Self-triggering in nonlinear systems: A small gain theorem approach

Abstract

This paper investigates stability of nonlinear con trol systems under intermittent information. Building on the small-gain theorem, we develop self-triggered control yielding stable closed-loop systems. We take the violation of the small gain condition to be the triggering event, and develop a sam pling policy that precludes this event by executing the control law with up-to-date information. Based on the properties of the external inputs to the plant, the developed sampling policy yields regular stability, asymptotic stability and Lp-stability.Control loops are modeled as interconnections of hybrid sys tems, and novel results on Lp-stability of hybrid systems are presented. Prediction of the triggering event is achieved by employing Lp-gains over a finite horizon. In addition, Lp-gains over a finite horizon produce larger intersampling intervals when compared with standard Lp-gains. Furthermore, a novel approach for calculation of Lp-gains over a finite horizon is devised. Finally, our approach is successfully applied to a trajectory tracking control system.

Event-Triggered Control of Nonlinear Systems With Updating Threshold

“…The event-based strategies require the constant monitoring of a certain mechanism. In order to reduce the computation time and resources, self-triggered control methodologies were proposed where the next controller update time is generated based on the last measurement of the system's state, see for instance [1], [2], [13], [25], [26]. Several of the aforementioned works require certain inputto-state stability (ISS) assumptions.…”

Self- Triggered Control under Actuator Delays

“…Analogous techniques have also been used for a variety of problems, see for instance [3], [9], [13], [14], [17], [18], and [30]. To avoid the constant monitoring of the state, self-triggered techniques have been utilized for linear systems in [15], [27], [28], and [29], and for nonlinear systems in [1], [2], [11], [13], [16], [24], [25]. In particular, homogeneity and ISS assumptions were exploited in [1], small-gain conditions in [13] and [25] and high-gain designs in [16].…”

Aperiodic triggering mechanisms for networked control systems

“…This scheme does not require con- 52 tinuous checking of the state, rather it predicts update time on the basis of previously sampled state and plant dynamics. 53 Hence, ET mechanism is reactive and ST is proactive. 54 In literature, ET scheme is referred using various terminologies such as, event-based sampling, event-driven sampling, 55 Lebesgue sampling, dead-band sampling, send-on-delta sampling, level-crossing sampling, and state-triggered sampling.…”

“…For sampled data system (40) along with the assumptions stated above, ST sampler, kf ðx à ; jðx k Þ; d à Þk ensures GUUB of the closed-loop system, with L ¼ L f ;u L j;x and ðx à ; d Ã Þ :¼ argmax ðy 1 ;y 2 Þ2R n ÂD d kf ðy 1 ; jðx k Þ; y 2 Þk. h Small-gain approach was used in[53] to develop STC, whereby the violation of small-gain condition marks a sampling 920 event and computation of fresh control law, yielding a stable nonlinear system. Additionally, the approach does not require 921 construction of a Lyapunov function.…”