In this paper, both event-triggered and self-triggered transmission strategies are proposed for dynamical systems subject to actuator saturation. The designed triggering condition, which is expected to save more network resources, is closely related to the cases where either the actuator saturates or it does not. The linear quadratic optimal control method is utilized to guarantee the asymptotic stability of the closed-loop systems. Global and local stability results are considered, respectively. For local stability, two sufficient conditions are presented to derive the asymptotic stability region. The minimum inter-transmission time of the proposed triggering mechanism is explicitly formulated to eliminate the Zeno behaviour. Finally, an example is provided to demonstrate the effectiveness of the theoretical results.
AströmKJBernhardssonB (2002) Comparison of Riemann and Lebesque sampling for first order stochastic systems. In: Proceedings of the 41st IEEE Conference on Decision and Controlvol. 2, Las Vegas, Nevada USA, pp. 2011–2016.
2.
ChenTFrancisBHagiwaraT (1998) Optimal sampled-data control systems. Proceedings of the IEEE86(4): 741–741.
3.
DaigleMJKoutsoukosXDBiswasG (2009) An event-based approach to integrated parametric and discrete fault diagnosis in hybrid systems. Transactions of the Institute of Measurement and Control36(8): 1074–1082.
4.
GoebelRTeelAR (2006) Solutions to hybrid inclusions via set and graphical convergence with stability theory applications. Automatica42(4): 573–587.
5.
HeemelsWPMHGorterRJAvan ZijlA. (1999) Asynchronous measurement and control: A case study on motor synchronization. Control Engineering Practice7(12): 1467–1482.
6.
Hristu–VarsakelisDKumarPR (2002) Interrupt-based feedback control over a shared communication medium. In: Proceedings of the 41st IEEE Conference on Decision and Controlvol. 3, Las Vegas, Nevada USA, pp. 3223–3228.
7.
JiangXHanQLLiuS. (2008) A new stabilization criterion for networked control systems. IEEE Transactions on Automatic Control53(4): 1025–1032.
8.
KienerGA (2012) Event-triggered control subject to actuator saturation. Master’s Thesis, KTH, Sweden.
9.
LehmannDJohanssonKH (2012) Event-triggered PI control subject to actuator saturation. In: Proceedings of IFAC Conference on Advances in PID Control, Brescia, Italy, pp. 3262–3267.
10.
LinZ (1998) Global control of linear systems with saturating actuators. Automatica34(7): 897–905.
11.
LinZSaberiA (1993) Semi-global exponential stabilization of linear systems subject to input saturation via linear feedbacks. Systems and Control Letters21(3): 225–239.
12.
NiWZhaoPWangX. (2014) Event-triggered control of linear systems with saturated inputs. Asian Journal of Control17(4): 1–13.
13.
NowzariCCortsJ (2012) Self-triggered coordination of robotic networks for optimal deployment. Automatica48(6): 1077–1087.
14.
SanfeliceRGGoebelRTeelAR (2007) Invariance principles for hybrid systems with connections to detectability and asymptotic stability. IEEE Transactions on Automatic Control52(12): 2282–2297.
TarbouriechSGarciaGda SilvaJMGJr. (2011) Stability and Stabilization of Linear Systems with Saturating Actuators. London, UK: Springer Science and Business Media.
17.
VelascoMFuertesJMartiP (2003) The self triggered task model for real-time control systems. In: Work-in-Progress Session of the 24th IEEE Real-time Systems Symposium, Cancun, Mexico, pp. 67–70.
18.
VelascoMMartiPYpezJ. (2011) Qualitative analysis of a one-step finite-horizon boundary for event-driven controllers. In: 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, FL, 12–15 December 2011, pp. 1662–1667.
19.
WangXLemmonMD (2009) Self-triggered feedback control systems with finite-gain stability. IEEE Transactions on Automatic Control54(3): 452–467.
20.
WangXLemmonMD (2011) Event-triggering in distributed networked control systems. IEEE Transactions on Automatic Control56(3): 586–601.
21.
WhalleyR (1990) Multi-dimensional, sample data system stability. Transactions of the Institute of Measurement and Control12(1): 9–14.
22.
WuWReimannSLiuS (2014) Event-triggered control for linear systems subject to actuator saturation. In: Proceedings of the 19th IFAC World Congress, Cape Town, South Africa, 24–29 August, pp. 9492–9497.
23.
XieDYuanDLuJ. (2013) Consensus control of second-order leader-follower multi-agent systems with event-triggered strategy. Transactions of the Institute of Measurement and Control35(4): 426–436.
24.
YookJKTilburyDMSoparkarNR (2002) Trading computation for bandwidth: Reducing communication in distributed control systems using state estimators. IEEE Transactions on Control Systems Technology10(4): 503–518.
25.
YpezJVelascoMMartiP. (2011) One-step finite horizon boundary with varying control gain for event-driven networked control systems. In: IECON 2011-37th Annual Conference on IEEE Industrial Electronics Society, Melbourne, Australia, pp. 2606–2611.
26.
YuJWangLXieG (2010) Disturbance rejection of switched systems subject to actuator saturation. Transactions of the Institute of Measurement and Control32(6): 603–634.
