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An elementary way to rigorously estimate convergence to equilibrium and escape rates
Numerical event-based ISS controller design via a dynamic game approach
1. | University of Bayreuth, Chair of Applied Mathematics, Universitätsstraße 30, 95440 Bayreuth |
2. | University of Bayreuth, Chair of Applied Mathematics, Universitãtsstraße 30, 95440 Bayreuth, Germany |
  The controller construction relies on the conversion of the ISpS design problem into a robust controller design problem which is solved by a set oriented discretization technique followed by the solution of a dynamic game on a hypergraph. We present and analyze this approach with a particular focus on keeping track of the quantitative dependence of the resulting gain and the size of the exceptional region for practical stability from the design parameters of our event-based controller.
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show all references
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[1] |
in Proc. 14th IFAC World Congress, 1999, 423-428. Google Scholar |
[2] |
in Proc. 14th IFAC World Congress, 1999, 301-306. Google Scholar |
[3] |
Springer US, 2015, 1-14.
doi: 10.1007/s13235-015-0156-0. |
[4] |
in Proc. 14th IFAC World Congress, 2011, 2401-2406. Google Scholar |
[5] |
SIAM, Philadephia, 2014. |
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International Journal of Control, 82 (2009), 2235-2248.
doi: 10.1080/00207170902978115. |
[7] |
Discrete Contin. Dyn. Syst., 32 (2012), 3539-3565.
doi: 10.3934/dcds.2012.32.3539. |
[8] |
Springer, Berlin, 2007. |
[9] |
at-Automatisierungstechnik (Special Issue on Networked Control Systems), 58 (2010), 173-182. Google Scholar |
[10] |
Systems Control Lett., 54 (2005), 169-180.
doi: 10.1016/j.sysconle.2004.08.005. |
[11] |
in Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, Louisiana, 2007, 702-707. Google Scholar |
[12] |
J. Optim. Theory Appl., 136 (2008), 411-429.
doi: 10.1007/s10957-007-9312-z. |
[13] |
IEEE Trans. Autom. Control, 59 (2014), 3098-3103.
doi: 10.1109/TAC.2014.2321667. |
[14] |
in Proc. 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS2008), CD-Rom, Paper 125.pdf, Blacksburg, Virginia, 2008. Google Scholar |
[15] |
in Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, China, 2009, 5311-5316. Google Scholar |
[16] |
in Proceedings of the 52nd IEEE Conference on Decision and Control, Florence, Italy, 2013, 1732-1737. Google Scholar |
[17] |
Texas State University-San Marcos, Department of Mathematics, San Marcos, TX, 2007, Available electronically at http://ejde.math.txstate.edu/. |
[18] |
Automatica, 37 (2001), 857-869.
doi: 10.1016/S0005-1098(01)00028-0. |
[19] |
Systems Control Lett., 45 (2002), 49-58.
doi: 10.1016/S0167-6911(01)00164-5. |
[20] |
ESAIM Control Optim. Calc. Var., 10 (2004), 259-270 (electronic).
doi: 10.1051/cocv:2004006. |
[21] |
Springer, 2014.
doi: 10.1007/978-3-319-01131-8. |
[22] |
Automatica, 46 (2010), 211-215.
doi: 10.1016/j.automatica.2009.10.035. |
[23] |
IEEE Trans. Autom. Control, 56 (2010), 2456-2461.
doi: 10.1109/TAC.2011.2164036. |
[24] |
Control Eng. Practice, 35 (2015), 22-34.
doi: 10.1016/j.conengprac.2014.10.002. |
[25] |
IEEE Trans. Autom. Control, 52 (2007), 1680-1685.
doi: 10.1109/TAC.2007.904277. |
[26] |
in Proc. Appl. Math. Mech. (PAMM), 7 (2007), 4130027-4130028.
doi: 10.1002/pamm.200700646. |
[27] |
in Proc. 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, Florida, 2011, 4698-4703.
doi: 10.1109/CDC.2011.6160699. |
[28] |
Automatica, 47 (2011), 2319-2322.
doi: 10.1016/j.automatica.2011.05.027. |
[29] |
in Proc. American Control Conference, 2011, 1674-1679. Google Scholar |
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