This paper considers the stabilization of nonlinear continuous-time dynamical systems employing periodic event-triggered control (PETC). Assuming knowledge of a stabilizing feedback law for the continuous-time system with a certain convergence rate, a dynamic, state dependent PETC mechanism is designed. The proposed mechanism guarantees on average the same worst case convergence behavior except for tunable deviations. Furthermore, a new approach to determine the sampling period for the proposed PETC mechanism is presented. This approach as well as the actual trigger rule exploit the theory of non-monotonic Lyapunov functions. An additional feature of the proposed PETC mechanism is the possibility to integrate knowledge about packet losses in the PETC design. The proposed PETC mechanism is illustrated with a nonlinear numerical example from literature. This paper is the accepted version of [1], containing also the proofs of the main results.
Self-triggered control (STC) is a well-established technique to reduce the amount of samples for sampled-data systems, and is hence particularly useful for Networked Control Systems. At each sampling instant, an STC mechanism determines not only an updated control input but also when the next sample should be taken. In this paper, a dynamic STC mechanism for nonlinear systems is proposed. The mechanism incorporates a dynamic variable for determining the next sampling instant. Such a dynamic variable for the trigger decision has been proven to be a powerful tool for increasing sampling interval…
Most approaches for self-triggered control (STC) of nonlinear networked control systems (NCS) require measurements of the full system state to determine transmission times. However, for most control systems only a lower dimensional output is available. To bridge this gap, we present in this paper an output-feedback STC approach for nonlinear NCS. An asymptotically stable observer is used to reconstruct the plant state and transmission times are determined based on the observer state. The approach employs hybrid Lyapunov functions and a dynamic variable to encode past state information and to m…
This paper addresses the co-design problem of control inputs and execution decisions for event- and self-triggered controls subject to constraints given by the control Lyapunov function and control barrier function. The proposed approach computes the control input in a way that allows for longer inter-execution intervals, which distinguishes it from many existing event- and self-triggered controllers or control Lyapunov-barrier function controllers. The proposed approach guarantees lower bounds on the minimum inter-execution times. The effectiveness of the proposed approach is demonstrated and…
This work deals with the event-triggered finite-time control for high-order systems based on an implicit Lyapunov function (ILF). With the construction of an inverse optimal problem, a novel expression of ILF is obtained. By designing the event-triggering mechanism elaborately, it is guaranteed that the trivial solution of the closed-loop system is globally finite-time stable and there exists no Zeno phenomenon. Extensions to the scenario with a multi-agent system are studied where a finite-time tracking control drives all the agents to reach a consensus. The obtained theoretical results are s…
Self-triggered control (STC) is a resource efficient approach to determine sampling instants for Networked Control Systems. At each sampling instant, an STC mechanism determines not only the control inputs but also the next sampling instant. In this article, an STC framework for perturbed nonlinear systems is proposed. In the framework, a dynamic variable is used in addition to current state information to determine the next sampling instant, rendering the STC mechanism dynamic. Using dynamic variables has proven to be powerful for increasing sampling intervals for the closely related concept …
A constructive tool of nonlinear control systems design, the method of Control Lyapunov Functions (CLF) has found numerous applications in stabilization problems for continuous time, discrete-time and hybrid systems. In this paper, we address the fundamental question: given a CLF, corresponding to the continuous-time controller with some predefined (e.g. exponential) convergence rate, can the same convergence rate be provided by an event-triggered controller? Under certain assumptions, we give an affirmative answer to this question and show that the corresponding event-based controllers provid…
It has been shown that self-triggered control has the ability to reduce computational loads and deal with the cases with constrained resources by properly setting up the rules for updating the system control when necessary. In this paper, self-triggered stabilization of Boolean control networks (BCNs), including deterministic BCNs, probabilistic BCNs and Markovian switching BCNs, is first investigated via semi-tensor product of matrices and Lyapunov theory of Boolean networks. The self-triggered mechanism with the aim to determine when the controller should be updated is given based on the dec…
Distributed state estimation is examined for a sensor network tasked with reconstructing a system's state through the use of a distributed and event-triggered observer. Each agent in the sensor network employs a deep neural network (DNN) to approximate the uncertain nonlinear dynamics of the system, which is trained using a multiple timescale approach. Specifically, the outer weights of each DNN are updated online using a Lyapunov-based gradient descent update law, while the inner weights and biases are trained offline using a supervised learning method and collected input-output data. The obs…
In this paper, we study the problem of hybrid event-triggered control for a class of nonlinear time-delay systems. Using a Razumikhin-type input-to-state stability result for time-delay systems, we design an event-triggered control algorithm to stabilize the given time-delay system. In order to exclude Zeno behavior, we combine the impulsive control mechanism with our event-triggered strategy. In this sense, the proposed algorithm is a hybrid impulsive and event-triggered strategy. Sufficient conditions for the stabilization of the nonlinear systems with time delay are obtained by using Lyapun…
Self-triggered control is an improvement on event-triggered control methods. Unlike the latter, self-triggered control does not require monitoring the behavior of the system constantly. Instead, self-triggered algorithms predict the events at which the control law has to be updated before they happen, relying on system model and past information.\\ In this work, we present a self-triggered version of an event-triggered control method in which events are generated when a pseudo-Lyapunov function (PLF) associated with the system increases up to a certain limit. This approach has been shown to co…
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 exponen…
This article studies the event-triggered control problem of general nonlinear systems with time delay. A novel event-triggering scheme is presented with two tunable design parameters, based on a Lyapunov functional result for the input-to-state stability of time-delay systems. The proposed event-triggered control algorithm guarantees the resulting closed-loop systems to be globally asymptotically stable, uniformly bounded, and/or globally attractive for different choices of these parameters. Sufficient conditions on the parameters are derived to exclude Zeno behavior. Two illustrative examples…
Self-triggered control (STC) is a resource efficient approach to determine sampling instants for Networked Control Systems (NCS). Recently, a dynamic STC strategy based on hybrid Lyapunov functions for nonlinear NCS has been proposed in Hertneck and Allgöwer (2021b), however with the limitation to NCS without transmission delays. In this paper, we extend this strategy for nonlinear NCS with transmission delays. The capability to handle systems with delays makes it possible to use the resulting dynamic STC mechanism in many practical scenarios where instant transmissions without delays cannot b…
In systems where the ability to actuate is a scarce resource, e.g., spacecrafts, it is desirable to only apply a given controller in an intermittent manner--with periods where the controller is on and periods where it is off. Motivated by the event-triggered control paradigm, where state-dependent triggers are utilized in a sample-and-hold context, we generalize this concept to include state triggers where the controller is off thereby creating a framework for intermittent control. Our approach utilizes certificates--either Lyapunov or barrier functions--to design intermittent trigger laws tha…
A Lyapunov redesign of coordination algorithms for cyberphysical systems
University of Groningen（格罗宁根大学）；Université de Lorraine, CRAN, UMR 7039 and the CNRS, CRAN, UMR 7039（洛林大学、CRAN实验室（UMR 7039）和法国国家科学研究中心（CNRS）、CRAN实验室（UMR 7039））
This study focuses on event-triggered control of nonlinear discrete-time systems with time delays. Based on a Lyapunov-Krasovskii type input-to-state stability result, we propose a novel event-triggered control algorithm that works as follows. The control inputs are updated only when a certain measurement error surpasses a dynamical threshold depending on both the system states and the evolution time. Sufficient conditions are established to ensure that the closed-loop system maintains its asymptotic stability. It is shown that the time-dependent portion in the dynamical threshold is essential…
We consider a remote state estimation problem in the presence of an eavesdropper over packet dropping links. A smart sensor transmits its local estimates to a legitimate remote estimator, in the course of which an eavesdropper can randomly overhear the transmission. This problem has been well studied for unstable dynamical systems, but seldom for stable systems. In this paper, we target at stable and marginally stable systems and aim to design an event-triggered scheduling strategy by minimizing the expected error covariance at the remote estimator and keeping that at the eavesdropper above a …
With the unceasing growth of intelligent production lines that integrate sensors, actuators, and controllers in a wireless communication environment via internet of things (IoT), we design an event-triggered boundary controller for a continuum model of highly re-entrant manufacturing systems for which the influx rate of products is the controlled quantity. The designed controller can potentially operate in networked control systems subject to limited information sharing resources. A Lyapunov argument is utilized to derive the boundary controller together with a feasible event generator that av…
This paper proposes an event-triggered boundary control for the safe stabilization of the Stefan PDE system with actuator dynamics. The control law is designed by applying Zero-Order Hold (ZOH) to the continuous-time safe stabilizing controller developed in our previous work. The event-triggering mechanism is then derived so that the imposed safety conditions associated with high order Control Barrier Function (CBF) are maintained and the stability of the closed-loop system is ensured. We prove that under the proposed event-triggering mechanism, the so-called ``Zeno" behavior is always avoided…
Decentralized Dynamic Event-triggered Output-feedback Control of Stochastic Non-triangular Interconnected Systems with Unknown Time-varying Sensor Sensitivity
On Optimal Event-Triggered Distributed Control for Stochastic Multi-Agent Systems via Reinforcement Learning
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；The Hong Kong University of Science and Technology（香港科技大学）；South China Normal University（华南师范大学）；KTH Royal Institute of Technology（皇家理工学院）
