Distributed fault diagnosis for continuous-time nonlinear systems: The input–output case

In this paper, some new results on distributed fault diagnosis of continuous-time nonlinear systems with partial state measurements are proposed. By exploiting an overlapping decomposition framework, the dynamics of a nonlinear uncertain large-scale dynamical system is described as the interconnections of several subsystems. Each subsystem is monitored by a Local Fault Diagnoser: a set of local estimators, based on the nominal local dynamic model and on an adaptive approximation of the interconnection and of the fault function, allows to derive a local fault decision. A consensus-based protocol is used in order to improve the detectability and the isolability of faults affecting variables shared among different subsystems because of the overlapping decomposition. A sufficient condition ensuring the convergence of the estimation errors is derived. Finally, possibly non-conservative time-varying threshold functions guaranteeing no false-positive alarms and theoretical results dealing with detectability and isolability sufficient conditions are presented.     

Robust fault diagnosis for a class of nonlinear systems

Robust fault diagnosis based on adaptive observer is studied for a class of nonlinear systems up to output injection. Adaptive fault updating laws are designed to guarantee the stability of the diagnosis system. The upper bounds of the state estimation error and fault estimation error of the adaptive observer are given respectively and the effects of parameter in the adaptive updating laws on fault estimation accuracy are also discussed. Simulation example demonstrates the effectiveness of the proposed methods and the analysis results.     

Robust fault isolation for a class of non-linear input?output systems

The design and analysis of fault diagnosis methodologies for non-linear systems has received significant attention recently. This paper presents a robust fault isolation scheme for a class of non-linear systems with unstructured modelling uncertainty and partial state measurement. The proposed fault diagnosis architecture consists of a fault detection and approximation estimator and a bank of isolation estimators. Each isolation estimator corresponds to a particular type of fault in the fault class. A fault isolation decision scheme is presented with guaranteed performance. If at least one component of the output estimation error of a particular fault isolation estimator exceeds the corresponding adaptive threshold at some finite time, then the occurrence of that type of fault can be excluded. Fault isolation is achieved if this is valid for all but one isolation estimator. Based on the class of non-linear systems under consideration, fault isolability conditions are rigorously investigated, characterizing the class of non-linear faults that are isolable by the proposed scheme. Moreover, the non-conservativeness of the fault isolability conditions is illustrated by deriving a subclass of nonlinear systems and faults for which this condition is also necessary for fault isolability. A simulation example of a simple robotic system is used to show the effectiveness of the robust fault isolation methodology.     

Continuous–discrete-time adaptive observers for nonlinear systems with sampled output measurements

This paper considers the continuous–discrete-time adaptive observer (CDAO) design for a class of nonlinear systems with unknown constant parameters and sampled output measurements. The proposed observer is actually an impulsive system, since the observer state flows according to a set of differential equations and with instantaneous state jumps corresponding to measured samples and their estimates, and an inter-sample output predictor is used to predict the output during sampling intervals. By assuming appropriate persistent excitation conditions and following a technical lemma, an upper bound of the sampling intervals is derived, with which the convergence of the observer state and unknown parameters can be ensured. Finally, the proposed observer is used in examples of chaotic oscillators and single-link flexible-joint robot manipulator to show the effectiveness.     

H∞ filter design for a class of nonlinear discrete-time singular systems

This paper deals with the H_∞ filter design problem for a class of discrete-time Lipschitz nonlinear singular systems. The approach is based on the parameterisation of the obtained algebraic constraints from the estimation errors. Sufficient conditions for the existence of the filters which guarantee stability and the worst case filter error energy over all bounded energy disturbances is minimised are given. The method also unifies the design for the full-order, reduced-order, minimal-order filters for discrete- time systems. The presented results are less conservative than those existing in the literature, this is due to the introduction of new slack variables. Application to systems with unknown input is presented via a numerical example.     

Detecting sensor fault for nonlinear systems in T–S form under sampled-data measurement: Exact direct discrete-time design approach

A direct discrete-time design methodology for sampled-data sensor fault detection for nonlinear systems in Takagi–Sugenos form is proposed. Contrary to the conventional schemes in this way that rely on an approximate discrete-time model of the nonlinear system, our result is established based on an exact one. Condition to design the observer and the residual gain under an H-/H _∞ performance criterion is presented in matrix inequality format. An example is given to illustrate the effectiveness of the proposed methodology.     

Learning nonlinear input–output maps with dissipative quantum systems

This paper proposes an efficient semi-quantum private comparison protocol (SQPC) using single photons, which allows two classical participants to securely compare the equality of their secret with the help of an almost-dishonest third party. Because of the use of single photons, the SQPC is more practical and the qubit efficiency of the proposed protocol is higher than the existing semi-quantum private comparison protocols. Moreover, the proposed protocol can resist several well-known attacks including outsider and insider’s attacks.

     

Adaptive practical output tracking of a class of nonlinear systems

Focus is hid on the adaptive practical output-tracking problem of a chss of nonlinear systems with high-order lower-triangular structure and uncontrollable unstable linearization. Using the modified adaptive addition of a power integrator technique as a basic tool, a new smooth adaptive state feedback controller is designed. This controller can ensure all signals of the closed-loop systems are globally bounded and output tracking error is arbitrary small.     

Rainfall–runoff multi-modelling for sensor fault diagnosis

In view of the limitations of flood and pollution prevention in urban sewage networks, the control of hydraulic equipment now calls for more reliable measurements provided by different sensors. The sensor fault detection and isolation described here requires the availability of a rainfall–runoff relationship in order to apply analytical redundancy-based diagnostic procedures. However, because this relationship is conspicuously non-linear and time varying, the latter relationship is identified by using a multi-model approach. The proposed modelling approach has been successfully tested on a watershed located in an urban area of Nancy, in eastern France, using actual rainfall and runoff data taken from the sewerage control centre database. The model obtained is then used to increase the degree of information redundancy in order to implement a sensor fault diagnostic procedure. Since no statistical hypothesis on measurement uncertainties can be made, interval arithmetic is used to derive residual tolerance.     

Synchronization of nonlinear heterogeneous cooperative systems using input–output feedback linearization

In this paper, input–output feedback linearization is used to design distributed controls for multi-agent systems with nonlinear and heterogeneous non-identical dynamics. Using feedback linearization, the nonlinear and heterogeneous dynamics of agents are transformed to identical linear dynamics and non-identical internal dynamics. Based on the dependence of agent outputs on agent inputs, feedback linearization may lead to a first-order or high-order tracking synchronization problem. The controller for each agent is designed to be fully distributed such that each agent only requires its own information and the information of its neighbors. The effectiveness of the proposed control protocols are verified by simulation on a microgrid test system.     

Stabilization of a class of discrete-time switched systems via observer-based output feedback

In this paper, observer-based static output feedback control problem for discrete-time uncertain switched systems is investigated under an arbitrary switching rule. The main method used in this note is combining switched Lyapunov function (SLF) method with Finsler’s Lemma. Based on linear matrix inequality (LMI) a less conservative stability condition is established and this condition allows extra degree of freedom for stability analysis. Finally, a simulation example is given to illustrate the efficiency of the result.     

Fault detection of discrete-time switched systems with distributed delays: input–output approach

This article is concerned with the ?_∞ fault detection of discrete-time switched systems with distributed delays. By using the input–output approach combining with the small-scale gain theorem, a sufficient condition is established in terms of linear matrix inequality, which guarantees the fault detection system to be exponentially stable with an ?_∞ performance. Then, a solvability condition for the desired fault detection filter is also proposed. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed theory.     

A unified approach to generating series for mixed cascades of analytic nonlinear input–output systems

The primary goal is to describe in a unified fashion the generating series for the cascade connection of any two analytic nonlinear input–output systems. In particular, it will be shown that a single general definition of a composition product can be formulated in terms of formal power series to describe any possible cascade connection of analytic integral operators (Fliess operators) and analytic functions provided that the composite system is well defined and resides in one of these two classes. In each case, the radius of convergence of the interconnection is computed.     

Fault diagnosis for a class of active suspension systems with dynamic actuators’ faults

In this paper, a new fault diagnosis and fault-tolerant control method for a class of active suspension systems with actuator faults is proposed. The considered actuators have uncertain dynamic characteristics, which are the electromagnetic actuators made up with a motor control system and a ball screw transmission mechanism. To detect such suspension system actuator faults, dynamic fault diagnosis observers are designed for the actuators to estimate the possible faults. The actuators are analyzed to first and second order dynamic models, respectively, whose output can be measured but the rate is non-measurable. Then, the fault diagnosis method is developed for these two kinds of models to obtain the fault information. Using the fault estimation and adaptive control technique, a robust fault-tolerant controller is constructed to guarantee the performance of the rail vehicles in the faulty case. Finally, using the parameters of a practical suspension system, a simulation study is conducted to show the effectiveness of the proposed method.     

Robust decentralized adaptive stabilization for a class of interconnected systems

The robust decentralized adaptive output-feedback stabilization for a class of interconnected systems with static and dynamic interconnections by using the MT-filters and backstepping design method is studied. By introducing a new filtered tramfomnation, the adaptive laws were derived for measurement. Under the assurnption of the nonlinear growth conditions imposed on the nonlinear interconnections and by constructing the error system and using a new proof method, the global stability of the closed-loop system was effectively analyzed, and the exponential convergence of all the signals except for parameter estimates were guaranteed.