This survey reviews recent developments in fault diagnosis for both linear and nonlinear dynamical systems, covering model-based and data-driven approaches as well as passive and active detection and estimation methods. A central focus is placed on the geometric interpretation of diagnosis filters and their connection to the concept of behavioral sets, providing an intuitive view of their performance. We also review optimization-based techniques that enhance the robustness of linear filters when applied to nonlinear or uncertain systems. Furthermore, we point out recent progress in active fault diagnosis, where input design plays a key role in improving detectability and estimation accuracy. To bridge theory and practice, we include a set of real-world industrial applications that demonstrate the implementation and effectiveness of these methods in realistic settings.

We address the problem of identifying a system subject to additive faults, while simultaneously reconstructing the fault signal via subspace methods. We do not require nominal data for the identification, neither do we impose any assumption on the class of faults, e.g., sensor or actuator faults. We show that, under mild assumptions on the fault signal, standard PI-MOESP can recover the system matrices associated to the input–output subsystem. Then we introduce the concept of output behavior equivalence, which characterizes systems with the same output behavior set, and present a method to establish this equivalence from system matrices. Finally, we show how to estimate from data the complete set of fault matrices for which there exist a fault signal with minimal dimension that explains the data.

We study the problem of fault isolation in linear systems with actuator and sensor faults within a data-driven framework. We propose a nullspace-based filter that uses solely fault-free input-output data collected under process and measurement noises. By reparameterizing the problem within a behavioral framework, we achieve a direct fault isolation filter design that is independent of any explicit system model. The underlying classification problem is approached from a geometric perspective, enabling a characterization of mutual fault discernibility in terms of fundamental system properties given a noise-free setting. In addition, the provided conditions can be evaluated using only the available data. Finally, a simulation study is conducted to demonstrate the effectiveness of the proposed method.

Motivated by the physical exchange of energy and its dissipation in electro-mechanical systems, we propose a new fault detection method based on data-driven dissipativity analysis. We first identify a dissipativity inequality using one or multiple shots of data obtained from a linear time-invariant system. This dissipativity inequality's storage and supply rate functions assume generic quadratic difference forms encompassing all LTI systems. By analysing the norm of the identified dissipative inequality as the residual function, we can detect the occurrence of faults in real-time without the need to model each fault the system is subjected to. Through academic examples, we demonstrate how we can identify supply rate and storage functions from persistently exciting data shots. We present a practical example of detecting faults on a two-degree-of-freedom planar manipulator with zero missed fault detection rate, which is compared to a standard PCA-based fault detection algorithm.

Event-triggered control (ETC) is a major recent development in cyber–physical systems due to its capability of reducing resource utilization in networked devices. However, while most of the ETC literature reports simulations indicating massive reductions in the sampling required for control, no method so far has been capable of quantifying these results. In this work, we propose an approach through finite-state abstractions to do formal quantification of the traffic generated by ETC of linear systems, in particular aiming at computing its smallest average inter-sample time (SAIST). The method involves abstracting the traffic model through l-complete abstractions, finding the cycle of minimum average length in the graph associated to it, and verifying whether this cycle is an infinitely recurring traffic pattern. The method is proven to be robust to sufficiently small model uncertainties, which allows its application to compute the SAIST of ETC of nonlinear systems.

Event-triggered control (ETC) is claimed to provide significant reductions in sampling frequency when compared to periodic sampling, but little is formally known about its generated traffic. This work shows that ETC can exhibit very complex, even chaotic traffic, especially when the triggering condition is aggressive in reducing communications. First, by looking at the map dictating the evolution of states sampled, we characterize limit traffic patterns by observing invariant lines and planes through the origin, as well as their attractivity. Then, we present abstraction-based methods to compute limit metrics, such as limit average and limit inferior inter-sample time (IST) of periodic ETC (PETC), with considerations to the robustness of such metrics, as well as measuring the emergence of chaos. The methodology and tools allow us to find ETC examples that provably outperform periodic sampling in terms of average IST. In particular for PETC, we prove that this requires aperiodic or chaotic traffic.

Event-triggered control (ETC) holds the potential to significantly improve the efficiency of wireless networked control systems. Unfortunately, its real-world impact has hitherto been hampered by the lack of a network stack able to transfer its benefits from theory to practice specifically by supporting the latency and reliability requirements of the aperiodic communication ETC induces. This is precisely the contribution of this article.Our Wireless Control Bus (WCB) exploits carefully orchestrated network-wide floods of concurrent transmissions to minimize overhead during quiescent, steady-state periods, and ensures timely and reliable collection of sensor readings and dissemination of actuation commands when an ETC triggering condition is violated. Using a cyber-physical testbed emulating a water distribution system controlled over a real-world multi-hop wireless network, we show that ETC over WCB achieves the same quality of periodic control at a fraction of the energy costs, therefore unleashing and concretely demonstrating its full potential for the first time.

This paper studies the reduction (abstraction) of finite-state transition systems for control synthesis problems. We revisit the notion of alternating simulation equivalence (ASE), a more relaxed condition than alternating bisimulations, to relate systems and their abstractions. As with alternating bisimulations, ASE preserves the property that the existence of a controller for the abstraction is necessary and sufficient for a controller to exist for the original system. Moreover, being a less stringent condition, ASE can reduce systems further to produce smaller abstractions. We provide an algorithm that produces minimal AS equivalent abstractions. The theoretical results are then applied to obtain (un)schedulability certificates of periodic event-triggered control systems sharing a communication channel. A numerical example illustrates the results.

We present ETCetera, a Python library developed for the analysis and synthesis of the sampling behaviour of event triggered control (ETC) systems. In particular, the tool constructs abstractions of the sampling behaviour of given ETC systems, in the form of timed automata (TA) or finite-state transition systems (FSTSs). When the abstraction is an FSTS, ETCetera provides diverse manipulation tools for analysis of ETC's sampling performance, synthesis of communication traffic schedulers (when networks shared by multiple ETC loops are considered), and optimization of sampling strategies. Additionally, the TA models may be exported to UPPAAL for analysis and synthesis of schedulers. Several examples of the tool's application for analysis and synthesis problems with different types of dynamics and event-triggered implementations are provided.

In the context of networked control systems, event-triggered control (ETC) has emerged as a major topic due to its alleged resource usage reduction capabilities. However, this is mainly supported by numerical simulations, and very little is formally known about the traffic generated by ETC. This work devises a method to estimate, and in some cases to determine exactly, the minimum average inter-sample time (MAIST) generated by periodic event-triggered control (PETC) of linear systems. The method involves abstracting the traffic model using a bisimulation refinement algorithm and finding the cycle of minimum average length in the graph associated to it. This always gives a lower bound to the actual MAIST. Moreover, if this cycle turns out to be related to a periodic solution of the closed-loop PETC system, the performance metric is exact.

Self-triggered control (STC) and periodic event-triggered control (PETC) are aperiodic sampling techniques aiming at reducing control data communication when compared to periodic sampling. In both techniques, the effects of measurement noise in continuous-time systems with output feedback are unaddressed. In this work we prove that additive noise does not hinder stability of output-feedback PETC of linear time-invariant (LTI) systems. Then we build an STC strategy that estimates PETC's worst-case triggering times. To accomplish this, we use set-based methods, more specifically ellipsoidal sets, which describe uncertainties on state, disturbances and noise. Ellipsoidal reachability is then used to predict worst-case triggering condition violations, ultimately determining the next communication time. The ellipsoidal state estimate is recursively updated using guaranteed state estimation (GSE) methods. The proposed STC is designed to be computationally tractable at the expense of some added conservatism. It is expected to be a practical STC implementation for a broad range of applications.

This paper addresses the problem of modeling and scheduling the transmissions generated by multiple event-triggered control (ETC) loops sharing a network. We present a method to build a finite-state similar model of the traffic generated by periodic ETC (PETC), which by construction mitigates the combinatorial explosion that is typical of symbolic models. The model is augmented with early triggering actions that can be used by a scheduler. The complete networked control system is then modeled as a network of timed game automata, for which existing tools can generate strategies that avoids communication conflicts, while keeping early triggers to a minimum. Our proposed model is relatively fast to build and is the first to constitute an exact simulation. Finally, we demonstrate modeling and scheduling for a numerical example.

In networked control systems (NCSs), extensive data exchange between plants and controllers leads to an unnecessary usage of communication and computational resources. Aperiodic sample-and-hold methods such as event-triggered control (ETC) can reduce the number of transmissions, allowing more applications to operate within the same network. However, most existing event-triggering mechanisms enforce a Lyapunov function of the continuous-time closed-loop system to be (almost) always decreasing. We propose a relaxed triggering condition for periodic event-triggered control (PETC) based on bounding the Lyapunov function with an exponentially decaying reference function, which reduces the communications while guaranteeing the same decay rate as competing strategies. We provide sufficient global exponential and input-to-state stability conditions for linear time-invariant (LTI) systems under our event-based state feedback, giving explicit performance guarantees in the presence of additive disturbances. Finally, some simulation results illustrate the performance of the proposed control strategy.

In this work we propose a Self-Triggered Control (STC) strategy for linear time-invariant (LTI) systems subject to bounded disturbances, using LTI discrete-time dynamic output-feedback. The STC logic computes worst-case triggering times from available information, based on a Periodic Event Triggered Control (PETC) triggering function. In the case of no perturbation and full state information, the discrete times can be determined exactly, defining unions of cones in the state space. When bounded disturbances are present, we compute worst-case triggering times and their associated state-space regions. If full state information is also not available, we use a special observer to compute the worst-case triggering times, yielding an STC logic that only needs the current system output and the controller state. For all cases, we provide sufficient conditions for stability and L₂-gain from disturbance to output.