Gain-Scheduled Fault Detection Filter For Discrete-time LPV Systems

The present work investigates a fault detection problem using a gain-scheduled filter for discrete-time Linear Parameter Varying systems. We assume that we cannot directly measure the scheduling parameter but, instead, it is estimated. On the one hand, this assumption imposes the challenge that the fault detection filter should perform properly even when using an inexact parameter. On the other, it avoids the burden associated with designing a complex estimation process for this parameter. We propose three design approaches: the ${\mathcal {H}_{2}}$ , ${\mathcal {H}_{\infty }}$ , and mixed ${\mathcal {H}_{2}} / {\mathcal {H}_{\infty }}$ gain-scheduled Fault Detection Filters designed via Linear Matrix Inequalities. We also provide numerical simulations to illustrate the applicability and performance of the proposed novel methods

Robust Fault Detection of Switched Linear Systems with State Delays

This correspondence deals with the problem of robust fault detection for discrete-time switched systems with state delays under an arbitrary switching signal. The fault detection filter is used as the residual generator, in which the filter parameters are dependent on the system mode. Attention is focused on designing the robust fault detection filter such that, for unknown inputs, control inputs, and model uncertainties, the estimation error between the residuals and faults is minimized. The problem of robust fault detection is converted into an H infin-filtering problem. By a switched Lyapunov functional approach, a sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed method

Fault detection for markovian jump systems with sensor saturations and randomly varying nonlinearities

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEE.This paper addresses the fault detection problem for discrete-time Markovian jump systems with incomplete knowledge of transition probabilities, randomly varying nonlinearities and sensor saturations. For the Markovian mode jumping, the transition probability matrix is allowed to have partially unknown entries, while the cases with completely known or completely unknown transition probabilities are also investigated as two special cases. The randomly varying nonlinearities and the sensor saturations are introduced to reflect the limited capacity of the communication networks resulting from the noisy environment, probabilistic communication failures, measurements of limited amplitudes, etc. Two energy norm indices are used for the fault detection problem in order to account for, respectively, the restraint of disturbance and the sensitivity of faults. The purpose of the problem addressed is to design an optimized fault detection filter such that 1) the fault detection dynamics is stochastically stable; 2) the effect from the exogenous disturbance on the residual is attenuated with respect to a minimized H∞-norm; and 3) the sensitivity of the residual to the fault is enhanced by means of a maximized H∞-norm. The characterization of the gains of the desired fault detection filters is derived in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programme method. Finally, a simulation example is employed to show the effectiveness of the fault detection filtering scheme proposed in this paper.This work was supported in part by the National 973 Project under Grant 2009CB320600, the National Natural Science Foundation of China under Grants 61028008, 61134009, 60825303, 90916005 and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information

Copyright q 2012 Hongli Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out. © 2012 Hongli Dong et al.This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of German

On design of quantized fault detection filters with randomly occurring nonlinearities and mixed time-delays

This paper is concerned with the fault detection problem for a class of discrete-time systems with randomly occurring nonlinearities, mixed stochastic time-delays as well as measurement quantizations. The nonlinearities are assumed to occur in a random way. The mixed time-delays comprise both the multiple discrete time-delays and the infinite distributed delays that occur in a random way as well. A sequence of stochastic variables is introduced to govern the random occurrences of the nonlinearities, discrete time-delays and distributed time-delays, where all the stochastic variables are mutually independent but obey the Bernoulli distribution. The main purpose of this paper is to design a fault detection filter such that, in the presence of measurement quantization, the overall fault detection dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Sufficient conditions are first established via intensive stochastic analysis for the existence of the desired fault detection filters, and then the explicit expression of the desired filter gains is derived by means of the feasibility of certain matrix inequalities. Also, the optimal performance index for the addressed fault detection problem can be obtained by solving an auxiliary convex optimization problem. A practical example is provided to show the usefulness and effectiveness of the proposed design method

Robust fault detection for networked systems with communication delay and data missing

n this paper, the robust fault detection problem is investigated for a class of discrete-time networked systems with unknown input and multiple state delays. A novel measurement model is utilized to represent both the random measurement delays and the stochastic data missing phenomenon, which typically result from the limited capacity of the communication networks. The network status is assumed to vary in a Markovian fashion and its transition probability matrix is uncertain but resides in a known convex set of a polytopic type. The main purpose of this paper is to design a robust fault detection filter such that, for all unknown inputs, possible parameter uncertainties and incomplete measurements, the error between the residual signal and the fault signal is made as small as possible. By casting the addressed robust fault detection problem into an auxiliary robust H∞ filtering problem of a certain Markovian jumping system, a sufficient condition for the existence of the desired robust fault detection filter is established in terms of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness and applicability of the proposed technique

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

On design of robust fault detection filter in finite-frequency domain with regional pole assignment

This brief is concerned with the fault detection (FD) filter design problem for an uncertain linear discrete-time system in the finite-frequency domain with regional pole assignment. An optimized FD filter is designed such that: 1) the FD dynamics is quadratically D-stable; 2) the effect from the exogenous disturbance on the residual is attenuated with respect to a minimized H∞-norm; and 3) the sensitivity of the residual to the fault is enhanced by means of a maximized H--norm. With the aid of the generalized Kalman-Yakubovich-Popov lemma, the mixed H--/H∞ performance and the D-stability requirement are guaranteed by solving a convex optimization problem. An iterative algorithm for designing the desired FD filter is proposed by evaluating the threshold on the generated residual function. A simulation result is exploited to illustrate the effectiveness of the proposed design technique.This work was supported in part by the Deanship of Scientific Research (DSR) at King Abdulaziz University in Saudi Arabia under Grant 16-135- 35-HiCi, the National Natural Science Foundation of China under Grants 61134009 and 61203139, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Recent advances on recursive filtering and sliding mode design for networked nonlinear stochastic systems: A survey

Copyright © 2013 Jun Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Some recent advances on the recursive filtering and sliding mode design problems for nonlinear stochastic systems with network-induced phenomena are surveyed. The network-induced phenomena under consideration mainly include missing measurements, fading measurements, signal quantization, probabilistic sensor delays, sensor saturations, randomly occurring nonlinearities, and randomly occurring uncertainties. With respect to these network-induced phenomena, the developments on filtering and sliding mode design problems are systematically reviewed. In particular, concerning the network-induced phenomena, some recent results on the recursive filtering for time-varying nonlinear stochastic systems and sliding mode design for time-invariant nonlinear stochastic systems are given, respectively. Finally, conclusions are proposed and some potential future research works are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61329301, 61333012, 61374127 and 11301118, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant no. GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Zonotopic fault detection observer design for Takagi–Sugeno fuzzy systems

This paper considers zonotopic fault detection observer design in the finite-frequency domain for discrete-time Takagi–Sugeno fuzzy systems with unknown but bounded disturbances and measurement noise. We present a novel fault detection observer structure, which is more general than the commonly used Luenberger form. To make the generated residual sensitive to faults and robust against disturbances, we develop a finite-frequency fault detection observer based on generalised Kalman–Yakubovich–Popov lemma and P-radius criterion. The design conditions are expressed in terms of linear matrix inequalities. The major merit of the proposed method is that residual evaluation can be easily implemented via zonotopic approach. Numerical examples are conducted to demonstrate the proposed methodPeer ReviewedPostprint (author's final draft