Abstract
Path-dependent impulse differential inclusions, and in particular, path-dependent hybrid control systems, are defined by a path-dependent differential inclusion (or path-dependent control system, or differential inclusion and control systems with memory) and a path-dependent reset map.
In this paper, we characterize the viability property of a closed subset of paths under an impulse path-dependent differential inclusion using the Viability Theorems for path-dependent differential inclusions.
Actually, one of the characterizations of the Characterization Theorem is valid for any general impulse evolutionary system that we shall defined in this paper.
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AUBIN J.-P. (1991) Viability Theory Birkhäuser, Boston, Basel, Berlin
AUBIN J.-P. (1999) Impulse Differential Inclusions and Hybrid Systems:A Viability Approach, Lecture Notes, University of California at Berkeley
AUBIN J.-P. (2000) Lyapunov Functions for Impulse and Hybrid Control Systems, Proceedings of the CDC 2000 Conference
AUBIN J.-P. (2000) Optimal Impulse Control Problems and Quasi-Variational Inequalities Thirty Years Later: a Viability Approach, in Contrôle optimal et EDP: Innovations et Applications, IOS Pressf
AUBIN J.-P. (to appear) Viability Kernels and Capture Basins of Sets under Differential Inclusions, SIAM J. Control
AUBIN J.-P. & FRANKOWSKA H. (1990) Set-Valued Analysis, Birkhäuser, Boston, Basel, Berlin
AUBIN J.-P. & HADDAD G. (to appear) Cadenced runs of impulse and hybrid control systems, International Journal Robust and Nonlinear Control
AUBIN J.-P., LYGEROS J., QUINCAMPOIX M., SASTRY S. & SEUBE N. (to appear) Impulse Differential Inclusions: A Viability Approach to Hybrid Systems
BENSOUSSAN A. & MENALDI (1997) Hybrid Control and Dynamic Programming, Dynamics of Continuous, Discrete and Impulse Systems, 3, 395–442
BRANICKY M.S., BORKAR V.S. & MITTER S. (1998) A unified framework for hybrid control: Background, model and theory, IEEE Trans. Autom. Control, 43, 31–45
CARDALIAGUET P., UINCAMPOIX M. & SAINT-PIERRE P. (1994) Temps optimaux pour des problèmes avec contraintes et sans contrôlabilité locale Comptes-Rendus de l’Académie des Sciences, Série 1, Paris, 318, 607–612
HADDAD G. (1981) Monotone trajectories of differential inclusions with memory, Isr. J. Math., 39, 83–100
HADDAD G. (1981) Monotone viable trajectories for functional differential inclusions, J. Diff. Eq., 42, 1–24
HADDAD G. (1981) Topological properties of the set of solutions for functional differential differential inclusions, Nonlinear Anal. Theory, Meth. Appl., 5, 1349–1366
MATVEEV A.S., SAVKIN A.V. (2000) Qualitative Theory of Hybrid Dynamical Systems, Birkhäuser
MATVEEV A.S., SAVKIN A.V. (2001) Hybrid dynamical systems: Controller and sensor switching problems, Birkhäuser
ROCKAFELLAR R.T. & WETS R. (1997) Variational Analysis, Springer-Verlag
SHAFT (van der) A. & SCHUMACHER H. (1999) An introduction to hybrid dynamical systems, Springer-Verlag, Lecture Notes in Control, 251
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Aubin, JP., Haddad, G. (2001). Path-Dependent Impulse and Hybrid Systems. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A. (eds) Hybrid Systems: Computation and Control. HSCC 2001. Lecture Notes in Computer Science, vol 2034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45351-2_13
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DOI: https://doi.org/10.1007/3-540-45351-2_13
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