Zonotopic fault detection observer for linear parameter‐varying descriptor systems

Abstract

This paper studies zonotopic fault detection observer design for a class of linear parameter-varying descriptor systems. The disturbance and measurement noise are unknown but can be bounded by zonotopes. A zonotopic method is presented to estimate the envelope of residual. To attenuate the effect of disturbance and measurement noise, a zonotopic size optimization criterion is implemented based on P-radius. To improve the fault detection performance, a finite-frequency H_ index is introduced based on the generalized Kalman-Yakubovich-Popov lemma. Simulation examples of a mass-spring and a direct-current motor are utilized to demonstrate the performance of the proposed method. KEYWORDSdescriptor systems, fault detection observer, linear parameter varying, zonotope INTRODUCTIONFaults may result in system performance deterioration and even lead to an unacceptable economic loss or personal injury. To enhance the systems reliability, model-based fault diagnosis technology has received much attention in recent decades. 1-3 In practice, the performance of model-based fault diagnosis may be affected by uncertainties such as modeling errors, unknown input disturbance, and measurement noise. Consequently, robust fault detection methods have been intensively studied in recent years. [4][5][6] The set-membership paradigm has been proven to be a suitable robust fault detection approach, since it only assumes that the modeling errors, disturbance, and measurement noise are unknown but bounded by some known compact sets. 7,8 These sets are represented by some simple geometrical forms such as polytopes, ellipsoids, intervals, 9 and zonotopes. 10 Recently, as a special type of polytopes, zonotopes have become popular considering their efficient computation of linear transformation and Minkowski sum. 11 In the work of Alamo et al, 12 a zonotopic approach is used to compute the envelope of state by considering the bounded disturbance and parameters. Two different optimization methods, volume minimization and segment minimization, are utilized to obtain tight bounds of zonotopes. The segment minimization calculates fast but leads to a conservative result. Volume minimization provides a good performance but at the cost of a loss in computational efficiency. Fortunately, the P-radius minimization 13 combines the advantage of the volume minimization (performance) and of the segment minimization (computation time). A zonotopic approach has been used to handle the problem of fault detection. 7,14,15 Nevertheless, these methods only take the effect of unknown disturbance and 3426The notations used in this paper are standard. ℝ n×m denotes the real matrices with dimensions n × m. j represents the imaginary unit, and 0 and I denote the zero and identity matrices, respectively. For a vector z ∈ ℝ n , its 2-norm and weighted 2-norm are denoted as ||z|| = √ z T z and ||z|| P = √ z T Pz, respectively. For a matrix A, A T , A * , and A ⟂ stand for its matrix transposition, complex conjugate transpose, and orthogonal complement, respectively. A † ...

Sensor fault estimation based on the constrained zonotopic Kalman filter

“…Set-membership estimation is a method to estimate the parameters or states of a system only with the limit bounds of the noise, which is consistent with the case that the noise in the actual industrial system is unknown but bounded. The commonly used set-membership estimation methods include ellipsoids, 13,14 polytopes, 15,16 zonotopes, 17,18 etc. Compare with ellipsoids, zonotopes have better accuracy and is less conservative, and at the same time, the computational complexity of zonotopes is less than polytopes.…”

“…Pourasghar et al 17 used the zonotopic sets to limit the uncertainty of linear system in the state estimation process, then analyzed and compared the performances of state estimation and fault detection based on the interval observer and set-membership method by a simulation case in a two-tanks system. Li et al 18 designed a zonotopic fault detection observer in order to solve the fault detection problem for linear parameter-varying descriptor system. The zonotopic set is used to contain the unknown disturbance and measurement noise, and the optimal zonotope is obtained based on the P-radius minimization criterion.…”

Fault detection and isolation for discrete-time Markovian jump systems with generally bounded transition probabilities: A zonotope-based method

“…To be specific, the FDI mainly serves to detect the fault occurrence, as well as to locate it. Up to now, various methods on the fault diagnosis have been proposed for different systems (Edwards et al, 2000;Han et al, 2019b;Hwang et al, 2010;Li and Yang, 2014;Li et al, 2020;Li et al, 2019a;Naderi and Khorasani, 2017;Wang and Yang, 2020;Wang et al, 2007;Yeu et al, 2005;Zhang et al, 2019b;Zhu and Yang, 2013), but very few for MJSs. Exceptionally, some works have been conducted for MJSs (Chen et al, 2019;Dong et al, 2012;Dong et al, 2018;Han et al, 2019a;Li et al, 2018aLi et al, , 2018cLi et al, , 2018bLi et al, , 2019bLi et al, , 2019c;Liang et al, 2018;Wang et al, 2019;Yang et al, 2020;Zhang et al, 2019a;Zhong et al, 2005).…”

Bilinear matrix inequality‐based nonquadratic controller design for polytopic‐linear parameter varying systems

“…Polytopic-linear parameter varying (LPV)-based controllers are widely used to stabilize complex nonlinear dynamical systems. [1][2][3] A polytopic-LPV model comprises a convex sum of several local dynamics of each vertex, which are obtained by the so-called sector nonlinearity approach or linearizing the nonlinear dynamics at each operating point. 4,5 The main feature of polytopic-LPV systems is that they can provide a systematic procedure to design a gain-scheduling controller which is constructed by the convex sum of several local linear controllers.…”

“…Polytopic‐linear parameter varying (LPV)‐based controllers are widely used to stabilize complex nonlinear dynamical systems 1‐3 . A polytopic‐LPV model comprises a convex sum of several local dynamics of each vertex, which are obtained by the so‐called sector nonlinearity approach or linearizing the nonlinear dynamics at each operating point 4,5 .…”