This study considers the problem of periodic event-triggered (PET) cooperative output regulation for a class of linear multi-agent systems. The advantage of the PET output regulation is that the data transmission and triggered condition are only needed to be monitored at discrete sampling instants. It is assumed that only a small number of agents can have access to the system matrix and states of the leader. Meanwhile, the PET mechanism is considered not only in the communication between various agents, but also in the sensor-to-controller and controller-to-actuator transmission channels for each agent. The above problem set-up will bring some challenges to the controller design and stability analysis. Based on a novel PET distributed observer, a PET dynamic output feedback control method is developed for each follower. Compared with the existing works, our method can naturally exclude the Zeno behavior, and the inter-event time becomes multiples of the sampling period. Furthermore, for every follower, the minimum inter-event time can be determined \textit{a prior}, and computed directly without the knowledge of the leader information. An example is given to verify and illustrate the effectiveness of the new design scheme.
This study focuses on periodic event-triggered (PET) cooperative output regulation problem for a class of nonlinear multi-agent systems. The key feature of PET mechanism is that event-triggered conditions are required to be monitored only periodically. This approach is beneficial for Zeno behavior exclusion and saving of battery energy of onboard sensors. At first, new PET distributed observers are proposed to estimate the leader information. We show that the estimation error converges to zero exponentially with a known convergence rate under asynchronous PET communication. Second, a novel PET…
We investigate the problem of practical output regulation, i.e., to design a controller that brings the system output in the vicinity of a desired target value while keeping the other variables bounded. We consider uncertain systems that are possibly nonlinear and the uncertainty of their linear parts is modeled element-wise through a parametric family of matrix boxes. An optimization-based design procedure is proposed that delivers a continuous-time control and estimates the maximal regulation error. We also analyze an event-triggered emulation of this controller, which can be implemented on …
In this paper, we present a model-based periodic event-triggered control mechanism for nonlinear continuous-time Networked Control Systems. A sampled-data prediction of the system behavior is used at the actuator to reduce the amount of required communication while maintaining a user-defined performance level. This prediction is based on a possibly inaccurate discretization of the nonlinear system dynamics and can be implemented on simple hardware. Nevertheless, guarantees for asymptotic stability and a user-defined performance level are given for the periodic event-triggered control (PETC) me…
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…
The paper deals with the problem of output regulation of nonlinear systems by presenting a learning-based adaptive internal model-based design strategy. We borrow from the adaptive internal model design technique recently proposed in [1] and extend it by means of a Gaussian process regressor. The learning-based adaptation is performed by following an "event-triggered" logic so that hybrid tools are used to analyse the resulting closed-loop system. Unlike the approach proposed in [1] where the friend is supposed to belong to a specific finite-dimensional model set, here we only require smoothne…
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 …
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.
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…
Event-triggered control (ETC) is claimed to provide enormous 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, 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-sam…
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 symbolic traffic model of periodic ETC (PETC), which by construction provides an exact simulation of such traffic. The model is made in such a way as to avoid the combinatorial explosion that is typical of symbolic models in many applications. It is augmented with early triggering actions that can be used by a scheduler to mitigate communication conflicts. The complete networked control system is then modeled a…
In this paper, we introduce a distributed secondary frequency control scheme for an islanded ac microgrid under event-triggered communication. An integral type event-triggered mechanism is proposed by which each distributed generator (DG) asynchronously and periodically checks its triggering condition and determines whether to update its control inputs and broadcast its states to neighboring DGs. In contrast to existing event-triggered strategies on secondary control of microgrids, under the proposed sampled-data based event-triggered mechanism, DGs need not be synchronized to a common clock a…
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 cy…
Design of optimal repetitive control based on EID estimator with adaptive periodic event-triggered mechanism for linear systems subjected to exogenous disturbances
Periodic Event-Triggered Prescribed Time Control of Euler-Lagrange Systems under State and Input Constraints
Center for Cyber-Physical Systems IISc（网络物理系统中心IISc）；Interdisciplinary Data Research Division CSIR-4PI（跨学科数据研究部CSIR-4PI）；Dept. of Mechanical Engineering IISc（机械工程系IISc）
We present a general emulation-based framework to address the distributed control of multi-agent systems over packet-based networks. We consider the setup where information is only transmitted at (non-uniform) sampling times and where packets are received with unknown delays. We design local dynamic periodic event-triggering mechanisms to generate the transmissions. The triggering mechanisms can run on non-synchronized digital platforms, i.e., we ensure that the conditions must only be verified at asynchronous sampling times, which may differ for each platform. Different stability and performa…
Recently, there have been efforts towards understanding the sampling behaviour of event-triggered control (ETC), for obtaining metrics on its sampling performance and predicting its sampling patterns. Finite-state abstractions, capturing the sampling behaviour of ETC systems, have proven promising in this respect. So far, such abstractions have been constructed for non-stochastic systems. Here, inspired by this framework, we abstract the sampling behaviour of stochastic narrow-sense linear periodic ETC (PETC) systems via Interval Markov Chains (IMCs). Particularly, we define functions over seq…
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…
Event-triggered consensus of multi-agent systems under directed topology based on periodic sampled-data
School of Mathematics and Statistics, Qingdao University（青岛大学数学与统计学院）；College of Automation and Electrical Engineering, Qingdao University（青岛大学自动化与电气工程学院）；School of Control Science and Engineering, Shandong University（山东大学控制科学与工程学院）
In linear systems theory it's a well known fact that a regulator given by the cascade of an oscillatory dynamics, driven by some regulated variables, and of a stabiliser stabilising the cascade of the plant and of the oscillators has the ability of blocking on the steady state of the regulated variables any harmonics matched with the ones of the oscillators. This is the well-celebrated internal model principle. In this paper we are interested to follow the same design route for a controlled plant that is a nonlinear and periodic system with period T : we add a bunch of linear oscillators, embe…
This paper investigates the design of self-triggered control for networked control systems (NCS), where the dynamics of the plant is unknown apriori. To deal with the nature of the self-triggered control, in which state measurements are transmitted to the controller a-periodically, we propose to lift the continuous-time dynamics to a novel dynamical model by taking an inter-event time as an additional input, and then, the lifted model is learned by the Gaussian processes (GP) regression. Moreover, we propose a learning-based approach, in which a self-triggered controller is learned by minimizi…
Efficiently handling time-triggered and possibly nondeterministic switches for hybrid systems reachability is a challenging task. In this paper we present an approach based on conservative set-based enclosure of the dynamics that can handle systems with uncertain parameters and inputs, where the uncertainties are bound to given intervals. The method is evaluated on the plant model of an experimental electro-mechanical braking system with periodic controller. In this model, the fast-switching controller dynamics requires simulation time scales of the order of nanoseconds. Accurate set-based com…
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 paper studies the formation stabilization problem of asynchronous nonlinear multi-agent systems (MAS) subject to parametric uncertainties, external disturbances and bounded time-varying communication delays. A self-triggered min-max distributed model predictive control (DMPC) approach is proposed to handle these practical issues. At triggering instants, each agent solves a local min-max optimization problem based on local system states and predicted system states of neighbors, determines its next triggering instant and broadcasts its predicted state trajectory to its neighbors. As a resul…
This paper addresses the problem of distributed secondary voltage control of an islanded microgrid (MG) from a cyber-physical perspective. An event-triggered distributed model predictive control (DMPC) scheme is designed to regulate the voltage magnitude of each distributed generators (DGs) in order to achieve a better trade-off between the control performance and communication and computation burdens. By using two novel event triggering conditions that can be easily embedded into the DMPC for the application of MG control, the computation and communication burdens are significantly reduced wi…
