Optimal fault detection for linear discrete time-varying systems

In this paper, adaptive optimal control is proposed for linear discrete time-varying (LDTV) systems subject to unknown system dynamics. The idea of the method is a direct application of the Q-learning adaptive dynamic programming for time-varying systems. In order to derive the optimal control policy, an actor-critic structure is constructed and the time-varying least square method is adopted for parameter adaptation. The derived control policy robustly stabilizes the time-varying system and guarantees an optimal control performance. As no particular system information is required throughout the process, the proposed method provides a feasible solution to a large variety of applications. The validity of the proposed method is verified through simulation studies.

This paper deal with the problem of the fault detection (FD) filter design for continuous-time switched systems with actuator faults. The actuator faults and the unknown disturbances of the system are set in finite frequency domain. By using the switched Lyapunov function and the average dwell-time (ADT) techniques, efficient conditions are obtained, which can realize the residual signal sensitive to the fault and robust to the unknown disturbances. In the design of fault detection filter, we use Linear matrix inequalities (LMIs) conditions to guarantee the finite frequency H∞ and H - performance index. Finally, a practical example is provided and simulation results are conducted to demonstrate the effectiveness of the proposed approach.

Iterative learning control approach for linear discrete time-varying systems with different initial time points

Finite-time stability and stabilization of linear discrete time-varying stochastic systems

This technical note deals with the problem of finite horizon H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> fault detection for linear discrete time-varying systems. Using an observer-based fault detection filter (FDF) with residual feedback as a residual generator, a new problem formulation of fault detection is first presented. Then the design of finite horizon H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -FDF is converted into a minimum problem of certain quadratic form. Through building a relationship with Krein space projection and applying innovation analysis, a sufficient and necessary condition for the minimum is derived and a solution to the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -FDF is obtained by recursively computing Riccai recursions. Numerical examples are given to show the effectiveness of the proposed method.

This study is concerned with the event-triggered fault detection (FD) filter design problem for the discrete-time non-linear systems with multi-data transmission and output quantisation. To reduce the transmission data size, the output signals are quantified by a logarithmic quantiser. Compared with the existing results, past output measurements are first introduced for packaging and transmission only when the event condition is satisfied. Based on this consideration, more data can be used by the FD filter, while using the traditional method, the FD filter can only use the current data. Finally, some simulation results show that the proposed design method can achieve a better FD performance than the existing method with current output measurements transmission.

SUMMARYIn this paper, the fault detection problem is investigated for a class of discrete‐time switched singular systems with time‐varying state delays. The residual generator is firstly constructed based on a switched filter, and the design of fault detection filter is formulated as an H ∞ filtering problem, that is, minimizing the error between residual and fault in the H ∞ sense. Then, by constructing an appropriate decay‐rate‐dependent piecewise Lyapunov function and using the average dwell time scheme, a sufficient condition for the residual system to be regular, causal, and exponential stable while satisfying a prescribed H ∞ performance is derived in terms of linear matrix inequalities (LMIs). The corresponding solvability condition for the desired fault detection filters is also established via LMI approach. Finally, a numerical example is presented to show the effectiveness of the developed theoretical results.Copyright © 2012 John Wiley &amp; Sons, Ltd.

In this paper, we show that for discrete time-varying linear control systems uniform complete controllability implies arbitrary assignability of dichotomy spectrum of closed-loop systems. This result significantly strengthens the result in [5] about arbitrary assignability of Lyapunov spectrum of discrete time-varying linear control systems.

This study investigates the problem of fault detection (FD) filter design for a class of uncertain Lipschitz systems with time delays, unknown faults, parameter uncertainties and bounded disturbances. A novel FD filter is proposed and the augmented filter system is converted to a linear parameter varying (LPV) system by the reformulated Lipschitz property. Then, two bounded real lemmas (BRLs) are given for the generated residual signal to achieve the fault sensitivity performance in low-/middle-/high-frequency domains and disturbance attenuation performance in the full-frequency domain. Next, the obtained BRLs are further converted into a set of linear matrix inequalities (LMIs) to implement the filter design. Finally, two illustrative simulations including a numerical example and Chua's circuit system clearly demonstrate the advantages of the developed FD scheme.

This paper is concerned with the event-triggered fault detection filter (FDF) design for an unmanned surface vehicle (USV) under the network environment. A framework of fault detection is established for a USV subject to wave-induced disturbance and actuator failures, in which an FDF is utilized to construct a residual model and an integral-based event generator is introduced to save communication resources. Compared with the traditional instantaneous value based event-triggering scheme and periodic sampling, the proposed event-triggering mechanism can not only reduce bandwidth utilization of the network more significantly, but also get rid of the Zeno phenomenon fundamentally. The event-triggering scheme and the FDF are co-designed. Finally, the efficient performance of the proposed fault detection method based on integral-based event-triggering scheme is illustrated by simulation.

This study deals with the problem of H∞ fault detection for linear discrete time-varying systems with delayed state in the framework of H∞ filtering. The design of the H∞ fault detection filter (FDF) is firstly converted into the minimum problem of an indefinite quadratic form. After introducing a corresponding Krein space stochastic system and building a relationship with projection, a sufficient and necessary condition on the existence of the minimum is derived by applying innovation analysis. A solution to the H∞-FDF is obtained in terms of matrix difference equations. Numerical examples are given to demonstrate the effectiveness of the proposed method.

The problem of fault detection for networked control systems with time-delay is investigated. Attention is focused on the design of fault detection filter based on states observer, which guarantees a pre-specified Hinfin performance for the closed-loop system with respect to all energy-bounded input signals. Using LMI and Lyapunov function technology, sufficient conditions for existence of such filter is established in terms of linear matrix inequalities, upon which the design of admissible filter is cast into a convex optimization problem. The proposed approach can be further extended to uncertain networked control systems. The simulation results demonstrate that the method is effective and robust.

SummaryThis article focuses on the issue of event‐triggered fault detection filters (FDF) design for networked switched systems. Compared with the existing fault detection literature, this article investigates the situation that all subsystems are unstable, and considers that stochastic cyber attacks will disrupt fault detection. An event‐triggered mechanism (ETM) that excludes Zeno behavior naturally is designed to economize limited network resources. Then considering the ETM‐induced delay term, the dynamics of the initial system combined with the ETM, fault detection filters, and the effects of cyber attacks are formulated as a new augment switched delayed residual model. Based on the constructed multiple piecewise discretized Lyapunov–Krasovskii function (MPDLKF) and the mode‐dependent dwell time (MDDT) method, sufficient conditions are obtained to guarantee globally mean‐square uniformly asymptotically stability of the new augment system. Moreover, a co‐design method of ETM matrices and FDF gains is proposed. Finally, simulation results are provided to verify the feasibility and effectiveness of the proposed method.

This paper proposes a novel full-order and reduced-order fault detection filters (FDFs) design method for singular continuous-time Markovian jump systems (SCTMJSs) with completely known transition rates (TRs). In order to strengthen the reliability of full-order and reduced-order (FDFs), we incorporates the idea of congruent transformation Lyapunov matrix to solve the convex optimization problem. The superiority of this kind of design method is that shows full-order and reduced-order FDFs can be expressed by an inequality and effective. Particularly necessary to point out that the reduced-order fault detection filter (FDF) has fewer variables and shortens the time of fault detection (FD) compared with full-order FDF. At the end of this paper, an illustrative simulation example is given to verify the effectiveness of the proposed method.

Covert Attack Detection Based on Hi/H∞ Optimization for Cyber-Physical Systems