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International audience; The complexity of modern control systems requires mitigating the effects of numerous anomalies, such as attacks, faults and network-induced disturbances. In this perspective, the synthesis problem of a dissipation block for anomaly-tolerant control is addressed. The dissipation technique consists in interconnecting a block to a system in order to make their interconnection dissipative. The underlying idea is that, if the resulting dissipative characterization is suitably chosen, the considered anomalies can be mitigated. In this paper, it is revealed how the block, here an LTI system, can be synthesized by deriving sufficient LMI-based conditions. A numerical example is provided to illustrate this result which is applied to design a control reconfiguration, providing a defense mechanism that ensures resilience with respect to a data-injection cyber attack.

International audience; Robust state estimation is addressed in a noisy environment and within a distributed and networked architecture. Both bounded disturbances and random noises are considered. A Distributed Zonotopic and Gaussian Kalman Filter (DZG-KF) is proposed where each network node implements a local state estimator using symbolic Zonotopes and Gaussian noise Mergers (s-ZGM), a class of Set-membership and Probabilistic Mergers (SPM). Each network node communicates its own state information only to its neighbours. The proposed system includes a dedicated service called Unique Symbols Provider (USP) giving unique identifiers. It also includes Matrices with Labelled Columns (MLC) featuring column-wise sparsity, and symbolic zonotopes (s-zonotopes). This significantly enhances the propagation of uncertainties and preserves global dependencies that would otherwise be lost (or impeded) by the peer-to-peer communication through the network. A number of other network-related constraints can be managed within this framework. Numerical simulations show significant improvements compared to a non-symbolic approach.

Enhancing the sensitivity to faults with respect to disturbances, rather than optimizing the precision of the state estimation using Kalman Filters (KF) is the subject of this paper. The stochastic paradigm (KF) is based on minimizing the trace of the state estimation error covariance. In the context of the bounded-error paradigm using Zonotopic Kalman Filters (ZKF), this is analog to minimize the covariation trace. From this analogy and keeping a similar observer-based structure as in ZKF, a criterion jointly inspired by set-membership approaches and approximate decoupling techniques coming from parity-space residual generation is proposed. Its on-line maximization provides an optimal time-varying observer gain leading to the so-called FD-ZKF filter that allows enhancing the fault detection properties. The characterization of minimum detectable fault magnitude is done based on a sensitivity analysis. The effect of the uncertainty is addressed using a set-membership approach and a zonotopic representation reducing set operations to simple matrix calculations. A case study based on a quadruple-tank system is used both to illustrate and compare the effectiveness of the results obtained from the FD-ZKF approach compared to a pure ZKF approach., This work has been partially funded by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERFD) through the projects DEOCS (ref. MINECO DPI2016-76493) and SCAV (ref. MINECO DPI2017-88403-R). This work has also been partially funded by AGAUR of Generalitat de Catalunya through the Advanced Control Systems (SAC) group Grant (2017 SGR 482) and by Agència de Gestió d’Ajuts Universitaris i de Recerca. Furthermore, the authors would like to thank Prof. A. Zolghadri for insightful discussions on ZKF extensions and applications within SysNum cluster activities (Idex Bordeaux, France).

This special issue contains papers applying a broad range of set-membership techniques to fault detection and isolation and fault tolerant control. Following the successful organization of special sessions on related topics in several international conferences as IFAC Safeprocess 2012, NOLCOS 2013 and IEEE CDC 2012, 2013, this special issue gives an overview on recent advances of set-membership-based fault detection and isolation and fault tolerant control. Special attention is paid on covering a significant range of application targets for the recent theoretical developments in this activefield. Copyright © 2016 John Wiley & Sons, Ltd.

Recent advances in the design of interval observers have made it possible to ensure the non-divergence of the computed state bounds from the stability of LTI systems under bounded inputs, with no need for additional monotony assumptions. Time-varying changes of coordinates can be used to that purpose. Most of the related works result in either continuous-time or discrete-time interval dynamics. This paper proposes a constructive algorithm to compute the exact sampled response of a linear interval predictor under bounded inputs, gives a stability equivalence result and discusses the design of interval observers. The exact sampling requires held input bounds but the uncertain input itself needs not to be held. A numerical example exhibiting an oscillatory behavior illustrates the main results.

Two usually distinct paradigms exist to model uncertainties. The stochastic one deals with random uncertainties. Strong assumptions about their probability distributions are often made, especially when online computation is required. For instance, assuming independent Gaussian distributions is common practice when using standard versions of the famous Kalman Filter. Though efficient to deal with measurement noises, the assumption of known probability distributions finds its limits to characterize epistemic uncertainties. Indeed, the lack of a precise knowledge about disturbances such as the load torque of a motor may be better characterized by interval bounds with no assumption about the values distribution. This is the usual motivation for using the set-membership paradigm to model uncertainties. Though explicitly computed sets can achieve a so-called guaranteed robustness to the worse cases resulting from the specified uncertainty bounds, the bounded-error paradigm however usually suffers from a poor management of random measurement noises. In this semi-plenary talk, a joint Zonotopic and Gaussian Kalman Filter (ZGKF) will be presented. It will be shown to provide a solution for the robust fault detection of uncertain discrete-time systems simultaneously subject to bounded disturbances and Gaussian noises. The covariation of a zonotope will be introduced as a set-membership analog to covariance, making it possible to compute a time-varying optimal observer gain jointly minimizing both kinds of uncertainties: bounded/zonotopic and Gaussian. Then, given a maximal probability of false alarms, an innovation-based detection test will be shown to merge the usually mutually exclusive benefits granted by set-membership techniques (robustness to the worse cases within specified bounds, domain computations) and stochastic approaches (taking noise distribution into account, probabilistic evaluation of tests). Numerical simulations will illustrate the significantly improved tradeoff between the sensitivity to faults and the robustness to disturbances/noises, while the computations (prediction/update, optimal gain, confidence domains, adaptive thresholds, detection test) remain explicit and can be efficiently implemented. Then, the new notion of Set-membership and Probabilistic Merger (SPM) will be introduced and particularized to Zono-topic and Gaussian Mergers (ZGM). The EZGKF algorithm, an extended version of ZGKF to non-linear filtering, will be also presented and discussed as an outline to future works.

This paper deals with fault diagnosis for a class of nonlinear continuous-time systems based on an interval extension of continuous-time parity equations. The parity equations are designed based on ordinary differential equations modeling some links between the successive output and input vector derivatives. The noisy inputs and outputs are evaluated through a high-order sliding-mode differentiator. The redundancy relations are formulated as a Constraint Satisfaction Problem (CSP) with faults as unknown variables. In this case, a reliable estimation of the fault magnitude can be performed by solving the CSP using interval techniques. This technique is well suited to deal with actuator faults as well as parametric or sensor faults. However, in this paper, we choose to focus on actuator faults and the performance of the proposed approach is illustrated through simulations on oscillatory failure detection in aircraft surface servo loops. input observer, fault reconstruction, consistency techniques, nonlinear systems.

This paper deals with a set-membership approach for the fast computation of robust adaptive thresholds. Dynamic model based fault detection under bounded additive and multiplicative disturbances is considered. Based on recent results related to the design of stable interval observers for linear systems with additive time-varying zonotopic input bounds, an extension guaranteeing the robustness with respect to structured and bounded multiplicative disturbances is proposed. A sufficient condition not only ensuring the stability of the initial uncertain model but also the non divergence of the computed bounds (i.e. adaptive thresholds) is also given. Then, a numerical example illustrates the proposed scheme.

The design of interval observers with proven stability for LTI systems was often subject to additional assumptions like monotone influences in the vector field. Recently, such restrictions have been overcome by using a time-varying change of variable. In this paper, a stable interval observer for stable (or observable) LTI systems with no multiple poles is proposed by using different mathematical tools and unified notations. Based on complex numbers, they provide an alternative understanding of the problem of designing stable interval observers. The results are applied to the verified model-based design of a vehicle suspension with an oscillatory behavior and bounded inputs modeling an uncertain road profile.

The computation of envelopes enclosing the possible states and/or outputs of a class of uncertain linear dynamical systems is the subject of this paper. The resulting algorithm can be useful in several areas of control systems such as verification of safety properties and fault diagnosis (in order to choose suitable thresholds on some residuals, for instance). A particular class of polytopes, zonotopes, can be used to implicitly represent the computed sets. The related reachability algorithms have shown to be well suited to control the wrapping effect in the case of linear dynamical systems. However, parametric uncertainties, when taken into account, are often modeled by interval matrices which lead to a loss of parametric dependencies and result in the computation of rather pessimistic sets. The main contribution of this paper consists in extending an existing algorithm based on zonotopes so that it can efficiently propagate structured parametric uncertainties. A 6th order oscillating mass-spring system illustrates the resulting control of the wrapping effect by comparison with Monte-Carlo simulations.

This paper deals with the design of guaranteed set-membership fault detection tests based on a continuous time linear dynamical system with parametric uncertainties. A guaranteed discretization scheme is proposed and, then, set-membership tests are designed based on the resulting uncertain discrete time model in which affine dependencies on the initial continuous time model parameters are preserved. The proposed scheme ensures a guaranteed robustness with respect to parametric uncertainties and ensures the logical consistency of the detection test results with the initial uncertain continuous time model.

Fault diagnosis based on the characterisation of operation ranges is proposed in this work. Set membership approaches are used to compute zonotopes used to implement detection and isolation tests. The proposed approach relies on the integration of residual generation and evaluation by testing the membership of the observations to some domains. An a priori evaluation of the worst case sensitivity of the tests is also proposed. The application to a current controlled DC motor illustrates the approach developed in the paper. Copyright © 2006 IFAC