We present a framework for model-free learning of event-triggered control strategies. Event-triggered methods aim to achieve high control performance while only closing the feedback loop when needed. This enables resource savings, e.g., network bandwidth if control commands are sent via communication networks, as in networked control systems. Event-triggered controllers consist of a communication policy, determining when to communicate, and a control policy, deciding what to communicate. It is essential to jointly optimize the two policies since individual optimization does not necessarily yield the overall optimal solution. To address this need for joint optimization, we propose a novel algorithm based on hierarchical reinforcement learning. The resulting algorithm is shown to accomplish high-performance control in line with resource savings and scales seamlessly to nonlinear and high-dimensional systems. The method's applicability to real-world scenarios is demonstrated through experiments on a six degrees of freedom real-time controlled manipulator. Further, we propose an approach towards evaluating the stability of the learned neural network policies.
University College Cork（科克大学学院）；Munster Technological University（芒斯特理工大学）
Networked control systems have gained considerable attention over the last decade as a result of the trend towards decentralised control applications and the emergence of cyber-physical system applications. However, real-world wireless networked control systems suffer from limited communication bandwidths, reliability issues, and a lack of awareness of network dynamics due to the complex nature of wireless networks. Combining machine learning and event-triggered control has the potential to alleviate some of these issues. For example, machine learning can be used to overcome the problem of a l…
In emerging Industrial Cyber-Physical Systems (ICPSs), the joint design of communication and control sub-systems is essential, as these sub-systems are interconnected. In this paper, we study the joint design problem of an event-triggered control and an energy-efficient resource allocation in a fifth generation (5G) wireless network. We formally state the problem as a multi-objective optimization one, aiming to minimize the number of updates on the actuators' input and the power consumption in the downlink transmission. To address the problem, we propose a model-free hierarchical reinforcement…
Nara Institute of Science and Technology（奈良先端科学技术大学院大学）
In this paper, we explore a multi-agent reinforcement learning approach to address the design problem of communication and control strategies for multi-agent cooperative transport. Typical end-to-end deep neural network policies may be insufficient for covering communication and control; these methods cannot decide the timing of communication and can only work with fixed-rate communications. Therefore, our framework exploits event-triggered architecture, namely, a feedback controller that computes the communication input and a triggering mechanism that determines when the input has to be updat…
Event-triggered control (ETC) and time-triggered control (TTC), the classical concepts to determine the transmission instants for networked control systems, each come with drawbacks: It is difficult to tune ETC such that a certain bandwidth is respected, whereas TTC cannot adapt the sampling interval to the current state of the control system. In this article, we provide an overview over rollout ETC, a method aimed at reconciling the advantages of ETC and TTC. We unite two variants of rollout ETC under a common framework and present conditions for convergence and compliance with a predefined b…
This paper studies the optimal output consensus problem for a group of heterogeneous linear multi-agent systems. Different from existing results, we aim at effective controllers for these high-order agents under both event-triggered control and event-triggered communication settings. We conduct an embedded design for the problem and constructively propose a multi-rate event-triggered controller with a set of applicable parameters. The proposed event-triggered rules are shown to be free of Zeno behaviors and can achieve the optimal output consensus goal for these high-order agents. A simulation…
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…
This work presents a rigorous analysis of the adverse effects of cyber-physical attacks on the performance of multi-agent consensus with event-triggered control protocols. It is shown how a strategic malicious attack on sensors and actuators can deceive the triggering condition of both state-based event-triggered mechanism and combinational state-based event-triggered mechanism, which are commonplace and widely used in the literature. More precisely, it is first shown that a deception attack in the case of combinational state-based event-triggered mechanism can result in a non-triggering misbe…
Universidad Nacional de Colombia（哥伦比亚国立大学）；Lehigh University（理海大学）；Universidad Santo Tomas（圣托马斯大学）；Bethune Cookman University（贝休恩-库克曼大学）
We develop an event-triggered control strategy for a weighted-unbalanced directed homogeneous robot network to reach a dynamic consensus in this work. We present some guarantees for synchronizing a robot network when all robots have access to the reference and when a limited number of robots have access. The proposed event-triggered control can reduce and avoid the periodic updating of the signals. Unlike some current control methods, we prove stability by making use of a logarithmic norm, which extends the possibilities of the control law to be applied to a wide range of directed graphs, in c…
Distributed Observers with Dynamic Event-Triggered Communication
School of Automation and Intelligent Sensing, Shanghai Jiao Tong University（上海交通大学自动化与智能传感学院）；Key Laboratory of System Control and Information Processing, Ministry of Education of China（教育部系统控制与信息处理重点实验室）；State Key Laboratory of Submarine Geoscience, Shanghai Jiao Tong University（上海交通大学海洋地质国家重点实验室）
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…
A framework for the event-triggered control synthesis under signal temporal logic (STL) tasks is proposed. In our previous work, a continuous-time feedback control law was designed, using the prescribed performance control technique, to satisfy STL tasks. We replace this continuous-time feedback control law by an event-triggered controller. The event-triggering mechanism is based on a maximum triggering interval and on a norm bound on the difference between the value of the current state and the value of the state at the last triggering instance. Simulations of a multi-agent system quantitativ…
This paper studies the tracking control problem of networked and quantized control systems under both multiple networks and event-triggered mechanisms. Multiple networks are to connect the plant and reference system with decentralized controllers to guarantee their information transmission, whereas event-triggered mechanisms are to reduce the information transmission via multiple networks. In this paper, all networks are independent and asynchronous and have local event-triggered mechanisms, which are based on local measurements and determine whether the local measurements need to be transmitt…
We study the problem of periodic event-triggered control of interconnected port-Hamiltonian systems subject to time-varying delays in their communication. In particular, we design a threshold parameter for the event-triggering condition, a sampling period, and a maximum allowable delay such that interconnected port-Hamiltonian control systems with periodic event-triggering mechanism under a time-delayed communication are able to achieve asymptotically stable behaviour. Simulation results are presented to validate the theory.
The paper considers the problem of multi-agent consensus in the presence of adversarial agents which may try to prevent and introduce undesired influence on the coordination among the regular agents. To our setting, we extend the so-called mean subsequence reduced algorithms with the aim to reduce the amount of communication via two measures: The agents exchange information in the form of ternary data at each transmission and moreover keep the frequency of data exchange low by employing self- and event-triggered communication. We will observe that in hostile environments with adversaries, the …
This paper investigates the communication strategy for second-order multi-agent systems with nonlinear dynamics. To save the scarce resources of communication channels, a novel event-triggered communication mechanism is designed without using continuous signals among the followers. To get rid of the centralized information depending on the spectrum of the Laplacian matrix, a consensus protocol with updated coupling gains and an event-triggered strategy of interagent communication with updated thresholds are presented. To minimize the impacts of noise, only relative positions among agents are e…
This paper addresses the following question: "Suppose that a state-feedback controller stabilizes an infinite-dimensional linear continuous-time system. If we choose the parameters of an event/self-triggering mechanism appropriately, is the event/self-triggered control system stable under all sufficiently small nonlinear Lipschitz perturbations?" We assume that the stabilizing feedback operator is compact. This assumption is used to guarantee the strict positiveness of inter-event times and the existence of the mild solution of evolution equations with unbounded control operators. First, for t…
This work attempts to discuss the observability of linear time-invariant systems with event-triggered measurements. A new notion of observability, namely, $ε$-observability is defined with parameter $ε$, which relates to the worst-case performance of inferring the initial state based on not only the received measurement but also the implicit information in the event-triggering conditions at no-event instants. A criterion is developed to test the proposed $ε$-observability of discrete-time linear systems, based on which an iterative event-triggered set-membership observer is designed to evaluat…
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…
Dynamic watermarking schemes can enhance the cyber attack detection capability of networked control systems (NCSs). This paper presents a linear event-triggered solution to conventional dynamic watermarking (CDW) schemes. Firstly, the limitations of CDW schemes for event-triggered state estimation based NCSs are investigated. Secondly, a new event-triggered dynamic watermarking (ETDW) scheme is designed by treating watermarking as symmetric key encryption, based on the limit convergence theorem in probability. Its security property against the generalized replay attacks (GRAs) is also discusse…
The efficient utilization of available resources while simultaneously achieving control objectives is a primary motivation in the event-triggered control paradigm. In many modern control applications, one such objective is enforcing the safety of a system. The goal of this paper is to carry out this vision by combining event-triggered and safety-critical control design. We discuss how a direct transcription, in the context of safety, of event-triggered methods for stabilization may result in designs that are not implementable on real hardware due to the lack of a minimum interevent time. We pr…
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…
The ubiquitous interdependencies among higher-dimensional states of neighboring agents can be characterized by matrix-weighted networks. This paper examines event-triggered global consensus of matrix-weighted networks subject to actuator saturation. Specifically, a distributed dynamic event-triggered coordination strategy, whose design involves sampled state of agents, saturation constraint and auxiliary systems, is proposed for this category of generalized network to guarantee its global consensus. Under the proposed event-triggered coordination strategy, sufficient conditions are derived to …
This paper proposes a distributed scheme with different estimators for the event-triggered formation control of polytopic homogeneously scheduled linear parameter-varying (LPV) multi-agent systems (MAS). Each agent consists of a time-triggered inner feedback loop and a larger event-triggered outer feedback loop to track a formation reference signal and reject input and output noise. If a local event-trigger condition is violated, the event-triggered outer feedback loop is closed through the communication network. The event-trigger condition is only based on locally available information. To de…
This paper proposes an event-triggered variational Bayesian filter for remote state estimation with unknown and time-varying noise covariances. After presetting multiple nominal process noise covariances and an initial measurement noise covariance, a variational Bayesian method and a fixed-point iteration method are utilized to jointly estimate the posterior state vector and the unknown noise covariances under a stochastic event-triggered mechanism. The proposed algorithm ensures low communication loads and excellent estimation performances for a wide range of unknown noise covariances. Finall…
Communication in parallel systems imposes significant overhead which often turns out to be a bottleneck in parallel machine learning. To relieve some of this overhead, in this paper, we present EventGraD - an algorithm with event-triggered communication for stochastic gradient descent in parallel machine learning. The main idea of this algorithm is to modify the requirement of communication at every iteration in standard implementations of stochastic gradient descent in parallel machine learning to communicating only when necessary at certain iterations. We provide theoretical analysis of conv…
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 is well known that the employed triggering scheme has great impact on the control performance when control loops operate under scarce communication resources. Various practical and simulative works have demonstrated the potential of event-triggered control to reduce communication while providing a similar performance level when compared to time-triggered control. For non-cooperative networked control systems, analytical performance comparisons of time- and event-triggered control support this finding under certain assumptions. While being well-studied in the non-cooperative setting, it rema…
This paper examines the event-triggered consensus of the multi-agent system on matrix-weighted networks, where the interdependencies among higher-dimensional states of neighboring agents are characterized by matrix-weighted edges in the network. Specifically, a novel distributed dynamic event-triggered coordination strategy is proposed for this category of generalized networks, in which an auxiliary system is employed for each agent to dynamically adjust the triggering threshold, which plays an essential role in guaranteeing that the triggering time sequence does not exhibit Zeno behavior. Dis…
In previous work, linear time-invariant event-triggered control (ETC) systems were abstracted to finite-state systems that capture the original systems' sampling behaviour. It was shown that these abstractions can be employed for scheduling of communication traffic in networks of ETC loops. In this paper, we extend this framework to the class of nonlinear homogeneous systems, however adopting a different approach in a number of steps. Finally, we discuss how the proposed methodology could be extended to general nonlinear systems.
This paper presents an observer-based event-triggered boundary control strategy for a class of reaction-diffusion PDEs with Robin actuation. The observer only requires boundary measurements. The control approach consists of a backstepping output feedback boundary controller, derived using estimated states, and a dynamic triggering condition, which determines the time instants at which the control input needs to be updated. It is shown that under the proposed observer-based event-triggered boundary control approach, there is a minimal dwell-time between two triggering instants independent of in…
This paper studies the tracking control problem of networked multi-agent systems under both multiple networks and event-triggered mechanisms. Multiple networks are to connect multiple agents and reference systems with decentralized controllers to guarantee their information transmission, whereas the event-triggered mechanisms are to reduce the information transmission via the networks. In this paper, each agent has a network to communicate with its controller and reference system, and all networks are independent and asynchronous and have local event-triggered mechanisms, which are based on lo…
This paper addresses the output synchronization problem for heterogeneous nonlinear multi-agent systems with distributed event-based controllers. Employing the two-step synchronization process, we first outline the distributed event-triggered consensus controllers for linear reference models under a directed communication topology. It is further shown that the subsequent triggering instants are based on intermittent communication. Secondly, by using certain input-to-state stability (ISS) property, we design an event-triggered perturbed output regulation controller for each nonlinear multi-agen…
In this paper, an event-triggered control protocol is developed to investigate flocking control of Lagrangian systems, where event-triggering conditions are proposed to determine when the velocities of the agents are transmitted to their neighbours. In particular, the proposed controller is distributed, since it only depends on the available information of each agent on their own reference frame. In addition, we derive sufficient conditions to avoid Zeno behaviour. Numerical simulations are provided to show the effectiveness of the proposed control law.
In this paper, we study the robustness of the event-triggered consensus algorithms against frequency-domain uncertainties. It is revealed that the sampling errors resulted by event triggering are essentially images of linear finite-gain $\mathcal{L}_2$-stable operators acting on the consensus errors of the sampled states and the event-triggered mechanism is equivalent to a negative feedback loop introduced additionally to the feedback system. In virtue of this, the robust consensus problem of the event-triggered network systems subject to additive dynamic uncertainties and network multiplicati…
