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Global optimal feedbacks for stochastic quantized nonlinear event systems
1. | Technische Universität München, Boltzmannstr. 3, 85747 Garching, Germany, Germany, Germany |
References:
[1] |
K. Aström, Event based control, in Analysis and Design of Nonlinear Control Systems (eds. A. Astolfi and L. Marconi), Springer-Verlag, 2008, 127-147.
doi: 10.1007/978-3-540-74358-3_9. |
[2] |
K. Åström and B. Wittenmark, Computer-Controlled Systems: Theory and Design, Third Edition, Dover Books on Electrical Engineering Series, Dover Publications, 2011, URL http://books.google.de/books?id=9Y6D5vviqMgC. |
[3] |
S.-I. Azuma and T. Sugie, Dynamic quantization of nonlinear control systems, Automatic Control, IEEE Transactions on, 57 (2012), 875-888.
doi: 10.1109/TAC.2011.2167824. |
[4] |
D. P. Bertsekas, Dynamic Programming and Optimal Control. Vol. 2., Belmont, MA: Athena Scientific, 1995. |
[5] |
R. S. Bucy, Stability and positive supermartingales, J. Differential Equations, 1 (1965), 151-155.
doi: 10.1016/0022-0396(65)90016-1. |
[6] |
C. De Persis and F. Mazenc, Stability of quantized time-delay nonlinear systems: A Lyapunov-Krasowskii-functional approach, in Proc. of IEEE Conf. on Decision and Control, (2009), 4093-4098. |
[7] |
W. Fleming, The convergence problem for differential games, Journal of Mathematical Analysis and Applications, 3 (1961), 102-116.
doi: 10.1016/0022-247X(61)90009-9. |
[8] |
D. Förstner, M. Jung and J. Lunze, A discrete-event model of asynchronous quantised systems, Automatica, 38 (2002), 1277-1286.
doi: 10.1016/S0005-1098(02)00023-7. |
[9] |
E. Fridman and M. Dambrine, Control under quantization, saturation and delay: An LMI approach, Automatica, 45 (2009), 2258-2264.
doi: 10.1016/j.automatica.2009.05.020. |
[10] |
L. Grüne and O. Junge, Approximately optimal nonlinear stabilization with preservation of the Lyapunov function property, in Proc. 46th IEEE CDC, (2007), 702-707. |
[11] |
L. Grüne and O. Junge, Global optimal control of perturbed systems, JOTA, 136 (2008), 411-429.
doi: 10.1007/s10957-007-9312-z. |
[12] |
L. Grüne and F. Müller, An algorithm for event-based optimal feedback control, in Proc. 48th IEEE CDC, 2009, 5311-5316. |
[13] |
J. P. Hespanha, P. Naghshtabrizi and Y. Xu, A survey of recent results in networked control systems, Proc. IEEE, 95 (2007), 138-162.
doi: 10.1109/JPROC.2006.887288. |
[14] |
O. Junge, Rigorous discretization of subdivision techniques, in EQUADIFF 99, Proceedings of the International Conference on Differential Equations (eds. B. Fiedler, K. Gröger and J. Sprekels), vol. 2, 2000, 916-918. |
[15] |
O. Junge and H. Osinga, A set oriented approach to global optimal control, ESAIM Control Optim. Calc. Var., 10 (2004), 259-270.
doi: 10.1051/cocv:2004006. |
[16] |
E. Kofman and J. Braslavsky, Level crossing sampling in feedback stabilization under data-rate constraints, in Proc. IEEE CDC, San Diego, USA, (2006), 4423-4428.
doi: 10.1109/CDC.2006.377483. |
[17] |
H. Kushner, On the stability of stochastic dynamical systems, Proc. Nat. Acad. Sci. USA, 53 (1965), 8-12.
doi: 10.1073/pnas.53.1.8. |
[18] |
H. Kushner, Stochastic Stability and Control, Mathematics in Science and Engineering, Vol. 33, Academic Press, 1967. |
[19] |
H. Kushner and G. Yin, Stochastic Approximation Algorithms and Applications, Applications of Mathematics, Vol. 35, Springer-Verlag, 1997. |
[20] |
D. Liberzon, Quantization, time delays, and nonlinear stabilization, IEEE Transactions on Automatic Control, 51 (2006), 1190-1195.
doi: 10.1109/TAC.2006.878780. |
[21] |
D. Liberzon, Nonlinear control with limited information, Commun. Inf. Syst., 9 (2009), 41-57.
doi: 10.4310/CIS.2009.v9.n1.a2. |
[22] |
L. Litz, T. Gabriel, M. Groß and O. Gabel, Networked Control Systems (NCS) - Stand und Ausblick, at - Automatisierungstechnik, 56 (2009), 4-19.
doi: 10.1524/auto.2008.0682. |
[23] |
T. Liu, Z.-P. Jiang and D. J. Hill, Small-gain based output-feedback controller design for a class of nonlinear systems with actuator dynamic quantization, Automatic Control, IEEE Transactions on, 57 (2012), 1326-1332.
doi: 10.1109/TAC.2012.2191870. |
[24] |
U. Lorenz and B. Monien, Error analysis in minimax trees, TCS, 313 (2004), 485-498.
doi: 10.1016/j.tcs.2002.10.004. |
[25] |
J. Lunze, Qualitative modelling of linear dynamical systems with quantized state measurements, Automatica, 30 (1994), 417-431.
doi: 10.1016/0005-1098(94)90119-8. |
[26] |
S. Mastellone, C. Abdallah and P. Dorato, Model-based networked control for nonlinear systems with stochastic packet dropout, in Proc. American Control Conference., 4 (2005), 2365-2370.
doi: 10.1109/ACC.2005.1470320. |
[27] |
D. Nesic and D. Liberzon, A unified framework for design and analysis of networked and quantized control systems, IEEE Transactions on Automatic Control, 54 (2009), 732-747.
doi: 10.1109/TAC.2009.2014930. |
[28] |
G. Pola, P. Pepe, M. D. D. Benedetto and P. Tabuada, Symbolic models for nonlinear time-delay systems using approximate bisimulations, Systems and Control Letters, 59 (2010), 365-373.
doi: 10.1016/j.sysconle.2010.04.001. |
[29] |
R. Sailer and F. Wirth, Stabilization of nonlinear systems with delayed data-rate-limited feedback, in Proc. European Control Conference, ECC2009, (2009), 1734-1739. |
[30] |
J. Schroeder, Modeling, State Observation and Diagnosis of Quantized Systems, Springer, Berlin, 2003. |
[31] |
P. Tabuada, Event-triggered real-time scheduling of stabilizing control tasks, IEEE Transactions on Automatic Control, 52 (2007), 1680-1685.
doi: 10.1109/TAC.2007.904277. |
[32] |
W. Tucker, A rigorous ODE solver and Smale's 14th problem, Found. Comp. Math., 2 (2002), 53-117. |
[33] |
M. von Lossow, A min-man version of Dijkstra's algorithm with application to perturbed optimal control problems., in In: Proceedings of the GAMM Annual Meeting, Zürich, Switzerland, 2007. |
[34] |
X. Wang and M. Lemmon, Event-triggering in distributed networked systems with data dropouts and delays, Hybrid Systems: Computation and control (HSCC), 366-380, Lecture Notes in Comput. Sci., 5469, Springer, Berlin, 2009.
doi: 10.1007/978-3-642-00602-9_26. |
[35] |
C. Zhang, K. Chen and G. Dullerud, Stabilization of markovian jump linear systems with limited information - a convex approach, in Proc. ACC, (2009), 4013-4019.
doi: 10.1109/ACC.2009.5160685. |
[36] |
C. Zhang and G. Dullerud, Uniform stabilization of markovian jump linear systems with logarithmic quantization, in Proc. IEEE CDC, (2009), 2094-2099.
doi: 10.1109/CDC.2009.5400361. |
[37] |
L. Zhang, H. Gao and O. Kaynak, Network-induced constraints in networked control systems-a survey, IEEE Transactions on Industrial Informatics, 9 (2013), 403-416.
doi: 10.1109/TII.2012.2219540. |
show all references
References:
[1] |
K. Aström, Event based control, in Analysis and Design of Nonlinear Control Systems (eds. A. Astolfi and L. Marconi), Springer-Verlag, 2008, 127-147.
doi: 10.1007/978-3-540-74358-3_9. |
[2] |
K. Åström and B. Wittenmark, Computer-Controlled Systems: Theory and Design, Third Edition, Dover Books on Electrical Engineering Series, Dover Publications, 2011, URL http://books.google.de/books?id=9Y6D5vviqMgC. |
[3] |
S.-I. Azuma and T. Sugie, Dynamic quantization of nonlinear control systems, Automatic Control, IEEE Transactions on, 57 (2012), 875-888.
doi: 10.1109/TAC.2011.2167824. |
[4] |
D. P. Bertsekas, Dynamic Programming and Optimal Control. Vol. 2., Belmont, MA: Athena Scientific, 1995. |
[5] |
R. S. Bucy, Stability and positive supermartingales, J. Differential Equations, 1 (1965), 151-155.
doi: 10.1016/0022-0396(65)90016-1. |
[6] |
C. De Persis and F. Mazenc, Stability of quantized time-delay nonlinear systems: A Lyapunov-Krasowskii-functional approach, in Proc. of IEEE Conf. on Decision and Control, (2009), 4093-4098. |
[7] |
W. Fleming, The convergence problem for differential games, Journal of Mathematical Analysis and Applications, 3 (1961), 102-116.
doi: 10.1016/0022-247X(61)90009-9. |
[8] |
D. Förstner, M. Jung and J. Lunze, A discrete-event model of asynchronous quantised systems, Automatica, 38 (2002), 1277-1286.
doi: 10.1016/S0005-1098(02)00023-7. |
[9] |
E. Fridman and M. Dambrine, Control under quantization, saturation and delay: An LMI approach, Automatica, 45 (2009), 2258-2264.
doi: 10.1016/j.automatica.2009.05.020. |
[10] |
L. Grüne and O. Junge, Approximately optimal nonlinear stabilization with preservation of the Lyapunov function property, in Proc. 46th IEEE CDC, (2007), 702-707. |
[11] |
L. Grüne and O. Junge, Global optimal control of perturbed systems, JOTA, 136 (2008), 411-429.
doi: 10.1007/s10957-007-9312-z. |
[12] |
L. Grüne and F. Müller, An algorithm for event-based optimal feedback control, in Proc. 48th IEEE CDC, 2009, 5311-5316. |
[13] |
J. P. Hespanha, P. Naghshtabrizi and Y. Xu, A survey of recent results in networked control systems, Proc. IEEE, 95 (2007), 138-162.
doi: 10.1109/JPROC.2006.887288. |
[14] |
O. Junge, Rigorous discretization of subdivision techniques, in EQUADIFF 99, Proceedings of the International Conference on Differential Equations (eds. B. Fiedler, K. Gröger and J. Sprekels), vol. 2, 2000, 916-918. |
[15] |
O. Junge and H. Osinga, A set oriented approach to global optimal control, ESAIM Control Optim. Calc. Var., 10 (2004), 259-270.
doi: 10.1051/cocv:2004006. |
[16] |
E. Kofman and J. Braslavsky, Level crossing sampling in feedback stabilization under data-rate constraints, in Proc. IEEE CDC, San Diego, USA, (2006), 4423-4428.
doi: 10.1109/CDC.2006.377483. |
[17] |
H. Kushner, On the stability of stochastic dynamical systems, Proc. Nat. Acad. Sci. USA, 53 (1965), 8-12.
doi: 10.1073/pnas.53.1.8. |
[18] |
H. Kushner, Stochastic Stability and Control, Mathematics in Science and Engineering, Vol. 33, Academic Press, 1967. |
[19] |
H. Kushner and G. Yin, Stochastic Approximation Algorithms and Applications, Applications of Mathematics, Vol. 35, Springer-Verlag, 1997. |
[20] |
D. Liberzon, Quantization, time delays, and nonlinear stabilization, IEEE Transactions on Automatic Control, 51 (2006), 1190-1195.
doi: 10.1109/TAC.2006.878780. |
[21] |
D. Liberzon, Nonlinear control with limited information, Commun. Inf. Syst., 9 (2009), 41-57.
doi: 10.4310/CIS.2009.v9.n1.a2. |
[22] |
L. Litz, T. Gabriel, M. Groß and O. Gabel, Networked Control Systems (NCS) - Stand und Ausblick, at - Automatisierungstechnik, 56 (2009), 4-19.
doi: 10.1524/auto.2008.0682. |
[23] |
T. Liu, Z.-P. Jiang and D. J. Hill, Small-gain based output-feedback controller design for a class of nonlinear systems with actuator dynamic quantization, Automatic Control, IEEE Transactions on, 57 (2012), 1326-1332.
doi: 10.1109/TAC.2012.2191870. |
[24] |
U. Lorenz and B. Monien, Error analysis in minimax trees, TCS, 313 (2004), 485-498.
doi: 10.1016/j.tcs.2002.10.004. |
[25] |
J. Lunze, Qualitative modelling of linear dynamical systems with quantized state measurements, Automatica, 30 (1994), 417-431.
doi: 10.1016/0005-1098(94)90119-8. |
[26] |
S. Mastellone, C. Abdallah and P. Dorato, Model-based networked control for nonlinear systems with stochastic packet dropout, in Proc. American Control Conference., 4 (2005), 2365-2370.
doi: 10.1109/ACC.2005.1470320. |
[27] |
D. Nesic and D. Liberzon, A unified framework for design and analysis of networked and quantized control systems, IEEE Transactions on Automatic Control, 54 (2009), 732-747.
doi: 10.1109/TAC.2009.2014930. |
[28] |
G. Pola, P. Pepe, M. D. D. Benedetto and P. Tabuada, Symbolic models for nonlinear time-delay systems using approximate bisimulations, Systems and Control Letters, 59 (2010), 365-373.
doi: 10.1016/j.sysconle.2010.04.001. |
[29] |
R. Sailer and F. Wirth, Stabilization of nonlinear systems with delayed data-rate-limited feedback, in Proc. European Control Conference, ECC2009, (2009), 1734-1739. |
[30] |
J. Schroeder, Modeling, State Observation and Diagnosis of Quantized Systems, Springer, Berlin, 2003. |
[31] |
P. Tabuada, Event-triggered real-time scheduling of stabilizing control tasks, IEEE Transactions on Automatic Control, 52 (2007), 1680-1685.
doi: 10.1109/TAC.2007.904277. |
[32] |
W. Tucker, A rigorous ODE solver and Smale's 14th problem, Found. Comp. Math., 2 (2002), 53-117. |
[33] |
M. von Lossow, A min-man version of Dijkstra's algorithm with application to perturbed optimal control problems., in In: Proceedings of the GAMM Annual Meeting, Zürich, Switzerland, 2007. |
[34] |
X. Wang and M. Lemmon, Event-triggering in distributed networked systems with data dropouts and delays, Hybrid Systems: Computation and control (HSCC), 366-380, Lecture Notes in Comput. Sci., 5469, Springer, Berlin, 2009.
doi: 10.1007/978-3-642-00602-9_26. |
[35] |
C. Zhang, K. Chen and G. Dullerud, Stabilization of markovian jump linear systems with limited information - a convex approach, in Proc. ACC, (2009), 4013-4019.
doi: 10.1109/ACC.2009.5160685. |
[36] |
C. Zhang and G. Dullerud, Uniform stabilization of markovian jump linear systems with logarithmic quantization, in Proc. IEEE CDC, (2009), 2094-2099.
doi: 10.1109/CDC.2009.5400361. |
[37] |
L. Zhang, H. Gao and O. Kaynak, Network-induced constraints in networked control systems-a survey, IEEE Transactions on Industrial Informatics, 9 (2013), 403-416.
doi: 10.1109/TII.2012.2219540. |
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