Zonotopic fault detection observer design for Takagi–Sugeno fuzzy systems

This paper considers zonotopic fault detection observer design in the finite-frequency domain for discrete-time Takagi–Sugeno fuzzy systems with unknown but bounded disturbances and measurement noise. We present a novel fault detection observer structure, which is more general than the commonly used Luenberger form. To make the generated residual sensitive to faults and robust against disturbances, we develop a finite-frequency fault detection observer based on generalised Kalman–Yakubovich–Popov lemma and P-radius criterion. The design conditions are expressed in terms of linear matrix inequalities. The major merit of the proposed method is that residual evaluation can be easily implemented via zonotopic approach. Numerical examples are conducted to demonstrate the proposed methodPeer ReviewedPostprint (author's final draft

Sensor-fault tolerance using robust MPC with set-based state estimation and active fault isolation

In this paper, a sensor fault-tolerant control (FTC) scheme using robust model predictive control (MPC) and set theoretic fault detection and isolation (FDI) is proposed. The MPC controller is used to both robustly control the plant and actively guarantee fault isolation (FI). In this scheme, fault detection (FD) is passive by interval observers, while fault isolation (FI) is active by MPC. The advantage of the proposed approach consists in using MPC to actively decouple the effect of sensor faults on the outputs such that one output component only corresponds to one sensor fault in terms of FI, which can utilize the feature of sensor faults for FI. A numerical example is used to illustrate the effectiveness of the proposed scheme.Postprint (author’s final draft

Fault detection and isolation using viability theory and interval observers

This paper proposes the use of interval observers and viability theory in fault detection and isolation (FDI). Viability theory develops mathematical and algorithmic methods for investigating the viability constraints characterisation of dynamic evolutions of complex systems under uncertainty. These methods can be used for checking the consistency between observed and predicted behaviour by using simple sets that approximate the exact set of possible behaviour (in the parameter or state space). In this paper, FDI is based on checking for an inconsistency between the measured and predicted behaviours using viability theory concepts and sets. Finally, an example is provided in order to show the usefulness of the proposed approachPeer ReviewedPostprint (author's final draft

Set-based state estimation and fault diagnosis using constrained zonotopes and applications

This doctoral thesis develops new methods for set-based state estimation and active fault diagnosis (AFD) of (i) nonlinear discrete-time systems, (ii) discrete-time nonlinear systems whose trajectories satisfy nonlinear equality constraints (called invariants), (iii) linear descriptor systems, and (iv) joint state and parameter estimation of nonlinear descriptor systems. Set-based estimation aims to compute tight enclosures of the possible system states in each time step subject to unknown-but-bounded uncertainties. To address this issue, the present doctoral thesis proposes new methods for efficiently propagating constrained zonotopes (CZs) through nonlinear mappings. Besides, this thesis improves the standard prediction-update framework for systems with invariants using new algorithms for refining CZs based on nonlinear constraints. In addition, this thesis introduces a new approach for set-based AFD of a class of nonlinear discrete-time systems. An affine parametrization of the reachable sets is obtained for the design of an optimal input for set-based AFD. In addition, this thesis presents new methods based on CZs for set-valued state estimation and AFD of linear descriptor systems. Linear static constraints on the state variables can be directly incorporated into CZs. Moreover, this thesis proposes a new representation for unbounded sets based on zonotopes, which allows to develop methods for state estimation and AFD also of unstable linear descriptor systems, without the knowledge of an enclosure of all the trajectories of the system. This thesis also develops a new method for set-based joint state and parameter estimation of nonlinear descriptor systems using CZs in a unified framework. Lastly, this manuscript applies the proposed set-based state estimation and AFD methods using CZs to unmanned aerial vehicles, water distribution networks, and a lithium-ion cell.Comment: My PhD Thesis from Federal University of Minas Gerais, Brazil. Most of the research work has already been published in DOIs 10.1109/CDC.2018.8618678, 10.23919/ECC.2018.8550353, 10.1016/j.automatica.2019.108614, 10.1016/j.ifacol.2020.12.2484, 10.1016/j.ifacol.2021.08.308, 10.1016/j.automatica.2021.109638, 10.1109/TCST.2021.3130534, 10.1016/j.automatica.2022.11042

Robust MPC for actuator-fault tolerance using set-based passive fault detection and active fault isolation

In this paper, an actuator fault-tolerant control (FTC) scheme is proposed, which is based on tube-based model predictive control (MPC) and set-theoretic fault detection and isolation (FDI). As a robust MPC technique, tube-based MPC, can effectively deal with system constraints and uncertainties with relatively low computational complexity. Set-based FDI can robustly detect and isolate actuator faults. Here, fault detection (FD) is passive by invariant sets, while fault isolation (FI) is active by tubes. Using the constraint-handling ability of MPC controllers, an active FI approach is implemented. A numerical example illustrates the effectiveness of the proposed approach.Postprint (author’s final draft

Robust Fault Diagnosis by Optimal Input Design for Self-sensing Systems

This paper presents a methodology for model based robust fault diagnosis and a methodology for input design to obtain optimal diagnosis of faults. The proposed algorithm is suitable for real time implementation. Issues of robustness are addressed for the input design and fault diagnosis methodologies. The proposed technique allows robust fault diagnosis under suitable conditions on the system uncertainty. The designed input and fault diagnosis techniques are illustrated by numerical simulation.Comment: Accepted in IFAC World Congress 201

Interval observer versus set-membership approaches for fault detection in uncertain systems using zonotopes

This paper presents both analysis and comparison of the interval observer–based and set-membership approaches for the state estimation and fault detection (FD) in uncertain linear systems. The considered approaches assume that both state disturbance and measurement noise are modeled in a deterministic context following the unknown but bounded approach. The propagation of uncertainty in the state estimation is bounded through a zonotopic set representation. Both approaches have been mathematically related and compared when used for state estimation and FD. A case study based on a two-tanks system is employed for showing the relationship between both approaches while comparing their performancePeer ReviewedPostprint (author's final draft

Conflict-driven Hybrid Observer-based Anomaly Detection

This paper presents an anomaly detection method using a hybrid observer -- which consists of a discrete state observer and a continuous state observer. We focus our attention on anomalies caused by intelligent attacks, which may bypass existing anomaly detection methods because neither the event sequence nor the observed residuals appear to be anomalous. Based on the relation between the continuous and discrete variables, we define three conflict types and give the conditions under which the detection of the anomalies is guaranteed. We call this method conflict-driven anomaly detection. The effectiveness of this method is demonstrated mathematically and illustrated on a Train-Gate (TG) system

FD-ZKF: A Zonotopic Kalman Filter optimizing fault detection rather than state estimation

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 approachPostprint (author's final draft

Set-based state estimation and fault diagnosis of linear discrete-time descriptor systems using constrained zonotopes

This paper presents new methods for set-valued state estimation and active fault diagnosis of linear descriptor systems. The algorithms are based on constrained zonotopes, a generalization of zonotopes capable of describing strongly asymmetric convex sets, while retaining the computational advantages of zonotopes. Additionally, unlike other set representations like intervals, zonotopes, ellipsoids, paralletopes, among others, linear static constraints on the state variables, typical of descriptor systems, can be directly incorporated in the mathematical description of constrained zonotopes. Therefore, the proposed methods lead to more accurate results in state estimation in comparison to existing methods based on the previous sets without requiring rank assumptions on the structure of the descriptor system and with a fair trade-off between accuracy and efficiency. These advantages are highlighted in two numerical examples.Comment: This paper was accepted and presented in the 1st IFAC Virtual World Congress, 202