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Preface
Determining the viability for hybrid control systems on a region with piecewise smooth boundary
1. | School of Management, University of Shanghai for Science and Technology, 516 Jungong Road, Shanghai, 200093, China |
2. | Business School, University of Shanghai for Science and Technology, Shanghai, 200093 |
References:
[1] |
P. J. Antsaklis and A. Nerode, Guest editorial hybrid control systems: an introductory discussion to the special issue, IEEE Transactions on Automatic Control, 43 (1998), 457-460. |
[2] |
J. P. Aubin, J. Lggeros, M. Quincampoix, S. Sastry and N. Seube, Impulse differential inclusions: A viability approach to hybrid systems, IEEE Transactions on Automatic Control, 47 (2002), 2-20.
doi: 10.1109/9.981719. |
[3] | |
[4] |
J. P. Aubin, Optima and Equilibria: An Introduction to Nonlinear Analysis, Springer, Berlin, 1993.
doi: 10.1007/978-3-662-02959-6. |
[5] |
F. Blanchini, Set invariance in control, Automatica, 35 (1999), 1747-1767.
doi: 10.1016/S0005-1098(99)00113-2. |
[6] |
R. W. Chaney, Piecewise $C^k$ functions in nonsmooth analysis, Nonlinear Analysis, 15 (1990), 649-660.
doi: 10.1016/0362-546X(90)90005-2. |
[7] |
F. H. Clark, Yu. S. Ledyaev, R. J. Stern and P. R. Wolenski, Nonsmooth Analysis and Control Theory, Springer-Verlag, New York, 1998. |
[8] |
V. F. Demyanov and A. M. Rubinov, Constructive Nonsmooth Analysis, Frankfurt am Main: Peterlang, 1995. |
[9] |
Y. Gao, Determining the viability for an affine nonlinear control system (in Chinese), Journal of Control Theory and Applications, 26 (2006), 654-656. |
[10] |
Y. Gao, Determining the viability for a class of nonlinear control system on a region with nonsmooth boundary (in Chinese), Control and Decision, 21 (2006), 923-925. |
[11] |
Y. Gao, J. Lggeros, M. Quincampoix and N. Seube, On the control of uncertain impulsive system: approximate stabilization and controlled invariance, International Journal of Control, 77 (2004), 1393-1407.
doi: 10.1080/00207170412331317431. |
[12] |
Y. Gao, J. Lggeros and M. Quincampoix, On the reachability problem of uncertain hybrid systems, IEEE Transactions on Automatic Control, 52 (2007), 1572-1586.
doi: 10.1109/TAC.2007.904449. |
[13] |
Y. Gao, Nonsmooth Optimization (in Chinese), Science Press, Beijing, 2008. |
[14] |
Y. Gao, Viability criteria for differential inclusions, Journal of Systems Science Complexity, 24 (2011), 825-834.
doi: 10.1007/s11424-011-9056-6. |
[15] |
Y. Gao, Piecewise smooth Lyapunov function for a nonlinear dynamical system, Journal of Convex Analysis, 19 (2012), 1009-1015. |
[16] |
B. E. A. Milani and C. E. T. Dorea, On invariant polyhedra of continuous-time linear systems subject to additive disturbances, Automatica, 32 (1996), 785-789.
doi: 10.1016/0005-1098(96)00002-7. |
[17] |
B. Nikolai and T. Varvara, Numerical construction of viable sets for autonomous conflict control systems, Mathematics, 2 (2014), 68-82.
doi: 10.3390/math2020068. |
[18] |
P. S. Pierre, Hybrid Kernels and Capture Basins for Impulse Constrained Systems, Proceedings of Hybrid Systems, 2003. |
[19] |
M. Quincampoix and N. Seube, Stabilization of uncertain control systems through piecewise constant feedback, Journal of Mathematical Analysis and Applications, 218 (1998), 240-255.
doi: 10.1006/jmaa.1997.5775. |
show all references
References:
[1] |
P. J. Antsaklis and A. Nerode, Guest editorial hybrid control systems: an introductory discussion to the special issue, IEEE Transactions on Automatic Control, 43 (1998), 457-460. |
[2] |
J. P. Aubin, J. Lggeros, M. Quincampoix, S. Sastry and N. Seube, Impulse differential inclusions: A viability approach to hybrid systems, IEEE Transactions on Automatic Control, 47 (2002), 2-20.
doi: 10.1109/9.981719. |
[3] | |
[4] |
J. P. Aubin, Optima and Equilibria: An Introduction to Nonlinear Analysis, Springer, Berlin, 1993.
doi: 10.1007/978-3-662-02959-6. |
[5] |
F. Blanchini, Set invariance in control, Automatica, 35 (1999), 1747-1767.
doi: 10.1016/S0005-1098(99)00113-2. |
[6] |
R. W. Chaney, Piecewise $C^k$ functions in nonsmooth analysis, Nonlinear Analysis, 15 (1990), 649-660.
doi: 10.1016/0362-546X(90)90005-2. |
[7] |
F. H. Clark, Yu. S. Ledyaev, R. J. Stern and P. R. Wolenski, Nonsmooth Analysis and Control Theory, Springer-Verlag, New York, 1998. |
[8] |
V. F. Demyanov and A. M. Rubinov, Constructive Nonsmooth Analysis, Frankfurt am Main: Peterlang, 1995. |
[9] |
Y. Gao, Determining the viability for an affine nonlinear control system (in Chinese), Journal of Control Theory and Applications, 26 (2006), 654-656. |
[10] |
Y. Gao, Determining the viability for a class of nonlinear control system on a region with nonsmooth boundary (in Chinese), Control and Decision, 21 (2006), 923-925. |
[11] |
Y. Gao, J. Lggeros, M. Quincampoix and N. Seube, On the control of uncertain impulsive system: approximate stabilization and controlled invariance, International Journal of Control, 77 (2004), 1393-1407.
doi: 10.1080/00207170412331317431. |
[12] |
Y. Gao, J. Lggeros and M. Quincampoix, On the reachability problem of uncertain hybrid systems, IEEE Transactions on Automatic Control, 52 (2007), 1572-1586.
doi: 10.1109/TAC.2007.904449. |
[13] |
Y. Gao, Nonsmooth Optimization (in Chinese), Science Press, Beijing, 2008. |
[14] |
Y. Gao, Viability criteria for differential inclusions, Journal of Systems Science Complexity, 24 (2011), 825-834.
doi: 10.1007/s11424-011-9056-6. |
[15] |
Y. Gao, Piecewise smooth Lyapunov function for a nonlinear dynamical system, Journal of Convex Analysis, 19 (2012), 1009-1015. |
[16] |
B. E. A. Milani and C. E. T. Dorea, On invariant polyhedra of continuous-time linear systems subject to additive disturbances, Automatica, 32 (1996), 785-789.
doi: 10.1016/0005-1098(96)00002-7. |
[17] |
B. Nikolai and T. Varvara, Numerical construction of viable sets for autonomous conflict control systems, Mathematics, 2 (2014), 68-82.
doi: 10.3390/math2020068. |
[18] |
P. S. Pierre, Hybrid Kernels and Capture Basins for Impulse Constrained Systems, Proceedings of Hybrid Systems, 2003. |
[19] |
M. Quincampoix and N. Seube, Stabilization of uncertain control systems through piecewise constant feedback, Journal of Mathematical Analysis and Applications, 218 (1998), 240-255.
doi: 10.1006/jmaa.1997.5775. |
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