اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدNon-causal regularized least-squares for continuous-time system identification with band-limited input excitations
148
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In continuous-time system identification, the intersample behavior of the input signal is known to play a crucial role in the performance of estimation methods. One common input behavior assumption is that the spectrum of the input is band-limited. The sinc interpolation property of these input signals yields equivalent discrete-time representations that are non-causal. This observation, often overlooked in the literature, is exploited in this work to study non-parametric frequency response estimators of linear continuous-time systems. We study the properties of non-causal least-square estimators for continuous-time system identification, and propose a kernel-based non-causal regularized least-squares approach for estimating the band-limited equivalent impulse response. The proposed methods are tested via extensive numerical simulations.
قيم البحث
اقرأ أيضاً
For many years, the Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC) has been widely used for identification. The intersample behaviour of the input plays an important role in this method, and it has been shown rece
ntly that the SRIVC estimator is not consistent if an incorrect assumption on the intersample behaviour is considered. In this paper, we present an extension of the SRIVC algorithm that is able to deal with continuous-time multisine signals, which cannot be interpolated exactly through hold reconstructions. The proposed estimator is generically consistent for any input reconstructed through zero or first-order-hold devices, and we show that it is generically consistent for continuous-time multisine inputs as well. The statistical performance of the proposed estimator is compared to the standard SRIVC estimator through extensive simulations.
Wireless sensor network has recently received much attention due to its broad applicability and ease-of-installation. This paper is concerned with a distributed state estimation problem, where all sensor nodes are required to achieve a consensus esti
mation. The weighted least squares (WLS) estimator is an appealing way to handle this problem since it does not need any prior distribution information. To this end, we first exploit the equivalent relation between the information filter and WLS estimator. Then, we establish an optimization problem under the relation coupled with a consensus constraint. Finally, the consensus-based distributed WLS problem is tackled by the alternating direction method of multiplier (ADMM). Numerical simulation together with theoretical analysis testify the convergence and consensus estimations between nodes.
Input design is an important issue for classical system identification methods but has not been investigated for the kernel-based regularization method (KRM) until very recently. In this paper, we consider in the time domain the input design problem
of KRMs for LTI system identification. Different from the recent result, we adopt a Bayesian perspective and in particular make use of scalar measures (e.g., the $A$-optimality, $D$-optimality, and $E$-optimality) of the Bayesian mean square error matrix as the design criteria subject to power-constraint on the input. Instead to solve the optimization problem directly, we propose a two-step procedure. In the first step, by making suitable assumptions on the unknown input, we construct a quadratic map (transformation) of the input such that the transformed input design problems are convex, the number of optimization variables is independent of the number of input data, and their global minima can be found efficiently by applying well-developed convex optimization software packages. In the second step, we derive the expression of the optimal input based on the global minima found in the first step by solving the inverse image of the quadratic map. In addition, we derive analytic results for some special types of fixed kernels, which provide insights on the input design and also its dependence on the kernel structure.
We study the statistical properties of the iterates generated by gradient descent, applied to the fundamental problem of least squares regression. We take a continuous-time view, i.e., consider infinitesimal step sizes in gradient descent, in which c
ase the iterates form a trajectory called gradient flow. Our primary focus is to compare the risk of gradient flow to that of ridge regression. Under the calibration $t=1/lambda$---where $t$ is the time parameter in gradient flow, and $lambda$ the tuning parameter in ridge regression---we prove that the risk of gradient flow is no less than 1.69 times that of ridge, along the entire path (for all $t geq 0$). This holds in finite samples with very weak assumptions on the data model (in particular, with no assumptions on the features $X$). We prove that the same relative risk bound holds for prediction risk, in an average sense over the underlying signal $beta_0$. Finally, we examine limiting risk expressions (under standard Marchenko-Pastur asymptotics), and give supporting numerical experiments.
In this paper, we first propose a method that can efficiently compute the maximal robust controlled invariant set for discrete-time linear systems with pure delay in input. The key to this method is to construct an auxiliary linear system (without de
lay) with the same state-space dimension of the original system in consideration and to relate the maximal invariant set of the auxiliary system to that of the original system. When the system is subject to disturbances, guaranteeing safety is harder for systems with input delays. Ability to incorporate any additional information about the disturbance becomes more critical in these cases. Motivated by this observation, in the second part of the paper, we generalize the proposed method to take into account additional preview information on the disturbances, while maintaining computational efficiency. Compared with the naive approach of constructing a higher dimensional system by appending the state-space with the delayed inputs and previewed disturbances, the proposed approach is demonstrated to scale much better with the increasing delay time.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
