- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 127185, 6 pages
Viability Discrimination of a Class of Control Systems on a Nonsmooth Region
1School of Mathematics, Physics and Biological Engineering, Inner Mongolia University of Science and Technology, Baotou 014010, China
2Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1
Received 27 July 2013; Revised 16 December 2013; Accepted 18 December 2013; Published 12 January 2014
Academic Editor: Zhigang Jiang
Copyright © 2014 Na Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- M. S. Shaikh and P. E. Caines, “On the hybrid optimal control problem: theory and algorithms,” IEEE Transactions on Automatic Control, vol. 52, no. 9, pp. 1587–1603, 2007.
- M. Boccadoro, Y. Wardi, M. Egerstedt, and E. Verriest, “Optimal control of switching surfaces in hybrid dynamical systems,” Journal of Discrete Event Dynamic Systems, vol. 15, no. 4, pp. 433–448, 2005.
- D. Liberzon, Calculus of Variations and Optimal Control Theory, A Concise Introduction, Princeton University Press, Princeton, NJ, USA, 2012.
- H. S. Witsenhausen, “A class of hybrid-state continuous-time dynamic systems,” IEEE Transactions on Automatic Control, vol. 11, pp. 161–167, 1966.
- H. Wong-Toi, “Synthesis of controllers for linear hybrid automata,” in Proceedings of the 36th IEEE Conference on Decision and Control, pp. 4607–4613, San Diego, Calif, USA, December 1997.
- J. Lygeros, C. Tomlin, and S. Sastry, “Controllers for reachability specifications for hybrid systems,” Automatica, vol. 35, no. 3, pp. 349–370, 1999.
- C. J. Tomlin, J. Lygeros, and S. Shankar Sastry, “A game theoretic approach to controller design for hybrid systems,” Proceedings of the IEEE, vol. 88, no. 7, pp. 949–969, 2000.
- J.-P. Aubin, Viability Theory, Birkhäuser, Boston, MA, 1991.
- J.-P. Aubin, “A survey of viability theory,” SIAM Journal on Control and Optimization, vol. 28, no. 4, pp. 749–788, 1990.
- J.-P. Aubin, J. Lygeros, M. Quincampoix, S. Sastry, and N. Seube, “Impulse differential inclusions: a viability approach to hybrid systems,” IEEE Transactions on Automatic Control, vol. 47, no. 1, pp. 2–20, 2002.
- P. Cardaliaguet, M. Quincampoix, and P. Saint-Pierre, “Pursuit differential games with state constraints,” SIAM Journal on Control and Optimization, vol. 39, no. 5, pp. 1615–1632, 2001.
- Y. Gao, J. Lygeros, and M. Quincampoix, “On the reachability problem for uncertain hybrid systems,” IEEE Transactions on Automatic Control, vol. 52, no. 9, pp. 1572–1586, 2007.
- Y. Gao, J. Lygeros, M. Quincampoix, and N. Seube, “On the control of uncertain impulsive systems: approximate stabilization and controlled invariance,” International Journal of Control, vol. 77, no. 16, pp. 1393–1407, 2004.
- M. Quincampoix and N. Seube, “Stabilization of uncertain control systems through piecewise constant feedback,” Journal of Mathematical Analysis and Applications, vol. 218, no. 1, pp. 240–255, 1998.
- F. Blanchini, “Set invariance in control,” Automatica, vol. 35, no. 11, pp. 1747–1767, 1999.
- B. E. A. Milani and C. E. T. Dórea, “On invariant polyhedra of continuous-time systems subject to additive disturbances,” Automatica, vol. 32, no. 5, pp. 785–789, 1996.
- J.-P. Aubin, Optima and Equilibria: An Introduction to Nonlinear Analysis, vol. 140, Springer, Berlin, Germany, 1993.
- Y. Gao, “Determining the viability for a affine nonlinear control system,” Control Theory and Applications, vol. 26, no. 6, pp. 654–656, 2009.
- N. U. Ahmed, “Optimal relaxed controls for systems governed by impulsive differential inclusions,” Nonlinear Functional Analysis and Applications, vol. 10, no. 3, pp. 427–460, 2005.
- Y. Gao, “Viability criteria for differential inclusions,” Journal of Systems Science & Complexity, vol. 24, no. 5, pp. 825–834, 2011.
- Y. Gao, “Determining the viability for a class of nonlinear control systems,” Information and Control, vol. 34, no. 4, pp. 510–512, 2005.