Set-membership estimation for linear time-varying descriptor systems. (English) Zbl 1436.93131
Summary: This paper considers the problem of set-membership estimation for discrete-time linear time-varying descriptor systems subject to unknown but bounded disturbance and noise. We propose a set-membership estimation method based on a descriptor system observer and a zonotopic estimator of the observer error bounds. The observer parameters are optimized in order to minimize the sizes of the zonotopes enclosing all admissible state trajectories. Finally, two simulation results are provided to demonstrate the effectiveness of the proposed method.
MSC:
| 93E10 | Estimation and detection in stochastic control theory |
| 93B53 | Observers |
| 93C55 | Discrete-time control/observation systems |
| 93C05 | Linear systems in control theory |
References:
| [1] | Alamo, T.; Bravo, J. M.; Camacho, E. F., Guaranteed state estimation by zonotopes, Automatica, 41, 6, 1035-1043 (2005) · Zbl 1091.93038 |
| [2] | Blanchini, F.; Miani, S., Set-theoretic methods in control (2008), Springer · Zbl 1140.93001 |
| [3] | Canale, M.; Fagiano, L.; Milanese, M., Set membership approximation theory for fast implementation of model predictive control laws, Automatica, 45, 1, 45-54 (2009) · Zbl 1154.93350 |
| [4] | Chernousko, F. L., Ellipsoidal state estimation for dynamical systems, Nonlinear Analysis. Theory, Methods & Applications, 63, 5, 872-879 (2005) · Zbl 1153.93345 |
| [5] | Combastel, C., Zonotopes and kalman observers: gain optimality under distinct uncertainty paradigms and robust convergence, Automatica, 55, 265-273 (2015) · Zbl 1377.93161 |
| [6] | Efimov, D.; Raïssi, T.; Chebotarev, S.; Zolghadri, A., Interval state observer for nonlinear time varying systems, Automatica, 49, 1, 200-205 (2013) · Zbl 1258.93032 |
| [7] | Efimov, D.; Raïssi, T.; Zolghadri, A., Control of nonlinear and LPV systems: interval observer-based framework, IEEE Transactions on Automatic Control, 58, 3, 773-778 (2013) · Zbl 1369.93546 |
| [8] | Fogel, E.; Huang, Y. F., On the value of information in system identification-bounded noise case, Automatica, 18, 2, 229-238 (1982) · Zbl 0433.93062 |
| [9] | Golub, G. H.; Van Loan, C. F., Matrix computations (1996), Johns Hopkins University Press: Johns Hopkins University Press Baltimore, MD, USA · Zbl 0865.65009 |
| [10] | Gouzé, J. L.; Rapaport, A.; Hadj-Sadok, M. Z., Interval observers for uncertain biological systems, Ecological Modelling, 133, 1, 45-56 (2000) |
| [11] | Hamdi, H.; Rodrigues, M.; Mechmeche, C.; Braiek, N. B., Robust fault detection and estimation for descriptor systems based on multi-models concept, International Journal of Control, Automation and Systems, 10, 6, 1260-1266 (2012) |
| [12] | Le, V. T.H.; Stoica, C.; Alamo, T.; Camacho, E. F.; Dumur, D., Zonotopic guaranteed state estimation for uncertain systems, Automatica, 49, 11, 3418-3424 (2013) · Zbl 1315.93077 |
| [13] | Markowitz, H., The optimization of a quadratic function subject to linear constraints, Naval Research Logistics Quarterly, 3, 1-2, 111-133 (1956) |
| [14] | Moisan, M.; Bernard, O.; Gouzé, J. L., Near optimal interval observers bundle for uncertain bioreactors, Automatica, 45, 1, 291-295 (2009) · Zbl 1154.93321 |
| [15] | Nikoukhah, R.; Willsky, A. S.; Levy, B. C., Kalman filtering and riccati equations for descriptor systems, (29th IEEE Conference on Decision and Control (1990)), 2886-2891 |
| [16] | Raïssi, T.; Efimov, D.; Zolghadri, A., Interval state estimation for a class of nonlinear systems, IEEE Transactions on Automatic Control, 57, 1, 260-265 (2012) · Zbl 1369.93074 |
| [17] | Scott, J. K.; Raimondo, D. M.; Marseglia, G. R.; Braatz, R. D., Constrained zonotopes: A new tool for set-based estimation and fault detection, Automatica, 69, 126-136 (2016) · Zbl 1338.93119 |
| [18] | Shamma, J. S.; Tu, K. Y., Set-valued observers and optimal disturbance rejection, IEEE Transactions on Automatic Control, 44, 2, 253-264 (1999) · Zbl 0958.93013 |
| [19] | Tang, W.; Wang, Z.; Wang, Y.; Raïssi, T.; Shen, Y., Interval estimation methods for discrete-time linear time-invariant systems, IEEE Transactions on Automatic Control, 64, 11, 4717-4724 (2019) · Zbl 1482.93337 |
| [20] | Wang, Z.; Lim, C. C.; Shen, Y., Interval observer design for uncertain discrete-time linear systems, Systems & Control Letters, 116, 41-46 (2018) · Zbl 1417.93086 |
| [21] | Wang, Y.; Olaru, S.; Valmorbida, G.; Puig, V.; Cembrano, G., Set-invariance characterizations of discrete-time descriptor systems with application to active mode detection, Automatica, 107, 255-263 (2019) · Zbl 1429.93216 |
| [22] | Wang, Y.; Puig, V.; Cembrano, G., Set-membership approach and kalman observer based on zonotopes for discrete-time descriptor systems, Automatica, 93, 435-443 (2018) · Zbl 1400.93295 |
| [23] | Wang, Z.; Shen, Y.; Zhang, X.; Wang, Q., Observer design for discrete-time descriptor systems: An LMI approach, Systems & Control Letters, 61, 6, 683-687 (2012) · Zbl 1250.93038 |
| [24] | Wang, Y.; Wang, Z.; Puig, V.; Cembrano, G., Zonotopic set-membership state estimation for discrete-time descriptor LPV systems, IEEE Transactions on Automatic Control, 64, 5, 2092-2099 (2019) · Zbl 1482.93071 |
| [25] | Xu, F.; Tan, J.; Wang, Y.; Wang, X.; Liang, B.; Yuan, B., Robust fault detection and set-theoretic UIO for discrete-time LPV systems with state and output equations scheduled by inexact scheduling variables, IEEE Transactions on Automatic Control, 64, 12, 4982-4997 (2019) · Zbl 1482.93246 |
| [26] | Zhang, J.; Swain, A. K.; Nguang, S. K., Robust \(H_\infty\) adaptive descriptor observer design for fault estimation of uncertain nonlinear systems, Journal of the Franklin Institute, 351, 11, 5162-5181 (2014) · Zbl 1307.93179 |
| [27] | Zhang, Y.; Yang, F.; Han, Q.; Zhu, Y., A novel set-membership control strategy for discrete-time linear time-varying systems, IET Control Theory & Applications, 13, 18, 3087-3095 (2019) |
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