Model falsification using set-valued observers for a class of discrete-time dynamic systems: a coprime factorization approach

Intl J Robust & Nonlinear

Hespanha

et al. 2017

Self Cite

SUMMARYIn the context of fault detection and isolation of Linear Parameter-Varying (LPV) systems, a challenging task appears when the dynamics and the available measurements render the model unobservable, which invalidates the use of standard Set-Valued Observers (SVOs). Two results are obtained in this paper, namely: using a left-coprime factorization, one can achieve set-valued estimates with ultimately bounded hypervolume and convergence dependent on the slowest unobservable mode; and, by rewriting the SVO equations and taking advantage of a coprime factorization, it is possible to have a low-complexity fault detection and isolation method. Performance is assessed through simulation, illustrating, in particular, the detection time for various types of faults.

“…In , one of the results states that knowing an initial set containing the initial conditions for a stable system with input

u (k) = 0, \forall k ⩾ 0

Section: Problem Statementmentioning

confidence: 99%

{(A_{k} - K_{k} C_{k})}^{n_{x}}

are equal to zero for any

k ⩾ n_{x}

with n x being the number of states of the system . If the system is detectable, the rate of convergence is governed by the slowest of the unobservable modes, as shown next.…”

Section: Svos For Detectable Systemsmentioning

confidence: 99%

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

Intl J Robust & Nonlinear

Hespanha

et al. 2017

Self Cite

“…In other words, if the time-evolution of the inputs and outputs of the plant cannot be explained by a model with uncertain parameter , such that 2 i , then region i cannot be the one to which the uncertain parameter belongs. The invalidation of these uncertainty regions is addressed by using SVOs, taking advantage of the recent developments presented in [9,10,39,40].…”

Section: Set-valued Observer-based Fault-tolerant Controlmentioning

confidence: 99%

Fault‐tolerant control of an air heating fan using set‐valued observers: An experimental evaluation

Simao

Adaptive Control & Signal

et al. 2015

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This paper proposes a multiple-model solution to the problem of controlling an air heating fan subject to faults. These faults are modeled by means of an abnormal unknown airflow input rate which the nominal controller is not designed for. Moreover, the average temperature of the air flowing through the system, which can be seen as an offset on the corresponding dynamics, is (slowly) time-varying and highly dependent on the ambient temperature. The fault-tolerant control (FTC) method adopted makes use of set-valued observers (SVOs) to invalidate possible models of the system. Unlike classical fault detection, this approach does not rely on residuals to detect abnormal system operation. This fact allows to reduce the conservatism of the solution and enables a straightforward design from the faulty and nominal models of the plant. Moreover, the absolute distinguishability concept is used to derive input signals that bolster the detection of faults. Although SVOs require heavy real-time calculations that hinder its implementability in systems with low computational power, it is shown that the architecture of the FTC strategy proposed is highly parallelizable and, thus, may take advantage of standard multi-core processing units. Experimental results are presented.

“…To consider the worst-case scenario, one needs to perform the union of all possible state sets, which, in general, returns a non-convex set [25]. Furthermore, the number of sets grows exponentially with the number of past time instants considered, i.e., the horizon N .…”

Section: Introductionmentioning

confidence: 99%

Self-Triggered and Event-Triggered Set-Valued Observers

Hespanha

et al. 2018

Information Sciences

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This paper addresses the problem of reducing the required network load and computational power for the implementation of Set-Valued Observers (SVOs) in Networked Control System (NCS). Event-and self-triggered strategies for NCS, modeled as discrete-time Linear Parameter-Varying (LPV) systems, are studied by showing how the triggering condition can be selected. The methodology provided can be applied to determine when it is required to perform a full ("classical") computation of the SVOs, while providing low-complexity state overbounds for the remaining time, at the expenses of temporarily reducing the estimation accuracy. As part of the procedure, an algorithm is provided to compute a suitable centrally symmetric polytope that allows to find hyper-parallelepiped and ellipsoidal overbounds to the exact set-valued state estimates calculated by the SVOs. By construction, the proposed triggering techniques do not influence the convergence of the SVOs, as at some subsequent time instants, set-valued estimates are computed using the conventional SVOs. Results are provided for the triggering frequency of the self-triggered strategy and two interesting cases: distributed systems when the dynamics of all nodes are equal up to a reordering of the matrix; and when the probability distribution of the parameters influencing the dynamics is known. The performance of the proposed algorithm is demonstrated in simulation by using a time-sensitive example.