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.
This paper proposes a method to synthesise controllers for cyber-physical systems such that the controlled systems satisfy specifications given as linear temporal logic formulas. The focus is on systems with disturbance, where future states cannot be predicted exactly due to uncertainty in the environment. The approach used to solve this problem is to first construct a finite-state abstraction of the original system and then synthesise a controller for the abstract system. For this approach, the robust stutter bisimulation relation is introduced, which preserves the existence of controllers fo…
This paper investigates the design of self-triggered controllers for networked control systems (NCSs), where the dynamics of the plant is \textit{unknown} apriori. To deal with the unknown transition dynamics, we employ the Gaussian process (GP) regression in order to learn the dynamics of the plant. To design the self-triggered controller, we formulate an optimal control problem, such that the optimal control and communication policies can be jointly designed based on the GP model of the plant. Moreover, we provide an overall implementation algorithm that jointly learns the dynamics of the pl…
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…
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…
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…
This paper studies the problem of stabilizing a self-triggered control system with quantized output. Employing a standard observer-based state feedback control law, a self-triggering mechanism that dictates the next sampling time based on quantized output is co-developed with an output encoding scheme. If, in addition, the transmission protocols at the controller-to-actuator (C-A) and sensor-to-controller (S-C) channels can be adapted, the self-triggered control architecture can be considerably simplified, leveraging a delicate observer-based deadbeat controller to eliminate the need for runni…
Learning event-triggered controllers for linear parameter-varying systems from data
State Key Laboratory of Robotics and Systems, Harbin Institute of Technology（哈尔滨工业大学机器人技术与系统国家重点实验室）；Nanyang Technological University（南洋理工大学）；The Hong Kong Polytechnic University（香港理工大学）；Adelaide University（阿德莱德大学）
Adaptive Event-triggered Control with Sampled Transmitted Output and Controller Dynamics
School of Artificial Intelligence and Automation, Huazhong University of Science and Technology（华中科技大学人工智能与自动化学院）；Key Laboratory of Imaging Processing and Intelligence Control（图像处理与智能控制重点实验室）
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…
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…
We propose a symbolic self-triggered controller synthesis procedure for non-deterministic continuous-time nonlinear systems without stability assumptions. The goal is to compute a controller that satisfies two objectives. The first objective is represented as a specification in a fragment of LTL, which we call 2-LTL. The second one is an energy objective, in the sense that control inputs are issued only when necessary, which saves energy. To this end, we first quantise the state and input spaces, and then translate the controller synthesis problem to the computation of a winning strategy in a …
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 al…
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…
The wide adoption of wireless devices in the Internet of Things requires controllers that are able to operate with limited resources, such as battery life. Operating these devices robustly in an uncertain environment, while managing available resources, increases the difficultly of controller design. This paper proposes a robust self-triggered model predictive control approach to optimize a control objective while managing resource consumption. In particular, a novel zero-order-hold aperiodic discrete-time feedback control law is developed to ensure robust constraint satisfaction for continuou…
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…
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…
Consider a network of multiple independent stochastic linear systems where, for each system, a scheduler collocated with the sensors arbitrates data transmissions to a corresponding remote controller through a shared contention-based communication network. While the systems are physically independent, their optimal controller design problems may, in general, become coupled, due to network contention, if the schedulers trigger transmissions based on state-dependent events. In this article we propose a class of probabilistic admissible schedulers for which the optimal controllers, with respect t…
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 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…
We present a data-based approach to design event-triggered state-feedback controllers for unknown continuous-time linear systems affected by disturbances. By an event, we mean state measurements transmission from the sensors to the controller over a digital network. By exploiting a sufficiently rich finite set of noisy state measurements and inputs collected off-line, we first design a data-driven state-feedback controller to ensure an input-to-state stability property for the closed-loop system ignoring the network. We then take into account sampling induced by the network and we present robu…
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 e…
We extend previous work on symbolic self-triggered control for non-deterministic continuous-time nonlinear systems without stability assumptions to a larger class of specifications. Our goal is to synthesise a controller for two objectives: the first one is modelled as a right-recursive LTL formula, and the second one is to ensure that the average communication rate between the controller and the system stays below a given threshold. We translate the control problem to solving a mean-payoff parity game played on a discrete graph. Apart from extending the class of specifications, we propose a h…
We consider abstraction-based design of output-feedback controllers for dynamical systems with a finite set of inputs and outputs against specifications in linear-time temporal logic. The usual procedure for abstraction-based controller design (ABCD) first constructs a finite-state abstraction of the underlying dynamical system, and second, uses reactive synthesis techniques to compute an abstract state-feedback controller on the abstraction. In this context, our contribution is two-fold: (I) we define a suitable relation between the original system and its abstraction which characterizes the …
This paper focuses on the issue of how to realize spacecraft attitude control with guaranteed performance while conspicuously reducing the actuator acting frequency simultaneously. The prescribed performance control (PPC) scheme is often employed for the control with guaranteed performance. However, conventional PPC controllers are designed from the perspective of continuous system, which contradicts the "discrete" control logic in actual spacecraft control system, and such a problem limited the application value of PPC scheme in actual applications. In order to significantly lower the actuato…
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…
On the trade-off between control performance and communication cost in event-triggered control
ACCESS Linnaeus Centre, School of Electrical Engineering, KTH Royal Institute of Technology（皇家理工学院电气工程学院）；University of Notre Dame（圣母大学）；University of Newcastle（纽卡斯尔大学）
RWTH Aachen University（亚琛工业大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；IAV GmbH Ingenieurgesellschaft Auto und Verkehr（IAV汽车与交通工程有限公司）
Robust controllers ensure stability in feedback loops designed under uncertainty but at the cost of performance. Model uncertainty in time-invariant systems can be reduced by recently proposed learning-based methods, which improve the performance of robust controllers using data. However, in practice, many systems also exhibit uncertainty in the form of changes over time, e.g., due to weight shifts or wear and tear, leading to decreased performance or instability of the learning-based controller. We propose an event-triggered learning algorithm that decides when to learn in the face of uncerta…
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…
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 …
