Integral‐based event‐triggered control scheme for a general class of non‐linear systems

Abstract

In this study, an integral-based event-driven mechanism is proposed for a general class of non-linear systems. The proposed scheme is less conservative than earlier work on the subject and achieves asymptotic stability without forcing the derivative of the Lyapunov function to be negative between samples. A rigorous proof is given, showing that the proposed triggering condition is more effective than the corresponding traditional approaches. Simulation results are provided to illustrate the effectiveness of the proposed solution. IntroductionMost digital control systems encountered today operate under the assumption that sampling takes place at regular intervals. 'Periodic' or 'time-driven' sampling is well understood and control design for such systems can be done following techniques analogous to the continuous time case. See for example [1,2]. In a time-driven system, the periodic nature of the information flow forces the controller to perform real-time computations and update information at every sample, consuming valuable computer time and demanding communication between different system components, even if the signals measured by the sensors experience no significant change. This issue makes time-driven systems potentially inefficient with respect to communication channel capacity and resource utilisation which may be significant when dealing with distributed and networked systems, where optimal usage of communication network capacity is of great preference, or embedded microprocessor systems with limited computational power and memory storage. Over the last several years, event-triggered systems have emerged as an attractive alternative to time-driven systems. In an event-driven system, information is exchanged between system components only if a pre-specified triggering condition (TC) is violated [3]. This condition can be defined in a number of ways, depending on the nature of the system. For example, in a power grid, a fault can be considered as an event, triggering a control action in the system [4]. Generally speaking, in most systems, an event occurs when changes in the sensor readings exceed a certain threshold [5]. Early works on event-based systems were proposed in late 1990s [6,7]. Because of use of different triggering strategies, event-triggered systems have also been called 'level crossing sampling' [8], 'event-driven systems' [9] and 'state-triggered feedback systems' [10].A fundamental contribution in the theory of event-driven systems was reported in reference [5]. In this paper, Tabuada formulated an input-to-state stable (ISS) Lyapunov function framework for event triggering design of a general class of non-linear systems. Assuming that a continuous-time feedback control has been already designed, Tabuada proposes an event generator condition to maintain the Lyapunov function V decreasing along the system trajectories. The work is important in that it provides a solid theoretical foundation to the fundamental stability problem of time-driven systems using classical tools. Following Tabuad...

Decentralized Integral-Based Event-Triggered Stabilization for Linear Plant with Actuator Saturation and Output Feedback

“…Similar to the analysis in [15] (Theorem 2), the integral-based event condition (4) is better than the relative one to some degree.…”

“…[15], the centralised state feedback was considered, and it was proved that the positive minimum inter-event time can be ensured automatically by the integral part of the event condition (4). According to [22,24], however, it is difficult to avoid Zeno behaviors in both the decentralised and the output feedback configurations.…”

“…The latest survey on event-triggered control can be found in [13,14]. To further improve the sampling performance, such as enlarging the average inter-event time or equivalently decreasing the sampling numbers within a fixed time interval, a novel integral-based event-triggered control scheme was recently proposed in [15,16].…”

“…Compared to [25], a different mathematical technique (which is based on the Cauchy-Schwarz inequality) is employed to design these intervals analytically from the integral-based event conditions. To the best of our knowledge, the existing contributions on integral-based event-triggered control (see, e.g., [15,16,26]) did not involve the decentralised output feedback configuration and/or the saturated input signals.…”

A novel integral-based event triggering control for linear time-invariant systems

“…In this paper, we propose a novel integralbased triggering condition (IBTC) for LTI systems that guarantees asymptotic stability of the event-based system while lessening the conservatism of [4]. This concept was recently explored by the authors in reference [9], in the more general case of nonlinear plants.…”