖核希尔伯特空间（RKHS）的概念。在最终的框架中，脉冲响应估计问题被提出为在无限维RKHS上定义的正规优化，该优化由稳定的脉冲响应组成。随之而来的估计问题在中心假设中明确定义，即卷积运算符限于RKHS是连续的线性函数。此外，根据这个假设，代表定理持有，因此可以通过求解有限维程序来估算脉冲响应。因此，连续性特征在基于内核的系统识别中起着重要作用。本文表明，在综合情况下，即当内核是可集成的函数并且输入信号的界定时，可以保证在相当普遍的情况下满足此中心假设。此外，优化问题的强大凸性和卷积运算符的连续性属性暗示基于内核的系统识别允许独特的解决方案。因此，因此，基于内核的系统识别是一种明确定义的方法。
The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In the resulting framework, the impulse response estimation problem is formulated as a regularized optimization defined on an infinite-dimensional RKHS consisting of stable impulse responses. The consequent estimation problem is well-defined under the central assumption that the convolution operators restricted to the RKHS are continuous linear functionals. Moreover, according to this assumption, the representer theorem hold, and therefore, the impulse response can be estimated by solving a finite-dimensional program. Thus, the continuity feature plays a significant role in kernel-based system identification. This paper shows that this central assumption is guaranteed to be satisfied in considerably general situations, namely when the kernel is an integrable function and the input signal is bounded. Furthermore, the strong convexity of the optimization problem and the continuity property of the convolution operators imply that the kernel-based system identification admits a unique solution. Consequently, it follows that kernel-based system identification is a well-defined approach.
