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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., Team Tamas Keviczky

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., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Tamas Keviczky, Team Manuel Mazo Jr

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., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Tamas Keviczky, Team Manuel Mazo Jr

Event-triggered control (ETC) and self-triggered control (STC) are sample-and-hold control paradigms in which sensor data is only updated to the controller when necessary, often aperiodically, in contrast to the well-established periodic sampling paradigm. In ETC, a state-dependent event triggers a transmission, while in STC the controller decides when to request the next sample. The main objective of ETC and STC is to reduce sampling and transmissions when either sampling/transmitting is costly or network resources are scarce. However, despite years of development in the ETC/STC field, little is known about their sampling performances or how to accommodate the generated aperiodic traffic of multiple ETC systems in a shared communication medium. This dissertation presents methods to (i) schedule multiple ETC systems in a shared network, (ii) evaluate ETC systems' sampling performance, and (iii) creating STC strategies that improve ETC systems' sampling performance. In particular, we focus for the most part on ETC applied to linear time-invariant (LTI) systems. To solve these problems, we first model the timing behavior of ETC/STC systems, obtaining what we call traffic models. The states of a traffic model are the transmitted samples and its output is the elapsed time between consecutive transmissions, the inter-sample time (IST). These models are infinite-state systems that can exhibit very complex—even chaotic—behavior, as we demonstrate. To solve synthesis problems such as scheduling and optimal STC sampling strategies, we augment the models with early-sampling choices, which are guaranteed to preserve control stability and performance. The models are then abstracted into finite-state systems or timed automata, on which many of our problems can be computationally solved. Using these abstractions, the obtained schedulers are always valid for the real systems, and the obtained metrics are always formal bounds to the real system's performance. Ou, Team Manuel Mazo Jr.

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., Team Manuel Mazo Jr.

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., Team Manuel Mazo Jr., Team Tamas Keviczky

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., Team Tamas Keviczky, Team Manuel Mazo Jr.

Event-triggered control (ETC) and self-triggered control (STC) are sample-and-hold control paradigms in which sensor data is only updated to the controller when necessary, often aperiodically, in contrast to the well-established periodic sampling paradigm. In ETC, a state-dependent event triggers a transmission, while in STC the controller decides when to request the next sample. The main objective of ETC and STC is to reduce sampling and transmissions when either sampling/transmitting is costly or network resources are scarce. However, despite years of development in the ETC/STC field, little is known about their sampling performances or how to accommodate the generated aperiodic traffic of multiple ETC systems in a shared communication medium. This dissertation presents methods to (i) schedule multiple ETC systems in a shared network, (ii) evaluate ETC systems' sampling performance, and (iii) creating STC strategies that improve ETC systems' sampling performance. In particular, we focus for the most part on ETC applied to linear time-invariant (LTI) systems. To solve these problems, we first model the timing behavior of ETC/STC systems, obtaining what we call traffic models. The states of a traffic model are the transmitted samples and its output is the elapsed time between consecutive transmissions, the inter-sample time (IST). These models are infinite-state systems that can exhibit very complex—even chaotic—behavior, as we demonstrate. To solve synthesis problems such as scheduling and optimal STC sampling strategies, we augment the models with early-sampling choices, which are guaranteed to preserve control stability and performance. The models are then abstracted into finite-state systems or timed automata, on which many of our problems can be computationally solved. Using these abstractions, the obtained schedulers are always valid for the real systems, and the obtained metrics are always formal bounds to the real system's performance. Ou, Team Manuel Mazo Jr

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., Team Tamas Keviczky, Team Manuel Mazo Jr

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., Team Manuel Mazo Jr, Team Tamas Keviczky

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., Team Manuel Mazo Jr

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., Team Manuel Mazo Jr.

Self-triggered control (STC) is a sample-and-hold control method aimed at reducing communications in networked-control systems; however, existing STC mechanisms often maximize how late the next sample is, thus not optimizing sampling performance in the long-term. In this work, we devise a method to construct self-triggered policies that provide near-maximal average inter-sample time (AIST) while respecting given control performance constraints. To achieve this, we rely on finite-state abstractions of a reference event-triggered control, while also allowing earlier samples. These early triggers constitute controllable actions of the abstraction, for which an AIST-maximizing strategy can be obtained by solving a mean-payoff game. We provide optimality bounds, and how to further improve them through abstraction refinement techniques., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Manuel Mazo Jr.

Self-triggered control (STC) is a sample-and-hold control method aimed at reducing communications in networked-control systems; however, existing STC mechanisms often maximize how late the next sample is, thus not optimizing sampling performance in the long-term. In this work, we devise a method to construct self-triggered policies that provide near-maximal average inter-sample time (AIST) while respecting given control performance constraints. To achieve this, we rely on finite-state abstractions of a reference event-triggered control, while also allowing earlier samples. These early triggers constitute controllable actions of the abstraction, for which an AIST-maximizing strategy can be obtained by solving a mean-payoff game. We provide optimality bounds, and how to further improve them through abstraction refinement techniques., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Manuel Mazo Jr

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., Team Manuel Mazo Jr

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., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Tamas Keviczky

We provide a method to construct finite abstractions exactly bisimilar to linear systems under a modified periodic event-triggered control (PETC), when considering as output the inter-event times they generate. Assuming that the initial state lies on a known compact set, these finite-state models can exactly predict all sequences of sampling times until a specified Lyapunov sublevel set is reached. Based on these results, we provide a way to build tight models simulating the traffic of conventional PETC. These models allow computing tight bounds of the PETC average frequency and global exponential stability (GES) decay rate. Our results are demonstrated through a numerical case study., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Tamas Keviczky

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., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Tamas Keviczky

We provide a method to construct finite abstractions exactly bisimilar to linear systems under a modified periodic event-triggered control (PETC), when considering as output the inter-event times they generate. Assuming that the initial state lies on a known compact set, these finite-state models can exactly predict all sequences of sampling times until a specified Lyapunov sublevel set is reached. Based on these results, we provide a way to build tight models simulating the traffic of conventional PETC. These models allow computing tight bounds of the PETC average frequency and global exponential stability (GES) decay rate. Our results are demonstrated through a numerical case study., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Tamas Keviczky

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., Team Tamas Keviczky

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., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Tamas Keviczky

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., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Tamas Keviczky

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., Team Tamas Keviczky

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., Team Tamas Keviczky