Dynamic event-Triggered control under packet losses: The case with acknowledgements

In this paper, a dynamic ETC strategy for nonlinear state-feedback systems is proposed that results in guarantees for a finite ℓp-gain from disturbance input to performance output and a strictly positive lower bound on the inter-event times despite the presence of packet losses. The proposed dynamic ETC strategy has several advantages with respect to the commonly studied static ETC strategy including significantly larger average inter-event times. The proposed design methodology results in tradeoffs between the maximum allowable number of successive packet dropouts, (minimum and average) inter-event times and ℓp-gains, which will be illustrated by means of a numerical example

Event-triggered control systems under packet losses

Networked control systems (NCSs) offer many benefits in terms of increased flexibility and maintainability but might also suffer from inevitable imperfections such as packet dropouts and limited communications resources. In this paper, (static and dynamic) event-triggered control (ETC) strategies are proposed that aim at reducing the utilization of communication resources while guaranteeing desired stability and performance criteria and a strictly positive lower bound on the inter-event times despite the presence of packet losses. For the packet losses, we consider both configurations with an acknowledgement scheme (as, e.g., in the transmission control protocol (TCP)) and without an acknowledgement scheme (as, e.g., in the user diagram protocol (UDP)). The proposed design methodology will be illustrated by means of a numerical example which reveals tradeoffs between the maximum allowable number of successive packet dropouts, (minimum and average) inter-event times and Lp-gains of the closed-loop NCS

Output-based and decentralized dynamic event-Triggered control with guaranteed Lp-Gain performance and zeno-freeness

Networked control systems are often subject to limited communication resources. By only communicating output measurements when needed, event-Triggered control is an adequate method to reduce the usage of communication resources while retaining desired closed-loop performance. In this work, a novel event-Triggered control (ETC) strategy for a class of nonlinear feedback systems is proposed that can simultaneously guarantee a finite L p-gain and a strictly positive lower bound on the inter-event times. The new ETC scheme can be synthesized in an output-based and/or decentralized form, takes the specific medium access protocols into account, and is robust to (variable) transmission delays by design. Interestingly, in contrast with the majority of existing event-generators that only use static conditions, the newly proposed event-Triggering conditions are based on dynamic elements, which has several advantages including larger average inter-event times. The developed theory leads to families of event-Triggered controllers that correspond to different tradeoffs between (minimum and average) inter-event times, maximum allowable delays and L p}-gains. A linear and a nonlinear numerical example will illustrate all the benefits of this new dynamic ETC scheme

Dynamic event-triggered control with time regularization for linear systems

We present a framework for the analysis and design of dynamic and static event-triggered controllers with time regularization for linear systems. This framework leads to guarantees on global exponential stability, L2-stability, and a positive minimum inter-event time, in addition to a reduction in the number of events compared to regular time-triggered controllers and other event-triggered controllers in literature. By using new analysis tools tailored to linear systems, we achieve a significant reduction in conservatism, in the sense that the novel framework yields new event-generator designs with much larger inter-event times and much tighter bounds on the L2-gain and convergence rate of the event-triggered control system compared to previous results for more general nonlinear systems. We demonstrate the benefits of our new results via a numerical example, and show that the conservatism in the estimates of the L2-gain is indeed small

Dynamic event-triggered control: tradeoffs between transmission intervals and performance

In this work, a novel dynamic event-triggered control (ETC) strategy for state-feedback systems is proposed that can simultaneously guarantee a finite p-gain from disturbance to output and a strictly positive lower bound on the inter-event times (implying Zeno-freeness). The developed theory leads to tradeoff curves between (minimum and average) inter-event times and p-gains that depend on the selected medium access protocol

Dynamic periodic event-triggered control for linear systems

In event-triggered control systems, events are typically generated when a static function of the output (or state) of the system exceeds a given threshold. Recently, event-generators have been proposed that generate events based on an additional dynamic variable, with dynamics that depend on the output of the system. It is shown that these dynamic eventgenerators are able to guarantee the same performance as their static counterparts, while typically generating significantly fewer events. However, all dynamic event-generators available in literature require continuous measuring of the output of the plant, which is difficult to realize on digital platforms. In this paper, we propose new dynamic eventgenerators for linear systems, which require only periodic sampling of the output, and are therefore easy to implement on digital platforms. Based on hybrid modelling techniques combined with constructive designs of Lyapunov/storage functions for the resulting hybrid models, it is shown that these (dynamic periodic) event-generators lead to closed-loop systems which are globally exponentially stable (GES) with a guaranteed decay rate and L2-stable with a guaranteed L2-gain. The benefits of these new event-generators are also demonstrated via a numerical example

Riccati-based design of event-triggered controllers for linear systems with delays

In event-triggered control (ETC) systems, the measured state or output of the plant is sent to the controller at so-called event times. In many ETC systems, these event times are generated based on a static function of the current state or output measurement of the system and its sampled-and-held version that is available to the controller. Hence, the event-generator does not include any dynamics of its own. In contrast, dynamic event-generators trigger events based on additional dynamic variables, whose dynamics depend on the state or output of the system. In this paper, we propose new static and dynamic continuous event-generators (which require continuous measuring of the plant output) and periodic eventgenerators (which only require periodic sampling of the plant output) for linear control systems with communication delays. All event-generators we propose lead to closed-loop systems which are globally exponentially stable with a guaranteed decay rate, L2 -stable with a guaranteed L2 - gain, and have a guaranteed positive minimum inter-event time. By using new Riccati-based analysis tools tailored to linear systems, the conservatism in our decay rate and L2 -gain estimates is small. The dynamic event-generators even further reduce this conservatism, and as a result typically generate significantly fewer events than their static counterparts, while guaranteeing the same control performance. The benefits of these new event-generators are demonstrated via two numerical examples