Analysis of the stochastic stability for fault tolerant control systems

Mahmoud, M.; Jiang, Jin; Zhang, Youmin

doi:10.1109/cdc.1999.827758

Cited by 20 publications

(15 citation statements)

References 13 publications

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“…It is important to mention that the rates q jk iv are determined by the nature of the FDI process. These rates are vital in deciding the stochastic stability of the closed-loop system (Srichander and Walker 1993, Mahmoud et al 1999, 2000. In other words, the stochastic stability of FTCSMP depends on the performance of the FDI process through q jk iv .…”

Section: Fdi and Failure Processesmentioning

confidence: 99%

Stochastic stability analysis for fault tolerant control systems with multiple failure processes

Mahmoud¹,

Jiang²,

Zhang³

2002

International Journal of Systems Science

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A new dynamical model is developed here to study the stochastic stability of Fault Tolerant Control Systems (FTCS) with multiple failure processes. In particular, two independent failure processes with Markovian characteristics are considered: one for plant component failures and the other for actuator failures. In this model, the Fault Detection and Isolation (FDI) process is also formulated as a Markov process with transition probabilities conditioned on the current state transition probabilities of the two failure processes. It is shown that the exponential stability in the mean square is su cient for almost sure asymptotic stability. In addition, a necessary and su cient condition for exponential stability in the mean square for FTCS is derived. Some previously known results are shown to be special cases of this new result. Failures in actuators with internal dynamics are also considered. A numerical example is included to demonstrate the theoretical analysis.

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Section: Fdi and Failure Processesmentioning

confidence: 99%

Stochastic stability analysis for fault tolerant control systems with multiple failure processes

Mahmoud¹,

Jiang²,

Zhang³

2002

International Journal of Systems Science

Self Cite

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“…The proposed general AFTCS is advantageous to the previous ones [19,20,39], in case of eliminating the need for a perfectly conducted FDD procedure. It also takes the prefault and postfault dynamical uncertainties into account and generalizes the previous results obtained for the certain AFTCSs.…”

Section: Introductionmentioning

confidence: 96%

“…Thus, the FDD algorithm output may not be identical to the actual fault mode. To analyze the effect of the imperfect FDD on the FTCS, another Markov chain, which depends to the fault chain, is added to the model [18,19]. Many researchers have studied AFTCSs modeled by two Markov processes.…”

Section: Introductionmentioning

confidence: 99%

“…Among the different classes of these systems, Markov jump linear systems (MJLSs) [22,23] are very interested because of their unique features in representing continuous dynamics of the system along with the abrupt occurrence of faults in a unified framework. To be precise, in an AFTCS based on a MJLS, the normal and fault dynamic behaviors of the system are described by a set of differential (or difference) equations with a transition between them that is governed by a finite-state Markov chain which represents the random nature of faults [14,18,19,21]. Although MJLSs have been extensively studied from the theoretical [24][25][26][27][28][29][30][31][32][33][34][35][36] and practical [26,28] point of views, AFTCSs by MJLSs still need further investigations.…”

Section: Introductionmentioning

confidence: 99%

“…AFTCSs are usually modeled in the form of hybrid stochastic structures [18][19][20]. Such structures can capture the abrupt changes in system characterization, induced by random faults [21].…”

Section: Introductionmentioning

confidence: 99%

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Stabilization of active fault‐tolerant control systems by uncertain nonhomogeneous markovian jump models

2016

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This article investigates the stabilization and control problems for a general active fault-tolerant control system (AFTCS) in a stochastic framework. The novelty of the research lies in utilizing uncertain nonhomogeneous Markovian structures to take account for the imperfect fault detection and diagnosis (FDD) algorithms of the AFTCS. The underlying AFTCS is supposed to be modeled by two random processes of Markov type; one characterizing the system fault process and the other describing the FDD process. It is assumed that the FDD algorithm is imperfect and provides inaccurate Markovian parameters for the FDD process. Specifically, it provides uncertain transition rates (TRs); the TRs that lie in an interval without any particular structures. This framework is more consistent with realworld applications to accommodate different types of faults. It is more general than the previously developed AFTCSs because of eliminating the need for an accurate estimation of the fault process. To solve the stabilizability and the controller design problems of this AFTCS, the whole system is viewed as an uncertain nonhomogeneous Markovian jump linear system (NHMJLS) with time-varying and uncertain specifications. Based on the multiple and stochastic Lyapunov function for the NHMJLS, first a sufficient condition is obtained to analyze the system stabilizability and then, the controller gains are synthesized. Unlike the previous fault-tolerant controllers, the proposed robust controller only needs to access the FDD process, besides it is easily obtainable through the existing optimization techniques. It is successfully tested on a practical inverted pendulum controlled by a fault-prone DC motor.

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Stochastic stability and stabilization of a class of piecewise-homogeneous Markov jump linear systems with mixed uncertainties

Niri

Jahed‐Motlagh

Yazdi

2016

Int. J. Robust. Nonlinear Control

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This paper investigates the stochastic stability and stabilization problem for a general class of uncertain, continuous-time Markov jump linear systems (MJLSs). The system under consideration is a piecewise-homogenous Markovian structure subject to piecewise-constant time-varying transition rates (TRs). The time variation of the TRs is characterized by a high-level Markovian signal, which is independent from the low-level Markovian mechanism that governs the switching between the system dynamics. It is assumed that the structure is subject to mixed uncertainties in the form of additive norm-bounded terms. The uncertainties help to consider the effect of imperfections induced by modeling errors for the system dynamics and the TRs of Markovian signals of both levels. This new uncertain, two-level Markovian jump linear system is a more general model than the existing ones and is applicable to more practical situations. Besides, it is capable of being specialized to uncertain piecewise-homogeneous MJLS with arbitrarily varying TRs, as well as the uncertain time-homogeneous MJLS. The stability/stabilizability of this system is first examined by constructing a Lyapunov function which depends on both switching signals. Then, based on the analysis results, the corresponding robust controller gains are synthesized through solving a set of linear matrix inequalities (LMIs). Finally, simulation results for an industrial stirred tank reactor (CSTR) are used to demonstrate the applicability and potentials of the proposed theoretical method. Comparative simulations are also provided to show the superiority of the presented approach to the existing ones. Remark 4The controller gains (22) need to a perfect measure of the switching modes of both levels. It should be fairly admitted that, practically, the assumption of perfectly measured Markov modes is very idealistic and restrictive, and considering the additive uncertain terms for the TR matrices of both 901 PIECEWISE-HOMOGENEOUS MARKOV JUMP LINEAR SYSTEMS and S(i, m) and R(i, m) are defined by (11) and (13). Thus, the controller is designed as K(i,m) = Y(i, m)X À1 (i,m). 902 M. FARAJI-NIRI, M.-R. JAHED-MOTLAGH AND M. BARKHORDARI-YAZDIThe condition of Eq. (34) is nonlinear in P(i,m) and K(i,m). In order to find controller gains it is desired to transform (34) into an LMI form, so let X(i,m) = P À1 (i,m).Pre-and post-multiplying Eq. (34) by X(i,m) gives Eq. (35). 903PIECEWISE-HOMOGENEOUS MARKOV JUMP LINEAR SYSTEMS

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Analysis of the stochastic stability for fault tolerant control systems

Cited by 20 publications

References 13 publications

Stochastic stability analysis for fault tolerant control systems with multiple failure processes

Stochastic stability analysis for fault tolerant control systems with multiple failure processes

Stabilization of active fault‐tolerant control systems by uncertain nonhomogeneous markovian jump models

Stochastic stability and stabilization of a class of piecewise-homogeneous Markov jump linear systems with mixed uncertainties

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