Sensor location for discrete mode observability of switching linear systems with unknown inputs

This paper deals with the problem of additional sensor placement in order to recover the discrete mode observability of switching structured linear systems with unknown inputs. Such a property is quite important for designing control laws, observers, fault detection and isolation schemes (when the fault occurrence implies a commutation between two modes), and so on. The proposed method, based on a graph-theoretic approach, assumes only the knowledge of the system’s structure. We express, in graphical terms, new necessary and sufficient conditions for discrete mode generic observability. When these conditions are not satisfied, we propose a sensor placement procedure which allows us to recover the mode observability. Our approach can be implemented by classical and quite simple graph-theory algorithms.     

Determining the characteristics of systems with multiple inputs and multiple outputs

A simple and computationally efficient method of determining the transfer function and other characteristics of systems with multiple inputs and multiple outputs (MIMO systems) described by autoregression equations is proposed. The method is based on the use of the discrete Fourier transformation. The algorithm is highly suitable for computer implementation. The efficiency and simplicity of the method are illustrated using the example of a system with three inputs and three outputs. The proposed concept may be applied to systems described by the autoregression sliding mean.     

不确定时滞系统执行器故障模式下的满意容错控制

针对含有不确定参数的离散时滞系统,在执行器增益故障情况下,研究了含时滞记忆的状态反馈满意容错控制器的设计问题.在采用合理的执行器故障描述条件下,分别给出了无外界扰动输入时含有时滞记忆和无时滞记忆状态反馈鲁棒容错控制器的存在条件;进一步给出了在H∞扰动衰减指标约束下,含有时滞记忆和无时滞记忆状态反馈鲁棒容错控制器的设计方法.仿真算例验证了该方法的有效性.     

Sensor selection for fault diagnosis in uncertain systems

ABSTRACT

Finding the cheapest, or smallest, set of sensors such that a specified level of diagnosis performance is maintained is important to decrease cost while controlling performance. Algorithms have been developed to find sets of sensors that make faults detectable and isolable under ideal circumstances. However, due to model uncertainties and measurement noise, different sets of sensors result in different achievable diagnosability performance in practice. In this paper, the sensor selection problem is formulated to ensure that the set of sensors fulfils required performance specifications when model uncertainties and measurement noise are taken into consideration. However, the algorithms for finding the guaranteed global optimal solution are intractable without exhaustive search. To overcome this problem, a greedy stochastic search algorithm is proposed to solve the sensor selection problem. A case study demonstrates the effectiveness of the greedy stochastic search in finding sets close to the global optimum in short computational time.     

Decentralized fault diagnosis approach without a global model for fault diagnosis of discrete event systems

Diagnosability property ensures that a predefined set of faults are diagnosable by a centralized diagnoser built using a global model of the system, while co-diagnosability guarantees that these faults are diagnosed in decentralized manner using a set of local diagnosers. A fault must be diagnosed by at least one local diagnoser by using its proper local observation of the system. The aim of using decentralized diagnosis approaches is to overcome the space complexity and weak robustness of centralized diagnosis approaches while at the same time preserving the diagnostic capability of a centralized diagnosis. However, co-diagnosability property is stronger than diagnosability property. If a system is co-diagnosable, then it is diagnosable, while a diagnosable system does not ensure that it is co-diagnosable. Therefore, the challenge of decentralized diagnosis approaches is to perform local diagnosis and to verify that it is equivalent to the centralized one without the need for a global model. In this paper, an approach is proposed to obtain co-diagnosable decentralized diagnosis structure of discrete event systems without the use of a global model. This approach is based on the synchronization of local diagnosis decisions in order to solve the ambiguity between local diagnosers. This synchronization allows obtaining local diagnosis equivalent to the global one without the use of a global model.     

Sensor deployment for fault diagnosis using a new discrete optimization algorithm

Optimal allocation of the sensor in a wireless sensor network (WSN) is required to have a satisfactory fault diagnosis within the system. In fact, the sensor nodes in the network should be located in an arrangement to maximize the failure diagnosis. In this paper, the sensor deployment optimization to diagnose the distributed failures in a wireless unmanned aerial vehicles (UAVs) network has been studied. In this way, a novel evolutionary optimization algorithm inspired by the gases Brownian and turbulent rotational motion is utilized which is called Discrete Gases Brownian Motion Optimization (DGBMO) algorithm. An integer linear programming (ILP) approach is used to formulate the sensor deployment. Then the sensor deployment optimization is solved by DGBMO as well as generic ILP solvers and Boolean satisfiability-based ILP solvers. The results show that DGBMO is suitable for sensor disposition optimization especially in large-sized UAV networks.     

Formal approach to fault diagnosis in distributed discrete event systems with OBDD

In this paper, we study the fault diagnosis problem for distributed discrete event systems. The model assumes that the system is composed of distributed components which are modeled in labeled Petri nets and interact with each other via sets of common resources (places). Further, a component’s own access to a common resource is an observable event. Based on the diagnoser approach proposed by Sampath et al., a distributed fault diagnosis algorithm with communication is presented. The distributed algorithm assumes that the local diagnosis process can exchange messages upon the occurrence of observable events. We prove the distributed diagnosis algorithm is correct in the sense that it recovers the same diagnostic information as the centralized diagnosis algorithm. Furthermore, we introduce the ordered binary decision diagrams (OBDD) in order to manage the state explosion problem in state estimation of the system.     

线性系统考虑执行器故障的鲁棒控制

针对线性定常系统，提出了考虑执行器故障的鲁棒控制器设计问题。利用更一般、更实际的执行器故障模型，给出了系统输出渐近跟踪参考输入信号的鲁棒控制存在的充分条件。通过求解线性矩阵不等式（LMI）完成状态反馈控制器的设计。数例仿真验证了本文提出设计方法的可行性，并且通过所设计的鲁棒控制系统与不考虑故障控制系统的比较，进一步说明对系统进行鲁棒设计的必要性。     

Observers for linear discrete multivariable systems with inaccessible inputs

The problem of observing the state vector of a discrete-time multivariable system subjected to inaccessible inputs is considered. Using a polynomial-type approximation for these inputs, a set of necessary and sufficient conditions that can be readily applied to determine the existence of an observer is obtained. Computer simulation results for a third-order two-input two-output system are included.     

Observer design for discrete systems with unknown exogenous inputs

A design procedure is developed for determining optimal discrete observers for estimating system states and unknown exogenous system inputs. This procedure is based on augmenting a standard system observer with an input model. The augmented model is then transformed into the discrete z-domain to determine relevant input/output transfer function matrices. The transfer function matrices are used to develop transfer function relationships between unknown exogenous inputs and the observer estimate of these inputs. It is shown that the optimal observer gains can be determined by implementing the observer as a Fisher filter. An example of the procedure is demonstrated with a third-order point-mass tracking filter     

Sensor bias fault diagnosis in a class of nonlinear systems

This note describes a robust sensor bias fault diagnosis architecture for dynamic systems represented by a class of nonlinear discrete-time models. The nonlinearity in the system nominal model is assumed to be a function of inputs and outputs only. Specifically, this note uses adaptive techniques to estimate an unknown sensor bias in the presence of modeling uncertainties. A simulation example is presented to illustrate the methodology. The robustness, sensitivity and stability properties of the bias fault diagnosis architecture are rigorously analyzed     

Sensor and actuator fault isolation by structured partial PCA with nonlinear extensions

Partial PCA based on principal component analysis (PCA) with ideas borrowed from parity relations is a useful method in fault isolation (J. Gertler, W. Li, Y. Huang, T.J. McAvoy, Isolation enhanced principal component analysis, AIChE Journal 45(2) (1999) 323–334). By performing PCA on subsets of variables, a set of structured residuals can be obtained in the same way as structured parity relations. The structured residuals are utilized in composing an isolation scheme for sensor and actuator faults, according to a properly designed incidence matrix. To overcome the limitations of PCA, nonlinear approaches based on generalized PCA (GPCA) and nonlinear PCA (NPCA) are proposed. The nonlinear methods are demonstrated on an artificial 2×2 system while simulation studies on the Tennessee Eastman process illustrate the linear method and some extensions.     

Real-time spacecraft actuator fault diagnosis with state-segmented particle filtering

Fault diagnosis permits computational redundancy, which renders a system sustainable and eventually leads to hardware cost reduction. To achieve the posterior distribution computation needed for fault diagnosis along with motion estimation, we suggest a particle filtering (PF)-based state-segmentation approach. Here, both a continuous state vector and fault states are segmented accordingly to allow flexible reasoning for fault diagnosis and motion estimation. For each segmented space, an attempt is made to construct a corresponding posterior distribution independently, resulting in a reduction of the number of particles. Our experimental simulation demonstrates fault diagnosis among billions of fault states. Our state-segmentation approach reduced 98% of particles compared with the ordinal PF approach.     

Left invertibility of discrete systems with finite inputs and quantised output

The aim of this article is to address left invertibility for dynamical systems with inputs and outputs in discrete sets. We study systems which evolve in discrete time within a continuous state-space. Quantised outputs are generated by the system according to a given partition of the state-space, while inputs are arbitrary sequences of symbols in a finite alphabet, which are associated to specific actions on the system. Our main results are obtained under some contractivity hypotheses. The problem of left invertibility, i.e. recovering an unknown input sequence from the knowledge of the corresponding output string, is addressed using the theory of iterated function systems (IFS), a tool developed for the study of fractals. We show how the IFS naturally associated to a system and the geometric properties of its attractor are linked to the invertibility property of the system. Our main result is a necessary and sufficient condition for left invertibility and uniform left invertibility for joint contractive systems. In addition, an algorithm is proposed to recover inputs from output strings. A few examples are presented to illustrate the application of the proposed method.     

Non-approximation-based outputs stabilization for switched large-scale nonlinear systems with quantized inputs and sensor uncertainties

A non-approximation-based output feedback control strategy for a class of switched large-scale nonlinear systems with quantized inputs and sensor uncertainties is proposed. A dynamic gain, which is shared by the state observers and controllers of all the subsystems, is designed so that the effects of sensor uncertainties, quantized inputs, unknown parameters, and external disturbances can be compensated. By constructing some common Lyapunov functions (CLFs) shared by the switched systems, it is proved that with the proposed scheme, the closed-loop system stability can be guaranteed under arbitrary switching, and the outputs of all the subsystems can be steered to within arbitrarily small neighborhoods of the origin.     

Data envelopment analysis with neutrosophic inputs and outputs

Since the recent appearance of neutrosophic theory as a generalization of fuzzy and intuitionistic fuzzy theories, many multicriteria decision methods have adopted this theory to deal with incomplete and indeterminate data. However, it has not yet been applied to the data envelopment analysis (DEA) methodology. Therefore, this study presents a DEA model with triangular neutrosophic inputs and outputs that considers the truth, indeterminacy, and falsity degrees of each data value. As an alternative, a parametric approach based on what we term the variation degree of a triangular neutrosophic number is developed. This approach transforms a neutrosophic DEA model into an interval DEA model that can be solved using one of many existing techniques. Interval efficiency scores obtained from our numerical example show the flexibility and authenticity of the proposed approach.     

Generation of candidates' tree for the fault diagnosis of discrete event systems

This paper presents a discrete event model-based approach for Fault Detection and Isolation of manufacturing systems. This approach considers a system as a set of independent Plant Elements (PEs). Each PE is composed of a set of interrelated Parts of Plant (PoPs) modeled by a Moore automaton. Each PoP model is only aware of its local behavior. The degraded and faulty behaviors are added to each PoP model in order to obtain extended PoP ones. An extrapolation of Gaussian learning is realized to obtain acceptable temporal intervals between the time occurrences of correlated events. Finally based on the PoP extended models and the links between them, a fault candidates' tree is established for each plant element. This candidates' tree corresponds to a local on-line fault event occurrence observer, called diagnoser. Thus, the diagnosis decision is distributed on each plant element. An application example is used to illustrate the approach.     

Simultaneous fault detection and control for switched systems with actuator faults

This paper is concerned with the fault detection and control problem for discrete-time switched systems. The actuator faults, especially ‘outage cases’, are considered. The detector/controller is designed simultaneously such that the closed-loop system switches under an average dwell time, and when a fault is detected, an alarm is generated and then the controller is switched to allow the norm of the states of the subsystem to increase within the acceptable limits. Thus, a switching strategy which combines average dwell time switching with event-driven switching is proposed. Under this switching strategy, the attention is focused on designing the detector/controller such that estimation errors between residual signals and faults are minimised for the fulfillment of fault detection objectives; simultaneously, the closed-loop system becomes asymptotically stable for the fulfillment of control objectives. A two-step procedure is adopted to obtain the solutions through satisfying a set of linear matrix inequalities. An example comprising of three cases is considered. Through these cases, it is demonstrated that the fault detection and control for switched systems using a two-stage switching strategy and asynchronous switching are feasible.