Sampled-data observer design for delayed output-injection state-affine systems. (English) Zbl 1454.93154
Summary: We are considering the problem of observer design for a general class of state-affine systems in presence of output delay and sampling. Two novelties characterize the considered class of systems: (i) the state equation is subject to output injection involving future output values (not accessible to measurement); (ii) the injected output values come in the state equation not only through a driving term but also through the state matrix. These novel characteristics entail the loss of the system state-affine nature and lead to a new observer design problem never investigated so far. The solution we develop in this paper is a sampled-data based observer of Kalman-like type, augmented with inter-sample predictors and signal saturations. Using both Lyapunov and small-gain arguments, we show that the observer is exponentially convergent for sufficiently small sampling interval and delay, provided an observability condition is satisfied.
MSC:
| 93C57 | Sampled-data control/observation systems |
| 93B53 | Observers |
| 93C43 | Delay control/observation systems |
References:
| [1] | Ahmed-Ali, T.; Cherrier, E.; Lamnabhi-Lagarrigue, F., Cascade high gain predictors for a class of nonlinear systems, IEEE Transactions on Automatic Control, 57, 1, 221-226 (2012) · Zbl 1369.93003 · doi:10.1109/TAC.2011.2161795 |
| [2] | Ahmed-Ali, T.; Fridman, E.; Giri, F.; Burlion, L.; Lamnabhi-Lagarrigue, F., Using exponential time-varying gains for sampled-data stabilization and estimation, Automatica, 67, 244-251 (2016) · Zbl 1335.93083 · doi:10.1016/j.automatica.2016.01.048 |
| [3] | Ahmed-Ali, T.; Giri, F.; Krstic, M.; Kahelras, M., PDE based observer design for nonlinear systems with large output delay, Systems & Control Letters, 113, 1-8 (2018) · Zbl 1386.93054 · doi:10.1016/j.sysconle.2018.01.001 |
| [4] | Ahmed-Ali, T.; Karafyllis, I.; Krstic, M.; Lamnabhi-Lagarrigue, F.; Malisoff, M.; Mazenc, F.; Pepe, P.; Karafyllis, I., Robust stabilization of nonlinear globally Lipschitz delay systems, Recent results on nonlinear time delayed systems, 43-60 (2016), Basel: Springer, Basel · Zbl 1384.93127 |
| [5] | Ahmed-Ali, T.; Karafyllis, I.; Lamnabhi-Lagarrigue, F., Global exponential sampled-data observers for nonlinear systems with delayed measurements, Systems and Control Letters, 62, 7, 539-549 (2013) · Zbl 1277.93051 · doi:10.1016/j.sysconle.2013.03.008 |
| [6] | Ahmed-Ali, T.; Van Assche, V.; Massieu, J. M.; Dorleans, P., Continuous-Discrete observer for state affine systems with sampled and delayed measurements, IEEE Transactions on Automatic Control, 58, 4, 1085-1091 (2013) · Zbl 1369.93358 · doi:10.1109/TAC.2012.2225555 |
| [7] | Besançon, G.; Bornard, G.; Hammouri, H., Observer synthesis for a class of nonlinear control systems, European Journal of Control, 2, 176-192 (1996) · Zbl 0864.93018 · doi:10.1016/S0947-3580(96)70043-2 |
| [8] | Besançon, G.; De Leön-Morales, J.; Huerta-Guevara, O., On adaptive observers for state affine systems, International Journal of Control, 79, 6, 581-591 (2006) · Zbl 1179.93109 · doi:10.1080/00207170600552766 |
| [9] | Besancon, G., Georges, D., and Benayache, Z. (2007). Asymptotic state prediction for continuous-time systems with delayed input and application to control. In European Control Conference, Kos, Greece, pp. 1786-1791. |
| [10] | Besançon, G.; Ticlea, A., An Immersion-based observer design for rank-observable nonlinear systems, IEEE Transactions on Automatic Control, 52, 1, 83-88 (2007) · Zbl 1366.93193 · doi:10.1109/TAC.2006.889867 |
| [11] | Cacace, F.; Germani, A.; Manes, C., An observer for a class of nonlinear systems with time varying observation delay, Systems & Control Letters, 59, 5, 305-312 (2010) · Zbl 1191.93016 · doi:10.1016/j.sysconle.2010.03.005 |
| [12] | Cacace, F.; Germani, A.; Manes, C., A chain observer for nonlinear systems with multiple time-varying measurement delays, SIAM Journal on Control and Optimization, 52, 3, 1862-1885 (2014) · Zbl 1295.93019 · doi:10.1137/120876472 |
| [13] | Folin, T.; Ahmed-Ali, T.; Giri, F.; Burlion, L.; Lamnabhi-Lagarrigue, F., Sampled-data adaptive observer for a class of state-affine output-injection nonlinear systems, IEEE Transactions on Automatic Control, 61, 2, 462-467 (2016) · Zbl 1359.93063 |
| [14] | Fridman, E., Introduction to time-delay systems: Analysis and control (2014), Basel: Birkhauser, Basel · Zbl 1303.93005 |
| [15] | Germani, A.; Manes, C.; Pepe, P., A new approach to state observation of nonlinear systems with delayed output, IEEE Transactions on Automatic Control, 47, 1, 96-101 (2002) · Zbl 1364.93371 · doi:10.1109/9.981726 |
| [16] | Hespanha, J.; Naghshtabrizi, P.; Xu, Y., A survey of recent results in networked control systems. Proc. Of the IEEE, Special Issue on Technology of Networked Control Systems, 95, 1, 138-162 (2007) |
| [17] | Kahelras, M.; Ahmed-Ali, T.; Folin, T.; Giri, F.; Lamnabhi-Lagarrigue, F., Observer design for Triangular nonlinear systems using delayed sampled-output measurements (2016) |
| [18] | Kahelras, M.; Ahmed-Ali, T.; Giri, F.; Lamnabhi-Lagarrigue, F., Sampled-data chain-observer design for a class of delayed nonlinear systems, International Journal of Control, 91, 5, 1076-1090 (2018) · Zbl 1390.93511 · doi:10.1080/00207179.2017.1305512 |
| [19] | Karafyllis, I.; Kravaris, C., From continuous-time design to sampled-data design of observers, IEEE Transactions on Automatic Control, 54, 9, 2169-2174 (2009) · Zbl 1367.93350 · doi:10.1109/TAC.2009.2024390 |
| [20] | Karafyllis, I.; Krstic, M., Stabilization of nonlinear delay systems using approximate predictors and high-gain observers, Automatica, 49, 3623-3631 (2013) · Zbl 1315.93063 · doi:10.1016/j.automatica.2013.09.006 |
| [21] | Karafyllis, I.; Malisoff, M.; Mazenc, F.; Pepe, P., Recent results on nonlinear delay control systems (2016), Basel: Springer, Basel |
| [22] | Kazantzis, N.; Wright, R. A., Nonlinear observer design in the presence of delayed output measurements, Systems & Control Letters, 54, 9, 877-886 (2005) · Zbl 1129.93333 · doi:10.1016/j.sysconle.2004.12.005 |
| [23] | Krstic, M., Delay compensation for nonlinear, adaptive, and PDE systems (2009), Boston: Birkhäuser, Boston · Zbl 1181.93003 |
| [24] | Léchappé, V.; De Leon, J.; Moulay, E.; Plestan, F.; Glumineau, A., Delay and state observer for SISO LTI systems (2015) |
| [25] | Michiels, W. and Niculescu, S.-I. (2014). Stability, control and computation for time-delay systems. An eigenvalue based approach. SIAM, Philadelphia, Series: “Advances in design and control”, vol. DC 27. · Zbl 1305.93002 |
| [26] | Raff, T.; Kögel, M.; Allgöwer, F., Observer with sample-and-hold Updating for Lipschitz nonlinear systems with Nonuniformly sampled measurements, 5254-5257 (2008) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
