Stability analysis of markovian jump systems with multiple delay components and polytopic uncertainties

This paper investigates the stability problem of Markovian jump systems with multiple delay components and polytopic uncertainties. A new Lyapunov-Krasovskii functional is used for the stability analysis of Markovian jump systems with or without polytopic uncertainties. Two numerical examples are provided to demonstrate the applicability of the proposed approach. © Springer Science+Business Media, LLC 2011.published_or_final_versio

H ’infinite’ estimates for discrete-time Markovian jump linear systems.

This paper deals with the problem of H∞ filtering for discrete-timeMarkovian jump linear systems. Predicted and filtered estimates\ud are obtained based on the game theory. Both filters are solved through recursive algorithms. The Markovian system considered\ud assumes that the jump parameters are not accessible. Necessary and sufficient conditions are provided to the existence of the filters.\ud A numerical example is provided in order to show the effectiveness of the approach proposed

Fault Detection of Markov Jumping Linear Systems

In this paper, the fault detection (FD) problems of discrete-time Markov jumping linear systems (MJLSs) are studied. We first focus on the stationary MJLS. The proposed FD system consists of two steps: residual generation and residual evaluation. A new reference model strategy is applied to construct a residual generator, such that it is robust against disturbances and sensitive to system faults. The generated residual signals are then evaluated according to their stochastic properties, and a threshold is computed for detecting the occurrences of faults. The upper bound of the corresponding false alarm rate (FAR) is also given. For the nonstationary MJLS, similar results are also obtained. All the solutions are presented in the form of linear matrix inequalities (LMIs). Finally, a numerical example is used to illustrate the results

A Geometric Approach to Fault Detection and Isolation of Continuous-Time Markovian Jump Linear Systems

This paper is concerned with development of novel fault detection and isolation (FDI) strategies for the Markovian jump linear systems (MJLS's) and the MJLS's with time-delays (MJLSD's). First a geometric property that is related to the unobservable subspace of MJLS's is presented. The notion of a finite unobservable subspace is then introduced for the MJLSD's. The concept of unobservability subspace is introduced for both the MJLS's and the MJLSD's and an algorithm for its construction is described. The necessary and sufficient conditions for solvability of the fundamental problem of residual generation (FPRG) for the MJLS's are developed by utilizing our introduced unobservability subspace. Furthermore, sufficient solvability conditions of the FPRG for the MJLSD's are also derived. Finally, sufficient conditions for designing an H∞-based FDI algorithm for the MJLS's with an unknown transition matrix that are also subject to input and output disturbances are developed

Observer-based fault detection of technical systems over networks

The introduction of networks into technical systems for facilitating remote data transmission, low complexity in wiring and easy diagnosis and maintenance, raises new challenges in fault detection (FD), such as how to handle network-induced time-varying transmission delays, packet dropouts, quantization errors and bit errors. These factors lead to increasing interest in developing new structures and design schemes for FD of technical systems over networks. In this thesis all network-induced effects are analyzed and modeled systematically at first. By observing the stochastic inheritance of networks, an FD framework of Markov jumping linear systems is presented as a basis for the later developments. Then two observer-based schemes for the purpose of FD over networks with guaranteed false alarm rate (FAR) are proposed: a remote FD system and an FD system of networked control systems (NCSs). The remote FD scheme is for detecting faults in technical systems at a remote site, where system measurements are transmitted via networks. In this scheme, the coding mechanism of communication channels is investigated from the view point of control engineering and new methods are developed for optimal residual generation and evaluation by considering network-induced data loss and corruption. A novel design scheme of FD system is also developed for NCSs, where the technical system is networked, i.e. controllers, actuators and sensors are connected with communication channels. In this scheme, network-induced transmission delays, packet dropouts, quantization errors are taken into account for the design of the optimal FD system. The linear matrix inequalities (LMIs) and convex optimization techniques are applied for assisting the design procedures. The developed schemes are tested with numerical examples and implemented in a three-tank system benchmark, and their superiority to existing solutions is demonstrated. Existing restrictions are overcome and new observer-based FD schemes over networks are introduced having the following characteristics: (1) the residual generators in both schemes are optimal in the sense of achieving the best trade-off between sensitivity to system faults and robustness against system disturbances and network-induced effects; (2) the proposed schemes can provide reliability information of rising fault alarms by analyzing the mean and variance of residual signals. Such information is very useful for practical applications in industries; (3) the design of residual generators and computation of thresholds can be efficiently solved by means of existing LMI-solvers

Fault detection and isolation in a networked multi-vehicle unmanned system

Recent years have witnessed a strong interest and intensive research activities in the area of networks of autonomous unmanned vehicles such as spacecraft formation flight, unmanned aerial vehicles, autonomous underwater vehicles, automated highway systems and multiple mobile robots. The envisaged networked architecture can provide surpassing performance capabilities and enhanced reliability; however, it requires extending the traditional theories of control, estimation and Fault Detection and Isolation (FDI). One of the many challenges for these systems is development of autonomous cooperative control which can maintain the group behavior and mission performance in the presence of undesirable events such as failures in the vehicles. In order to achieve this goal, the team should have the capability to detect and isolate vehicles faults and reconfigure the cooperative control algorithms to compensate for them. This dissertation deals with the design and development of fault detection and isolation algorithms for a network of unmanned vehicles. Addressing this problem is the main step towards the design of autonomous fault tolerant cooperative control of network of unmanned systems. We first formulate the FDI problem by considering ideal communication channels among the vehicles and solve this problem corresponding to three different architectures, namely centralized, decentralized, and semi-decentralized. The necessary and sufficient solvability conditions for each architecture are also derived based on geometric FDI approach. The effects of large environmental disturbances are subsequently taken into account in the design of FDI algorithms and robust hybrid FDI schemes for both linear and nonlinear systems are developed. Our proposed robust FDI algorithms are applied to a network of unmanned vehicles as well as Almost-Lighter-Than-Air-Vehicle (ALTAV). The effects of communication channels on fault detection and isolation performance are then investigated. A packet erasure channel model is considered for incorporating stochastic packet dropout of communication channels. Combining vehicle dynamics and communication links yields a discrete-time Markovian Jump System (MJS) mathematical model representation. This motivates development of a geometric FDI framework for both discrete-time and continuous-time Markovian jump systems. Our proposed FDI algorithm is then applied to a formation flight of satellites and a Vertical Take-Off and Landing (VTOL) helicopter problem. Finally, we investigate the problem of fault detection and isolation for time-delay systems as well as linear impulsive systems. The main motivation behind considering these two problems is that our developed geometric framework for Markovian jump systems can readily be applied to other class of systems. Broad classes of time-delay systems, namely, retarded, neutral, distributed and stochastic time-delay systems are investigated in this dissertation and a robust FDI algorithm is developed for each class of these systems. Moreover, it is shown that our proposed FDI algorithms for retarded and stochastic time-delay systems can potentially be applied in an integrated design of FDI/controller for a network of unmanned vehicles. Necessary and sufficient conditions for solvability of the fundamental problem of residual generation for linear impulsive systems are derived to conclude this dissertation