| Title:
|
Finite element-based observer design for nonlinear systems with delayed measurements (English) |
| Author:
|
Rehák, Branislav |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
55 |
| Issue:
|
6 |
| Year:
|
2019 |
| Pages:
|
1050-1069 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper presents a computational procedure for the design of an observer of a nonlinear system. Outputs can be delayed, however, this delay must be known and constant. The characteristic feature of the design procedure is computation of a solution of a partial differential equation. This equation is solved using the finite element method. Conditions under which existence of a solution is guaranteed are derived. These are formulated by means of theory of partial differential equations in $L^2$-space. Three examples demonstrate viability of this approach and provide a comparison with the solution method based on expansions into Taylor polynomials. (English) |
| Keyword:
|
nonlinear observer |
| Keyword:
|
delayed-output system |
| Keyword:
|
finite element method |
| MSC:
|
65P99 |
| MSC:
|
93C10 |
| idZBL:
|
Zbl 07217226 |
| idMR:
|
MR4077144 |
| DOI:
|
10.14736/kyb-2019-6-1050 |
| . |
| Date available:
|
2020-05-20T15:20:50Z |
| Last updated:
|
2020-08-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148091 |
| . |
| Reference:
|
[1] G., Birkhoff,, M., Lane, S.: A Survey of Modern Algebra..CRC Press, 2017. MR 0054551, 10.1201/9781315275499 |
| Reference:
|
[2] A., Borri,, F., Cacace,, De, Gaetano, A., A., Germani,, C., Manes,, P., Palumbo,, S., Panunzi,, P., Pepe,: Luenberger-like observers for nonlinear time-delay systems with application to the artificial pancreas: The attainment of good performance..IEEE Control Syst. 37 (2017), 4, 33-49. MR 3701062, 10.1109/mcs.2017.2696759 |
| Reference:
|
[3] F., Cacace,, A., Germani,, C., Manes,: An observer for a class of nonlinear systems with time varying observation delay..Systems Control Lett. 59 (2010), 305-312. Zbl 1191.93016, MR 2668922, 10.1016/j.sysconle.2010.03.005 |
| Reference:
|
[4] F., Cacace,, A., Germani,, C., Manes,: A chain observer for nonlinear systems with multiple time-varying measurement delays..SIAM J. Control Optim. 52 (2014), 1862-1885. MR 3213788, 10.1137/120876472 |
| Reference:
|
[5] S., Čelikovský,, B., Rehák,: Output regulation problem with nonhyperbolic zero dynamics: Femlab-based approach..IFAC Proc. Vol. 37 (2004), 21, 651-656. 10.1016/S1474-6670(17)30544-X |
| Reference:
|
[6] S., Čelikovský,, A., Torres-Munoz, J., A., Dominguez-Bocanegra,: Adaptive high gain observer extension and its application to bioprocess monitoring..Kybernetika 54 (2018), 1, 155-174. MR 3780961, 10.14736/kyb-2018-1-0155 |
| Reference:
|
[7] M., Farza,, O., Hernández-González,, T., Ménard,, B., Targui,, M., M'Saad,, C.-M., Astorga-Zaragoza,: Cascade observer design for a class of uncertain nonlinear systems with delayed outputs..Automatica 89 (2018), 125-134. MR 3762040, 10.1016/j.automatica.2017.12.012 |
| Reference:
|
[8] A., Germani,, C., Manes,, P., Pepe,: A new approach to state observation of nonlinear systems with delayed output..IEEE Trans. Automat Control 47 /2002), 1, 96-101. MR 1879694 |
| Reference:
|
[9] N., Kazantzis,, C., Kravaris,: Nonlinear observer design using Lyapunov's auxiliary theorem..Systems Control Lett. 34 (1998), 241-247. MR 1639021, 10.1016/s0167-6911(98)00017-6 |
| Reference:
|
[10] N., Kazantzis,, R., Wright,: Nonlinear observer design in the presence of delayed output measurements..Systems Control Lett. 54 (2005), 877-886. MR 2152866, 10.1016/j.sysconle.2004.12.005 |
| Reference:
|
[11] H., Khalil,: Nonlinear Systems..Prentice Hall, New Jersey 2001. Zbl 1194.93083 |
| Reference:
|
[12] V., Lynnyk,, B., Rehák,: Design of a nonlinear observer using the finite element method with application to a biological system..Cybernet. Physics 8 (2019), 292-297. 10.35470/2226-4116-2019-8-4-292-297 |
| Reference:
|
[13] B., Rehák,: Alternative method of solution of the regulator equation: {L2} -space approach..Asian J. Control 14 (2011), 1150-1154. MR 2955458, 10.1002/asjc.416 |
| Reference:
|
[14] B., Rehák,: Sum-of-squares based observer design for polynomial systems with a known fixed time delay..Kybernetika 51 (2015), 856-873. MR 3445988, 10.14736/kyb-2015-5-0856 |
| Reference:
|
[15] B., Rehák,: Observer design for a time delay system via the {Razumikhin} approach..Asian J. Control 19 (2017), 6, 2226-2231. MR 3730209, 10.1002/asjc.1507 |
| Reference:
|
[16] B., Rehák,: Finite-element based observer design for nonlinear systems with delayed measurements..IFAC-PapersOnLine 51 (2018), 14, 201-206. 10.1016/j.ifacol.2018.07.223 |
| Reference:
|
[17] B., Rehák,, J., Orozco-Mora,, S., Čelikovský,, J., Ruiz-León,: Real-time error-feedback output regulation of nonhyperbolically nonminimum phase system..In: 2007 American Control Conference 2007, pp. 3789-3794. 10.1109/acc.2007.4282643 |
| Reference:
|
[18] B., Rehák,, S., Čelikovský,: Numerical method for the solution of the regulator equation with application to nonlinear tracking..Automatica 44 (2008), 5, 1358-1365. MR 2531803, 10.1016/j.automatica.2007.10.015 |
| Reference:
|
[19] B., Rehák,, S., Čelikovský,, J., Ruiz-León,, J., Orozco-Mora,: A comparison of two {Fem}-based methods for the solution of the nonlinear output regulation problem..Kybernetika 45 (2009), 427-444. MR 2543132 |
| Reference:
|
[20] H.-G., Roos,, M., Stynes,, L., Tobiska,: Numerical Methods for Singularly Perturbed Differential Equations..Springer, Berlin 1996. MR 1477665, 10.1007/978-3-662-03206-0 |
| Reference:
|
[21] N., Sakamoto,, B., Rehák,: Iterative methods to compute center and center-stable manifolds with application to the optimal output regulation problem..In: Proc. 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), Orlando 2011. 10.1109/cdc.2011.6161089 |
| Reference:
|
[22] N., Sakamoto,, B., Rehák,, K., Ueno,: Nonlinear Luenberger observer design via invariant manifold computation..In: Proc. 19th IFAC World Congress, 2014, Cape Town 2014. 10.3182/20140824-6-za-1003.01103 |
| Reference:
|
[23] T., Tran, A., S., Suzuki,, N., Sakamoto,: Nonlinear optimal control design considering a class of system constraints with validation on a magnetic levitation system..IEEE Control Systems Lett. 1 (2017), 2, 418-423. 10.1109/lcsys.2017.2717932 |
| Reference:
|
[24] Y., Yu,, Y., Shen,: Robust sampled-data observer design for Lipschitz nonlinear systems..Kybernetika 54 (2018), 4, 699-717. MR 3863251, 10.14736/kyb-2018-4-0699 |
| . |
