Stochastic and deterministic fault detection for randomized gossip algorithms

Abstract

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.

Fault Detection for Discrete‐Time Uncertain Systems with Polytopic Uncertainties: A Markov Approach

“…Moreover, due to the higher requirements on safety and stability of industrial systems, the other characters of performance should be taken into account, such as quickness [10], robustness [11][12][13] and isolation of fault diagnosis [14][15][16]. When the underlying system is not deterministic but with jump processes [17][18][19], the problem of fault detection for such systems were considered in [20][21][22][23].…”

Set‐based fault detection and isolation for detectable linear parameter‐varying systems

“…The algorithm requires a centralized detection scheme and is only applicable to the specific linear time-invariant (LTI) model. In this paper, we derive an alternative approach based on setvalued observers (SVOs), which enable a distributed detection for the observable subspace if we consider a strategy such that of [8].In [8], the use of SVOs for distributed fault detection was firstly introduced for the specific case of consensus. The overall system is modeled as an uncertain LPV system where communications are seen as a parameter-dependent dynamics matrix.…”

“…Even though, the whole system is not observable in every time instant, for a sufficiently long-time interval, the system is observable, as long as the underlying network topology is strongly connected. Whereas in [8], each node has access to its own state, and the state of one neighbor to which it communicates, in this paper, it is assumed that nodes have access only to relative information. The distributed detection can also be improved by resorting to exchanging state estimates whenever the systems communicate or take measurements by using a similar algorithm to the one presented in [8].The SVOs framework, whose concept was introduced in [9] and [10] (further information can be found in [11] and [12] and references therein), is used as a way to represent and propagate the setvalued state estimates.…”

“…Whereas in [8], each node has access to its own state, and the state of one neighbor to which it communicates, in this paper, it is assumed that nodes have access only to relative information. The distributed detection can also be improved by resorting to exchanging state estimates whenever the systems communicate or take measurements by using a similar algorithm to the one presented in [8].The SVOs framework, whose concept was introduced in [9] and [10] (further information can be found in [11] and [12] and references therein), is used as a way to represent and propagate the setvalued state estimates. The approach allows us to consider virtually any kind of linear dynamics for the agents and also to incorporate disturbances and model uncertainties.An alternative method to the SVOs is the use of the reachability concept to construct set-valued estimates.…”

“…The alternative approach presented in this paper is deterministic and relies on a worst-case detection. A similar stochastic detection strategy can achieved with the extension of the framework proposed here, following the methodology described in [8].Fault detection in smart grids has also been performed resorting to the concept of Petri Nets [17]. The procedure consists in mapping the possible concurrent actions of each of the nodes in the network to determine the current state of the system and checking if it is compatible with the measurements.…”