Event-Driven Communication for Sampled-Data Control Systems* Xiangyu Meng 1 and Tongwen Chen 1 Abstract— In this paper, a sampled-data event detection strategy is proposed for linear continuous-time systems, whose output is sampled periodically to be tested for determining the transmission. Dynamic logic conditions are provided to char- acterize the asymptotic stability property for event-triggered control systems by defining discrete Lyapunov functions. State and output feedback control laws with event-driven communi- cation are proposed such that the states of event based control systems converge to zero eventually, in the regulation setting. Some examples are presented which demonstrate the utility of this new definition. I. INTRODUCTION Event based control has been investigated comprehen- sively as an alternative means to reduce communication requirements between interconnected subsystems for the sake of more easily scheduling the overall system. Specifically, the event based control idea has proved useful in networked control systems [1], multi-agent systems [2], [3], [4] and decentralized systems [5], and in many cases it outperforms the traditional time-triggered control [6], [7]. Lyapunov technique is the workhorse of stability analysis for event based control systems [8]. In existing results, the control law is designed in advance to guarantee the global asymptotic stability of the continuous closed-loop system, and then construct an event condition to combine this pas- sivity information comprising the event based control system. The stability is then ensured by updating the controller when possible violation of particular event condition occurs. The main advantage of this methodology is that the stability relies on passivity inequalities as abstractions of their detailed dynamical models. However, there are two deficiencies in this technique. The first is that the continuous Lyapunov function is required to be monotonically decreasing in the event based control system as it is in the continuous system; this, however, is not necessary as shown in [9]. Second, the event detectors based on dissipation inequalities as well as other continuous event detectors assume that sampling at event instants is instantaneous. As pointed out in [6], It is more realistic to approximate the continuous supervision by a high fast rate sampling. To implement the continuous event detectors also requires delicate hardware to monitor the output signal and judge the logic condition constantly; this may become a major source of energy consumption. Based on the above observation, the concept of a discrete event detector is defined as periodic evaluation of the event *This work was supported by NSERC and an iCORE PhD Recruitment Scholarship from the Province of Alberta. 1 The authors are with the Department of Electrical and Computer Engineering, University of Alberta, AB T6G2V4, Canada xmeng2 at ualberta.ca; tchen at ualberta.ca condition. The asymptotic stability property is characterized by a discrete Lyapunov function, which eliminates the need for dissipative inequalities. This discrete event detector is also a predictor, which predicts the value of the discrete Lyapunov function at next few sampling instants. If the predicted values will exceed a pre-specified threshold, an event is generated in advance to bound the discrete Lyapunov function by the current threshold until a new threshold is calculated. The discrete Lyapunov function is not required to decrease at each sampling instants, but to be bounded. The monotonically decreasing requirement is thus relaxed. Event based state and output feedback control algorithms are proposed for solving asymptotical stability problem with the aid of ideas from switched systems. In addition to the commonly used analog controller design method for event based control, the digital controller design method is also given to facilitate the utilization of a discrete-time event detector. Compared with traditional sampled-data control, the key advantage of the proposed technique is that it arrives at less communication bandwidth usages which ensuring that the system is asymptotically stable. The main contributions of this paper are summarized as follows: (a) suggest the utilization of discrete event detectors which are superior to continuous ones for energy saving; (b) propose a unified framework of event based control algorithms with both state and output feedback, where the latter is a supplement to the existing literature since there are limited results available for event based control without availability of the state; (c) use both analog and digital methods to design event based controllers, where the digital design method is relatively new for the event based control paradigm. II. THE GENERAL STRUCTURE AND PRELIMINARIES The typical topology structure of an event based control system is shown in Fig. 1, which consists of the process, an ideal sampler, a discrete event detector, a discrete controller, and a zero-order hold (ZOH) operator. In this figure, the signals are transmitted continuously along the solid lines, periodically along the dotted line, and intermittently based on events along the dashed line. Suppose the physical process is given by G : ˙ x (t)= Ax (t)+ Bu (t) , y (t)= Cx (t) . (1) Here x (t) ∈ R n is the state vector; y (t) ∈ R m is the measured output; u (t) ∈ R p is the control input; A,B,C are system matrices with appropriate dimensions. The plant 2013 American Control Conference (ACC) Washington, DC, USA, June 17-19, 2013 978-1-4799-0176-0/$31.00 ©2013 AACC 3008