Approximation of Nonnegative Systems by Finite Impulse Response Convolutions

Optimal Impulse Control of a Simple Reparable System in a Nonreflexive Banach Space

We discuss the problem of optimal impulse control representing the preventive maintenance of a simple reparable system. The system model is governed by coupled transport and integro-differential equations in a nonreflexive Banach space. The objective of this paper is to construct nonnegative impulse control inputs at given system running times that minimize the probability of the system in failure mode. To guarantee the nonnegativity of the controlled system, we consider the control inputs to depend on the system state. This essentially leads to a bilinear control problem. We first present a r…

Approximation of nonnegative systems by moving averages of fixed order

We pose the approximation problem for scalar nonnegative input-output systems via impulse response convolutions of finite order, i.e. finite order moving averages, based on repeated observations of input/output signal pairs. The problem is converted into a nonnegative matrix factorization with special structure for which we use Csiszár's I-divergence as the criterion of optimality. Conditions are given, on the input/output data, that guarantee the existence and uniqueness of the minimum. We propose an algorithm of the alternating minimization type for I-divergence minimization, and present its…

使用脉冲响应/平衡模型结构时的预测误差界

Bounds on Prediction Error When Using an Impulse Response/Equilibrium Model Structure

本文针对脉冲响应/平衡模型结构，给出了可观测性条件以及预测误差的界，并可直接通过系统脉冲响应评估。

The Existence and Uniqueness of Solutions for Kernel-Based System Identification

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…