Nonstandard anti-windup approach for event-triggered control purpose. (English) Zbl 1537.93465
Summary: This paper aims at designing both a nonstandard anti-windup action and an event-triggering mechanism that reduce the transmission activity on the network while preserving the asymptotic stability of a linear system under a dynamic output-feedback controller. The event-triggering policy is based on the use of an additional internal dynamic variable. The nonstandard anti-windup term, which uses the difference between the transmitted and the current control output, is added to the controller structure to further save the communication resources. Sufficient conditions in terms of matrix inequalities are proposed to compute the anti-windup gain and the triggering parameters while avoiding the Zeno behavior. Numerical algorithms with feasibility guarantees allow to reduce the amount of data transmissions. Through numerical examples, we illustrate the efficacy of the proposed approach.
MSC:
| 93C65 | Discrete event control/observation systems |
| 93D20 | Asymptotic stability in control theory |
| 93C05 | Linear systems in control theory |
| 93B52 | Feedback control |
Keywords:
event-triggered control; anti-windup; linear matrix inequalities; dynamic event-triggering mechanismReferences:
| [1] | W.P.M.H. Heemels, K.H. Johansson, P. Tabuada, An introduction to event-triggered and self-triggered control, in: 51th IEEE Conference on Decision and Control, Maui, Hawaii, 2012, pp. 3270-3285. |
| [2] | Tabuada, P., Event-triggered real-time scheduling of stabilizing control tasks, IEEE Trans. Automat. Control, 52, 9, 1680-1685, 2007 · Zbl 1366.90104 |
| [3] | Wang, X.; Lemmon, M. D., Event design in event-triggered feedback control systems, (47th IEEE Conference on Decision and Control, 2008, IEEE), 2105-2110 |
| [4] | Aström, K. J., Event based control, (Analysis and Design of Nonlinear Control Systems, 2008, Springer-Verlag: Springer-Verlag Berlin Heidelberg), 127-147 · Zbl 1189.93089 |
| [5] | Lunze, J.; Lehmann, D., A state-feedback approach to event-based control, Automatica, 46, 1, 211-215, 2010 · Zbl 1213.93063 |
| [6] | Zhang, J.; Feng, G., Event-driven observer-based output feedback control for linear systems, Automatica, 50, 7, 1852-1859, 2014 · Zbl 1296.93117 |
| [7] | Moreira, L. G.; Groff, L. B.; Gomes da Silva, J. M.; Tarbouriech, S., PI event-triggered control under saturating actuators, Internat. J. Control, 92, 7, 1634-1644, 2019 · Zbl 1417.93266 |
| [8] | De Souza, C.; Leite, V. J.S.; Tarbouriech, S.; Castelan, E. B.; Silva, L. F.P., A direct parameter-error co-design approach of discrete-time saturated LPV systems, IEEE Trans. Automat. Control, 2022 · Zbl 1537.93464 |
| [9] | Girard, A., Dynamic triggering mechanisms for event-triggered control, IEEE Trans. Automat. Control, 60, 7, 1992-1996, 2015 · Zbl 1360.93423 |
| [10] | S. Tarbouriech, A. Girard, LMI-based design of dynamic event-rriggering mechanism for linear systems, in: IEEE Conference on Decision and Control, CDC, Miami, USA, 2018, pp. 121-126. |
| [11] | Moreira, L. G.; Groff, L. B.; Gomes da Silva, J. M.; Tarbouriech, S., Event-triggered PI control for continuous plants with input saturation, (American Control Conference. American Control Conference, ACC, 2016, IEEE), 4251-4256 |
| [12] | Postoyan, R.; Tabuada, P.; Nešić, D.; Anta, A., A framework for the event-triggered stabilization of nonlinear systems, IEEE Trans. Automat. Control, 60, 4, 982-996, 2014 · Zbl 1360.93567 |
| [13] | Abdelrahim, M.; Postoyan, R.; Daafouz, J.; Nešić, D., Stabilization of nonlinear systems using event-triggered output feedback controllers, IEEE Trans. Automat. Control, 61, 9, 2682-2687, 2015 · Zbl 1359.93358 |
| [14] | Dinh, Q. T.; Gumussoy, S.; Michiels, W.; Diehl, M., Combining convex-concave decompositions and linearization approaches for solving BMIs, with application to static output feedback, IEEE Trans. Automat. Control, 57, 6, 1377-1390, 2011 · Zbl 1369.90170 |
| [15] | Tarbouriech, S.; Garcia, G.; Gomes da Silva, J.-M.; Queinnec, I., Stability and stabilization of linear systems with saturating actuators, 2011, Springer: Springer London · Zbl 1279.93004 |
| [16] | Tarbouriech, S.; Seuret, A.; Gomes da Silva, J.-M.; Sbarbaro, D., Observer-based event-triggered control co-design for linear systems, IET Control Theory Appl., 10, 18, 2466-2473, 2016 |
| [17] | Seuret, A.; Prieur, C.; Tarbouriech, S.; Zaccarian, L., LQ-based event-triggered controller co-design for saturated linear systems, Automatica, 74, 47-54, 2016 · Zbl 1348.93191 |
| [18] | P. Tallapragada, N. Chopra, Event-triggered dynamic output feedback control of LTI systems, in: 51th IEEE Conference on Decision and Control, Maui, Hawaii, 2012, pp. 6597-6602. |
| [19] | Tallapragada, P.; Chopra, N., On event triggered tracking for nonlinear systems, IEEE Trans. Automat. Control, 58, 9, 2343-2348, 2013 · Zbl 1369.93256 |
| [20] | Moreira, L. G.; Tarbouriech, S.; Seuret, A.; Gomes da Silva, J. M., Observer based event-triggered control in the presence of cone-bounded nonlinear inputs, Nonlinear Anal. Hybrid Syst., 33, 17-32, 2019 · Zbl 1429.93228 |
| [21] | Seuret, A., A novel stability analysis of linear systems under asynchronous samplings, Automatica, 48, 1, 177-182, 2012 · Zbl 1244.93095 |
| [22] | Yamamoto, Y., New approach to sampled-data control systems - a function space method, (Proceedings of the IEEE Conference on Decision and Control, 1990, IEEE: IEEE Honolulu), 1882-1887 |
| [23] | Briat, C.; Seuret, A., A looped-functional approach for robust stability analysis of linear impulsive systems, Systems Control Lett., 61, 10, 980-988, 2012 · Zbl 1270.93084 |
| [24] | Seuret, A.; Gomes da Silva, J.-M., Taking into account period variations and actuator saturation in sampled-data systems, Systems Control Lett., 61, 12, 1286-1293, 2012 · Zbl 1255.93083 |
| [25] | Briat, C., Convergence and equivalence results for the Jensen’s inequality - Application to time-delay and sampled-data systems, IEEE Trans. Automat. Control, 56, 7, 1660-1665, 2011 · Zbl 1368.26020 |
| [26] | Gomes da Silva, J. M.; Bender, F. A.; Tarbouriech, S.; Biannic, J. M., Dynamic anti-windup synthesis for state delayed systems: an lmi approach, (Conference on Decision and Control. Conference on Decision and Control, CDC, 2009, IEEE), 6904-6909 |
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