Stability and stabilization for a class of complex production processes via LMIs

Abstract

Summary This paper deals with the problem of stability and stabilization for a non‐Newton mechanical system, and the system is described by the so‐called pattern class variable rather than a state or output variable. At the beginning of this paper, the method of pattern‐moving–based dynamics description is introduced, and it describes the dynamic properties of a concerned production process at a larger granularity. Then, a pattern‐moving–based nonlinear state space model is put forward. Moreover, a feature of output‐class partition is defined and extracted, and two constraint conditions are given for the system based on the feature. Through dealing with difference of a Lyapunov function in two cases, new methods of stability and stabilization are proposed by using the LMI and S‐procedure approaches. They guarantee the stability and robust stabilization of the system and present the relationship between the feature of output‐class partition and system stability. A sintering process and numerical examples are used to demonstrate the effectiveness and practicability of the proposed method.

Pattern-Moving-Based Parameter Identification of Output Error Models with Multi-Threshold Quantized Observations

“…1) Different from the previous system identification problem of ARX or IARX models based on pattern moving and single metric [6,7], this paper considers hybrid metrics, the model noise distribution and proves the convergence of the designed M-AM-SGRPIA.…”

“…A novel pattern-moving-based system dynamics description method was proposed in [5]. Its basic idea is to take the pattern class as a moving variable, and it is mapped to a computable space by class centers [6,7], interval numbers [8], and cells [9] due to its lack of arithmetic operation attribute. Furthermore, in view of various metric methods of pattern class, the linear autoregressive model with exogenous input (ARX) or interval ARX (IARX) model was established, and the parameter identification algorithm based on least square [6], minimumvariance-based controller [5], optimal controller [10], state-feedback controller [7] and predictive controller [11] were designed.…”

Modified Model Free Adaptive Control for a Class of Nonlinear Systems with Multi-threshold Quantized Observations

“…Qu [1] pointed out that this kind of production system conforms to the characteristics of statistical movement law to some extent, and a group of identical or similar working conditions correspond to the production of products with similar quality index parameters. A system dynamics description method based on pattern moving was proposed for this kind of systems in [2][3][4][5]. Firstly, through the feature extraction and pattern classification of a large number of high-dimensional offline working condition data, the extraction rule T (•), classification rule M(•), numbers of pattern class N, class centers c i , class radii r i and class thresholds C i ( C i − c i 2 = r i , i = 1, 2, • • • , N) were determined.…”

An improved pattern-based prediction model for a class of industrial processes

“…And based on the measurement methods, system dynamical properties were described, and controllers were designed (Li et al, 2020(Li et al, , 2021Xu and Wang, 2016;Xu et al, 2013Xu et al, , 2018. Moreover, system stability and influence of output-class partition were analyzed (Wang et al, 2019(Wang et al, , 2020Xu et al, 2019Xu et al, , 2020. However, the common characteristic of these works was that the description method was composed of three parts: a measurement mapping, an initial model, and a classification mapping.…”

“…So, the description method could be simplified. Most of the initial models were linear (Wang et al, 2019(Wang et al, , 2020Xu et al, 2019Xu et al, , 2020. But it was difficult to estimate their structure and parameters of the initial model for some complex dynamical properties.…”