Robust H∞ Triggered Control of Linear Systems
Keywords:
vent-triggered control, Self-triggered control, Robust H1 control, Cart and pendulum systemvent-triggered control, Cart and pendulum systemEAbstract
In this paper, we study the impact of triggered control strategies for a class of uncertain linear systems. The event condition is proposed based on the relative error between the current state and the state at last sample time. We introduce robust H∞ theory into self-triggered sample strategy, and achieve both resource utilization and disturbance attenuation properties. We investigate the full-information feedback H∞ control for the perturbed linear system and develop a linear matrix inequality (LMI)-based sufficient condition guaranteeing the robust asymptotic stability of the closed-loop system. Employing a self-triggered control, we provide a method of designing the longest sampling period for the relevant H∞ controller when the system is stabilized and robust. A cart and pendulum example is given to show the efficiency of the theoretical result.
References
J. P. Hespanha, P. Naghshtabrizi and Y. Xu, A survey of recent results in networked controlled systems, Proc. the IEEE, vol. 95, no. 1, pp. 138–162, 2007.
L. A. Montestruque and P. Antsaklis, Stability of model-based networked control systems with time varying transmission times, IEEE Trans. Autom. Control, vol. 49, no. 9, pp. 1562–1572, 2004.
[3] E. Hendricks, M. Jensen, A. Chevalier, and T. Vesterholm, Problems in event based engine control, Proc. Amer. Control Conf., vol. 2, pp. 1585-1587, 1994.
K. J. Astrom and B. M. Bernhardsson, Comparison of periodic and event based sampling for first order stochastic systems, Proc. IFAC World Conf., pp. 301-306, 1999.
K.-E. Arzn, A simple event-based PID controller, Preprints IFAC World Conf., vol. 18, pp. 423-428, 1999.
W. P. M. H. Heemels, R. J. A. Gorter, A. van Zijl, P. P. J. van den Bosch, S. Weiland, W. H. A. Hendrix, and M. R. Vonder, Asynchronous measurement and control: A case study on motor synchronization, Control Engineering Practice, vol. 7, pp. 1467-1482, 1999.
K. J. Astrom, Event based control, in Analysis and design of nonlinear control systems, Part 3, 2008, pp. 127–147.
M. Velasco, P. Martl, and E. Bini, Control-driven tasks: modeling and analysis, Proc. the Real-Time Systems Symposium, pp. 280-290, Barcelona, Spain, 2008.
M. Mazo and P. Tabuada, On event-triggered and self-triggered control over sensor/actuator networks, Proc. the 47th IEEE Conference on Decision and Control, (CDC08), pp. 435-440, 2008.
P. Tabuada, Event-triggered real-time scheduling of stabilizing control tasks, IEEE Trans. Automatic Control, vol. 52, no. 9, pp. 1680-1685, 2007.
W. P. M. H. Heemels, J. H. Sandee, and P. P. J. Van Den Bosch, Analysis of event-driven controllers for linear systems, Int. J. Control, vol. 81, no. 4, pp. 571-590, 2008.
M. C. F. Donkers and W. P. M. H. Heemels, â€Output-based event-triggered control with guaranteed L1-gain and improved event-triggeringâ€, Proc. 49th IEEE Conference on Decision and Control, Hilton Atlanta Hotel, Atlanta, GA, USA, pp. 3246–3251, 2010.
H. Yu and P. J. Antsaklis, â€Event-triggered output feedback control for networked control systems using passivity: time-varying network induced delaysâ€, Proc. 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), pp. 205–210, 2011.
L. Li and M. Lemmon, â€Event-triggered output feedback control of finite horizon discrete-time multi-dimensional linear processesâ€, Proc. 49th IEEE Conference on Decision and Control (CDC), pp. 3221–3226, 2010.
L. Li and M. Lemmon, â€Weakly coupled event triggered output feedback system in wireless networked control systemsâ€, Discrete Event Dynamic Systems, pp. 1–14, 2013.
M. S. Mahmoud, Resilient Control of Uncertain Dynamical Systems, Springer, Heidelberg, 2004.
M. S. Mahmoud, â€Resilient Decentralized Stabilization of Interconnected Discrete-Time Systemsâ€, J. Optimization Theory and Applications, vol. 145, no. 3, pp. 507–525, 2010.
M. S. Mahmoud and Naif B Almutairi, â€Resilient Decentralized Stabilization of Interconnected Time-Delays Systems with Polytopic Uncertaintiesâ€, Int. J. Robust and Nonlinear Control, vol. 21, no. 1, pp. 355–372, 2011.
E. Kaufman and J. H. Braslavsky, Level crossing sampling in feedback stabilization under data-rate constraints, Proc. the 45th IEEE Conf. on Decision and Control, pp. 4423–4428, 2006.
K. J. Astrom and B. M. Bernhardsson, Comparison of Riemann and Lebesgue sampling for first order stochastic systems, Proc. Conf. Decision Control, pp. 2011-2016, 2002.
T. Henningsson, E. Johannesson, and A. Cervin, Sporadic event-based control of first-order linear stochastic systems, Automatica, vol. 44, pp. 2890-2895, 2008.
J. Lunze and D. Lehmann, A state-feedback approach to event-based control, Automatica, vol. 46, pp. 211-215, 2010.
P. J. Gawthrop and L. B. Wang, Event-driven intermittent control, Int. J. Control, vol. 82, pp. 2235-2248, 2009.
T. Estrada and P. J. Antsaklis, Stability of discrete-time plants using model-based control with intermittent feedback, Proc. Mediterranean Conf. Control Autom., pp. 1130-1136, 2008.
X. Wang and M. D. Lemmon, Event-triggering in distributed net-worked systems with data dropouts and delays, Proc. Conf. Hybrid Syst.: Comput. Control, pp. 366-380, 2009.
P. Tabuada, Event-triggered real-time scheduling of stabilizing control tasks, IEEE Trans. Autom. Control, vol. 52, no. 9, pp. 1680-1685, 2007.
A. Anta, and P. Tabuada, Self-triggered stabilization of homogeneous control systems, Proc. the American Control Conference, pp. 4129-4134, 2008.
E. Kofman and J. H. Braslavsky, Level crossing sampling in feedback stabilization under data-rate constraints, Proc. IEEE Conf. Decision Control, pp. 4423-4428, 2006.
P. Otanez, J. Moyne, and D. Tilbury, Using dead bands to reduce communication in networked control systems, Proc. Amer. Control Conf., pp. 3015-3020, 2002.
M. Miskowicz, Send-on-delta concept: An event-based data-reporting strategy, Sensors, vol. 6, pp. 49-63, 2006.
B. Liu, Y. Xia, M. S. Mahmoud and H. Wu, New predictive control scheme for networked control systems, J. Circuits, Systems and Signal Processing, vol. 31, no. 2, pp. 945–960, 2012.
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