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Bisimilar symbolic models for stochastic control systems without state-space discretization. (English) Zbl 1362.93147

Proceedings of the 17th ACM international conference on hybrid systems: computation and control, HSCC 2014, Berlin, Germany, April 15–17, 2014. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-2732-9). 41-50 (2014).

MSC:

93E03 Stochastic systems in control theory (general)
68Q60 Specification and verification (program logics, model checking, etc.)
93E15 Stochastic stability in control theory

Software:

MPT; CPLEX; YALMIP
Full Text: DOI

References:

[1] IBM ILOG CPLEX Optimization Studio, 2013, http://www-01.ibm.com/software/integration/ optimization/cplex-optimization-studio/.
[2] F. Blanchini and S. Miani. Set-Theoretic Methods in Control. Birkh\"{} auser, Boston, Basel, Berlin, 2008. · Zbl 1140.93001
[3] F. Borrelli, M. Baotic, A. Bemporad, and M. Morari. An e.cient algorithm for computing the state feedback optimal control law for discrete time hybrid systems. In Proc. American Control Conf. (ACC), pages 4717 4722, Denver, CO, USA, 2003.
[4] H. Chen and F. Allg\"{}ower. A Quasi-In.nite Horizon Nonlinear Model Predictive Control Scheme with Guaranteed Stability. Automatica, 34(10):1205 1217, 1998. · Zbl 0947.93013
[5] G. Feng. Stability Analysis of Piecewise Discrete-Time Linear Systems. IEEE Trans. Automat. Control, 47(7):1108 1112, 2002. · Zbl 1364.93563
[6] E. Gilbert and K. Tan. Linear Systems with State and Control Constraints: The Theory and Application of Maximal Output Admissible Sets. IEEE Trans. Automat. Control, 36(9):1008 1020, 1991. · Zbl 0754.93030
[7] J.-C. Hennet. Une extension du lemme de Farkas et son application au probl‘eme de r\'{}e egulation lin\'{}eaire sous containtes. Comptes-Rendus de l Acad\'{}emie des Sciences, S\'{}erie I, 308:415 419, 1989.
[8] M. Herceg, M. Kvasnica, C. N. Jones, and M. Morari. Multi-Parametric Toolbox 3.0. In European Control Conf. (ECC), pages 502 510, Z\"{} urich, Switzerland, 2013, http://control.ee.ethz.ch/ mpt.
[9] M. Johansson and A. Rantzer. Computation of piecewise quadratic Lyapunov functions for hybrid systems. IEEE Trans. Automat. Control, 43(4):555 559, 1998. · Zbl 0905.93039
[10] M. Lazar. On in.nity norms as Lyapunov functions: Alternative necessary and su.cient conditions. In Proc. 49th IEEE Conf. Decision and Control (CDC), pages 5936 5942, Atlanta, GA, USA, 2010.
[11] M. Lazar, W. Heemels, and A. R. Teel. Lyapunov Functions , Stability and Input-to-State Stability Subtleties for Discrete-time Discontinuous Systems. IEEE Trans. Automat. Control, 54(10):2421 2425, 2009. · Zbl 1367.93471
[12] M. Lazar and A. Joki\'{}c. On In.nity Norms as Lyapunov Functions for Piecewise A.ne Systems. In Proc. 13th Int. Conf. Hybrid Systems: Computation and Control (HSCC), pages 131 141, Stockholm, Sweden, 2010. · Zbl 1360.93554
[13] J. L\"{}ofberg. YALMIP : A toolbox for modeling and optimization in MATLAB. In Proc. CACSD Conference, pages 284 289, Taipei, Taiwan, 2004, http://users.isy.liu.se/johanl/yalmip.
[14] L. Lu and W. P. M. H. Heemels and A. Bemporad. Synthesis of low-complexity stabilizing piecewise a.ne controllers: A control-Lyapunov function approach. In Proc. IEEE Conf. Decision and Control (CDC), European Control Conf. (ECC), pages 1227 1232, Orlando, FL, USA, 2011.
[15] D. Q. Mayne and S. Rakovi\'{}c. Model predictive control of constrained piecewise a.ne discrete-time systems. Int. J. Robust and Nonlinear Control , 13(3-4):261 279, 2003.
[16] D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert. Constrained model predictive control : Stability and optimality. Automatica, 36(6):789 814, 2000. · Zbl 0949.93003
[17] S. V. Rakovi\'{}c and M. Lazar. Minkowski terminal cost functions for MPC. Automatica, 48(10):2721 2725, 2012. · Zbl 1308.93080
[18] J. B. Rawlings and D. Q. Mayne. Model Predictive Control: Theory and Design. Nob Hill Publishing, Madison, WI, 2009.
[19] R. T. Rockafellar. Convex Analysis. Princeton University Press, Princeton, NJ, 1970. · Zbl 0193.18401
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