ARX modeling of unstable linear systems

Abstract

High-order ARX models can be used to approximate a quite general class of linear systems in a parametric model structure, and wellestablished methods can then be used to retrieve the true plant and noise models from the ARX polynomials. However, this commonly used approach is only valid when the plant is stable or if the unstable poles are shared with the true noise model. In this contribution, we generalize this approach to allow the unstable poles not to be shared, by introducing modifications to correctly retrieve the noise model and noise variance.

Local Module Identification in Dynamic Networks Using Regularized Kernel-Based Methods

“…Even though the estimate of unstable poles are with high accuracy for the latter method, the EBDM performs significantly better in terms of accuracy with less variance in the identified frequency response. Since we have limited data (N " 500), the estimated model with the method in [14] is of high order, which can be verified from figure 7.…”

“…Also, the estimated model will be of high order unless there is sufficiently large data. Figure 7 shows the bode magnitude plot of the estimates after 50 MC simulations with the experimental setup in case study 2 using EBDM and the method of ARX modeling in [14]. ARX models of 15 th order are used for the latter method.…”

“…Analogous to the factorization technique used in [13] and [14], we factorize each F jk (from now on superscript 0 is dropped for convenience) as, where F psq jk pqq contains the stable roots of F jk pzq and F paq jk pqq contains the anti-stable roots of F jk pzq, which are given by assuming without loss of generality that f jk paq n f ‰ 0. Then, we define F a pqq as the product of all polynomials with anti-stable roots i.e.…”

“…Bode magnitude plot to compare the estimates of the introduced approach(upper) and the approach in[14](lower).…”

Gradient-Based Particle Filter Algorithm for an ARX Model With Nonlinear Communication Output

“…The focus of this paper is to develop an on-line identification algorithm for the non-standard ARX model whose measurement noise has different properties. The ARX model identification has been extensively studied in theory [5], [6]. Many identification methods, such as the recursive least squares (RLS) algorithms [7], the hierarchical algorithms [8], the stochastic gradient (SG) algorithms [9] and the iterative algorithms [10], have been proposed for ARX models.…”