Weitian Chen

Fuzzy Nonlinear Unknown Input Observer Design with Fault Diagnosis Applications

An approach for nonlinear unknown input observer (NUIO) design is proposed for a class of nonlinear systems representable by a Takagi—Sugeno (TS) fuzzy system. The proposed NUIO design for TS fuzzy systems is carried out for two cases: (1) the premise variables do not depend on the unmeasured state variables; and (2) the premise variables depend on the unmeasured state variables. Sufficient conditions for the existence of NUIOs are derived, and a linear matrix inequality (LMI)-based design strategy is presented for NUIO design purposes. The proposed NUIO design approach is then applied to solve actuator fault detection and isolation problems for nonlinear systems described by TS fuzzy systems. To this end, a system structure with two groups of inputs where one group of inputs is treated as unknown inputs is developed. Based on the system structure, a bank of NUIOs are then designed using the developed NUIO design approach in order to investigate the following fault diagnosis problems. (1) How can the NUIOs be used for detecting faults? (2) Under what conditions is it possible to isolate single and/or multiple faults? (3) What is the maximum number of faults that can be isolated simultaneously? (4) How can multiple fault isolation be achieved? In this article we present a NUIO-based fault-detection scheme for problem (1), give sufficient conditions for problem (2), determine the maximum number of faults that can be isolated for problem (3), and propose a fault-diagnosis scheme using a bank of NUIOs to solve problem (4). As an illustrative example, Lorenz’s chaotic system with multi-inputs is chosen to show the effect of the designed NUIOs and the proposed fault detection and isolation scheme. Simulation results show that accurate state estimation is achieved and actuator faults can be detected and isolated successfully.

Brief paper: Actuator fault diagnosis for a class of nonlinear systems and its application to a laboratory 3D crane

In this paper, an actuator fault diagnosis scheme is proposed for a class of affine nonlinear systems with both known and unknown inputs. The scheme is based on a novel input/output relation derived from the considered nonlinear systems and the use of the recently developed high-order sliding-mode robust differentiators. The main advantages of the proposed approach are that it does not require a design of nonlinear observer and applies to systems not necessarily detectable. Conditions are provided to characterize the feasibility of fault detection and isolation using the proposed scheme and the maximum number of isolatable actuator faults. The efficacy of the proposed actuator fault diagnosis approach is tested through experiments on a laboratory 3D Crane, and the experimental results show that the proposed actuator fault diagnosis approach is promising and can achieve fault detection and isolation satisfactorily.

Properties of blocked linear systems

This paper presents a systematic study on the properties of blocked linear systems that have resulted from blocking discrete-time linear time invariant systems. The main idea is to explore the relationship between the blocked and the unblocked systems. Existing results are reviewed and a number of important new results are derived. Focus is given particularly on the zero properties of the blocked system as no such study has been found in the literature.

A Combined Multiple Model Adaptive Control Scheme and Its Application to Nonlinear Systems With Nonlinear Parameterization

A combined multiple model adaptive control (CMMAC) scheme, which is a proper combination of the estimator-based MMAC scheme and the unfalsified MMAC scheme, has been proposed with the aim of taking advantage of the strength of each scheme while avoiding their weaknesses. The major novelty of the CMMAC scheme lies in the fact that it monitors not only the adequacy of candidate models in terms of their estimation performances but also the performance of the active candidate controller. As an application of the CMMAC scheme and one example of such new multiple model adaptive controllers, a CMMAC based controller has been designed for a class of nonlinear systems with nonlinear parameterization. Under some sufficient conditions, a strong finite time switching result (which provides a characterization on the maximum number of switching) and the closed-loop stability have been established. A constructive design based on back-stepping is provided for the adaptive control problem of a special class of nonlinearly parameterized systems, which can satisfy all the sufficient conditions to ensure closed-loop stability.

On the zeros of blocked linear systems with single and mixed frequency data

This paper studies properties of blocked systems resulting from blocking discrete linear systems with mixed frequency data. The focus is on the zeros of the blocked systems. We first establish results on the simpler single frequency case, where the unblocked linear systems have all data at the same frequency. In particular, an explicit relation between the system matrix of the unblocked linear systems and that of their corresponding blocked systems is derived. Based on this relation, it is shown that the blocked systems are zero free if and only if the related unblocked systems are zero free. Furthermore, it is illustrated that square systems have zeros generically, i.e. for generic parameter matrices, and the corresponding kernel is of dimension one. With the help of the results obtained for the single frequency case, we then identify a situation in which the blocked systems can be zero free.

Identifiability of regular and singular multivariate autoregressive models from mixed frequency data

This paper is concerned with identifiability of an underlying high frequency multivariate AR system from mixed frequency observations. Such problems arise for instance in economics when some variables are observed monthly whereas others are observed quarterly. If we have identifiability, the system and noise parameters and thus all second moments of the output process can be estimated consistently from mixed frequency data. Then linear least squares methods for forecasting and interpolating nonobserved output variables can be applied. Two ways for guaranteeing generic identifiability are discussed.

Solutions of Yule‐Walker Equations for Singular AR Processes

A study is presented on solutions of the Yule-Walker equations for singular AR processes that are stationary outputs of a given AR system. If the Yule-Walker equations admit more than one solution and the order of the AR system is no less than two, the solution set includes solutions which define unstable AR systems. The solution set also includes one solution, the minimal norm solution, which defines an AR system whose characteristic polynomial has either only stable zeros (implying that only one stationary output exists for this system and it is linearly regular) or has stable zeros as well as zeros of unit modulus, (implying that stationary solutions of this system are a sum of a linearly regular process and a linearly singular process). The numbers of stable and unit circle zeros of the characteristic polynomial of the defined AR system can be characterized in terms of the ranks of certain matrices, and the characteristic polynomial of the AR system defined by the minimal norm solution has the least number of unit circle zeros and the most number of stable zeros over all possible solutions.

On the zeros of blocked time-invariant systems

Abstract This paper studies the zero properties of blocked linear systems resulting from blocking of linear time-invariant systems. The main idea is to establish a relation between the zero properties of blocked systems and the zero properties of their corresponding unblocked systems. In particular, it is shown that the blocked system has a zero if and only if the associated unblocked system has a zero. Furthermore, the zero properties of blocked systems under a generic setting i.e. a setting which parameter matrices A , B , C , D assume generic values, are examined. It is demonstrated that nonsquare blocked systems i.e. blocked systems with number of outputs unequal to the number of inputs, generically have no zeros; however, square blocked systems i.e. blocked systems with equal number of inputs and outputs, generically have only finite zeros and these finite zeros have geometric multiplicity one.

Autoregressive models of singular spectral matrices

This paper deals with autoregressive (AR) models of singular spectra, whose corresponding transfer function matrices can be expressed in a stable AR matrix fraction description D−1(q)B with B a tall constant matrix of full column rank and with the determinantal zeros of D(q) all stable, i.e. in |q|>1,q∈C. To obtain a parsimonious AR model, a canonical form is derived and a number of advantageous properties are demonstrated. First, the maximum lag of the canonical AR model is shown to be minimal in the equivalence class of AR models of the same transfer function matrix. Second, the canonical form model is shown to display a nesting property under natural conditions. Finally, an upper bound is provided for the total number of real parameters in the obtained canonical AR model, which demonstrates that the total number of real parameters grows linearly with the number of rows in W(q).

AR models of singular spectral matrices

This paper deals with autoregressive models of singular spectra. The starting point is the assumption that there is available a transfer function matrix W(q) expressible in the form D−1(q)B for some tall constant matrix B of full column rank and with the determinantal zeros of D(q) all stable. It is shown that, even if this matrix fraction representation of W(q) is not coprime, W(q) has a coprime matrix fraction description of the form D̃−1(q)[Im 0]T . It is also shown how to characterize the equivalence class of all autoregressive matrix fraction descriptions of W(q), and how canonical representatives can be obtained. A canonical representative can be obtained with a minimal set of row degrees for the submatrix of D̃(q) obtained by deleting the first m rows. The paper also considers singular autoregressive descriptions of nested sequences of Wp(q), p = p0, p0+1, …, where p denotes the number of rows, and shows that these canonical descriptions are nested, and contain a number of parameters growing linearly with p.