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This paper addresses the problem of fault detection for linear parameter-varying systems in the presence of measurement noise and exogenous disturbances using Set-Valued Observers (SVOs). The applicability of current methods is limited in the sense that, to increase accuracy, the detection requires a large number of past measurements and the boundedness of the set-valued estimates is only guaranteed for stable systems. In order to widen the class of systems to be modeled and also to reduce the associated computational cost, the aforementioned issues must be addressed. A solution involving left-coprime factorization and deadbeat observers is proposed that reduces the required number of past measurements without compromising accuracy and allowing the design of SVOs for fault detection of unstable systems by using the resulting coprime factorization stable subsystems. The algorithm is shown to produce bounded set-valued estimates and an example is provided. Performance is assessed through simulations, illustrating, in particular that small-magnitude faults (compared to exogenous disturbances) can be detected under mild assumptions. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of detecting faults in linear randomized gossip algorithms, where the selection of the dynamics matrix is stochastic. A fault is a disturbance signal injected by an attacker to corrupt the states of the nodes. We propose the use of Set-Valued Observers (SVOs) to detect if the state observations are compatible with the system dynamics for the worst case in a deterministic setting. The concept of Stochastic Set-Valued Observers (SSVOs) is also introduced to construct a set that is guaranteed to contain all possible states with, at least, a pre-specified desired probability. The proposed algorithm is stable in the sense that it requires a finite number of vertices to represent polytopic sets and it allows for the computation of the largest magnitude of the disturbance that an attacker can inject in the network without being detected. Results are presented to reduce the computational cost of this approach and, in particular, by considering only local information and representing the remainder of the network as a disturbance. The case of a consensus algorithm is discussed leading to the conclusion that, by using the proposed SVOs, finite-time consensus is achieved in non-faulty environments. A novel algorithm is proposed that produces less conservative set-valued state estimates by having nodes exchanging local estimates. The algorithm inherits all the previous properties and also enables finite-time consensus computation regardless of the value of the horizon. [ABSTRACT FROM AUTHOR]

SUMMARY This article introduces a new method for model falsification using set-valued observers, which can be applied to a class of discrete linear time-invariant dynamic systems with time-varying model uncertainties. In comparison with previous results, the main advantages of this approach are as follows: The computation of the convex hull of the set-valued estimates of the state can be avoided under certain circumstances; to guarantee convergence of the set-valued estimates of the state, the required number of previous steps is at most as large as the number of states of the nominal plant; and it provides a straightforward nonconservative method to falsify uncertain models of dynamic systems, including open-loop unstable plants. The results obtained are illustrated in simulation, emphasizing the advantages and shortcomings of the suggested method. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: A novel fault detection and isolation (FDI) method using set-valued observers (SVOs), for uncertain linear parameter-varying (LPV) systems, is introduced. The proposed method relies on SVO-based model invalidation to discard models incompatible with measured data. When compared to the most common strategies in the literature, the suggested approach: (i) under suitable conditions, guarantees false alarms are avoided; (ii) unlike residual-based architectures, does not require the computation of thresholds to declare faults; (iii) has applicability to a wide class of plants. The performance of the proposed approach is assessed in simulation, using the full nonlinear model of a fixed-wing aircraft longitudinal dynamics. [Copyright &y& Elsevier]