Interval estimation and fault detection for switched nonlinear systems based on zonotope method

Abstract

This paper investigates the state interval estimation and fault detection (FD) problems for a Lipschitz nonlinear switched system based on the combination of the H∞$$ {H}_{\infty } $$ observer and the zonotope method. To begin with, an H∞$$ {H}_{\infty } $$ observer that is robust to the disturbance is designed, and the stability of the observer error dynamic system is analyzed under the average dwell time (ADT) concept. After this, the zonotope theory is applied on the H∞$$ {H}_{\infty } $$ observer error dynamic system such that the interval state estimation can be calculated iteratively when the system suffers from no fault. Furthermore, for FD purpose, a residual is constructed based on the H∞$$ {H}_{\infty } $$ observer. Because the constructed residual contains disturbance, it cannot be used for FD directly. To overcome this drawback, the interval estimation method of the residual is proposed by using the zonotope method, and a residual‐based FD scheme is developed. Finally, a simulation example is given to verify the effectiveness of the proposed method.

Set‐membership estimation of switched LPV systems: Application to fault/disturbance estimation

“…Thus, the estimated state k can be obtained through an outer approximation of the intersection between the zonotope ( 14) and the measurement state set (16). Based on the Property 5, the intersection zonotope is parameterized with a switched parameter-dependent correction matrix 𝜆 𝜎(−) (𝜌(−)) ∈ R n x ×n y , and given by:…”

“…Meanwhile, great efforts have also been devoted to state estimation and fault diagnosis problems of switched systems, for example, the works of Ethabet et al, 13 Ifqir et al, 14 Du et al 15 and Li et al 16 In practice, some uncertainties, such as unknown parameters, process disturbances or measurement noises, are inevitable for most systems. Hence, the state estimation method needs to be robust against these uncertainties.…”

Residual evaluation of fault detection in discrete‐time systems

“…Theorem 2. Given a scalar 𝛽 > 0, subsystem ( 10) is stable and satisfies H − index shown in (12), if there exists a scalar 𝛿, and matrices…”

“…Theorem 3. Given scalars 𝛾 w > 0, 𝛾 v > 0 and 0 < 𝛼 < 1, 𝛽 > 0, system ( 8) is stable and satisfies H − index shown in (12) and L ∞ performance shown in (13), if there exist scalars 𝜆 > 0, 𝜁 > 0, 𝛿 and matrices 14), (15), and ( 24) hold.…”

“…Fault detection, as the prerequisite and basis of fault diagnosis, has been intensively studied in the past decades [4][5][6][7][8]. In the research of control system fault detection, observer-based fault detection technology is an important method [9][10][11][12]. Its main principle is to construct fault detection observer, generate residual signal, design fault residual evaluation method, and detect fault.…”