Fast Methods for Estimating the Distance to Uncontrollability
نویسندگان
چکیده
The distance to uncontrollability for a linear control system is the distance (in the 2-norm) to the nearest uncontrollable system. We present an algorithm based on methods of Gu and Burke–Lewis–Overton that estimates the distance to uncontrollability to any prescribed accuracy. The new method requires O(n4) operations on average, which is an improvement over previous methods which have complexity O(n6), where n is the order of the system. Numerical experiments indicate that the new method is reliable in practice.
منابع مشابه
New Methods for Estimating the Distance to Uncontrollability
Controllability is a fundamental concept in control theory. Given a linear control system, we present new algorithms for estimating its distance to uncontrollability, i.e., the norm of the norm-wise smallest perturbation that makes the given system uncontrollable. Many algorithms have been previously proposed to estimate this distance. Our new algorithms are the rst that correctly estimate this...
متن کاملThe structured distance to uncontrollability under multi-perturbations: An approach using multi-valued linear operators
In this paper we develop a unifying approach for computing the distance to uncontrollability of linear control systems. By using multi-valued linear operators in representing and estimating the system's equations and matrices we are able to derive computable formulas of the distance from a controllable linear system to the nearest uncontrollable system under the assumption that the system's mat...
متن کاملComparing ordinary kriging and advanced inverse distance squared methods based on estimating coal deposits; case study: East-Parvadeh deposit, central Iran
Finding a proper estimation method for ore resources/reserves is important in mining engineering. The aim of this work is to compare the Ordinary Kriging (OK) and Advanced Inverse Distance Squared (AIDS) methods based on the correlation between the raw and estimated data in the East-Parvadeh coal deposit, central Iran. The variograms and anisotropic ellipsoids are calculated to estimate the ash...
متن کاملPseudospectral Components and the Distance to Uncontrollability
We show that 2-norm pseudospectra ofm-by-nmatrices have no more than 2m(4m−1) connected components. Such bounds are pertinent for computing the distance to uncontrollability of a control system, since this distance is the minimum value of a function whose level sets are pseudospectra. We also discuss algorithms for computing this distance, including a trisection variant of Gu’s recent algorithm...
متن کاملOn the structured distance to uncontrollability
This article is concerned with the structured distance to uncontrollability of a linear time-invariant system and relates this concept to a variation of the μ-value. The developed framework is applied to derive computational expressions for the class of real perturbations as well as for Hermitian, symmetric, and skew-symmetric perturbations in a relatively simple manner. Examples demonstrate th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Matrix Analysis Applications
دوره 28 شماره
صفحات -
تاریخ انتشار 2006