Abstract
Instead of beginning with viability theorems for differential inclusions, we prefer to sketch in Chapter 1 the role of the concept of viability domain in the much simpler case of differential equations. (The first viability theorem was proved in 1942 by Nagumo.)
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Keywords
- Differential Inclusion
- Contingent Cone
- Viability Theory
- Viability Kernel
- Variational Differential Inequality
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
AUBIN J.-P., FRANKOWSKA H. (1990) SET-VALUED ANALYSIS, Birkhäuser, Systems and Control: Foundations and Applications
KURATOWSKI K. (1958) TOPOLOGIE, VOLS. 1 AND 2 4TH. ED. CORRECTED, Panstowowe Wyd Nauk, Warszawa. ( Academic Press, New York, 1966 )
AUBIN J.-P. (1984) Lipchitz behavior of solutions to convex minimization problems,Mathematics of Operations Research, 8, 87–111
AUBIN J.-P., FRANKOWSKA H. (1987) On the inverse function theorem, J. Math. Pures Appliquées, 66, 71–89
ROCKAFELLAR R.T. (1985) Lipschitzian properties of multifunctions,J. Nonlinear Anal. T.M.A., 9, 867–885
FRANKOWSKA H. (1990) Some inverse mapping theorems,Ann. Inst. Henri Poincaré, Analyse Non Linéaire, 3, 183–234
FRANKOWSKA H. (1992) CONTROL OF NONLINEAR SYSTEMS AND DIFFERENTIAL INCLUSIONS, Birkhäuser, Systems and Control: Foundations and Applications
ROCKAFELLAR R.T. (1967) MONOTONE PROCESSES OF CONVEX AND CONCAVE TYPE, Mem. of AMS # 77
ROCKAFELLAR R.T. (1970) CONVEX ANALYSIS, Princeton University Press
ROCKAFELLAR R.T. (1974) Convex algebra and duality in dynamic models of production, Mathematical Models in Economics, Los ( Ed ), North Holland Amsterdam
ROBINSON S.M. (1974) Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear-programming algorithms,Math. Programming, 7, 1–16
ROBINSON S.M. (1976) Regularity and stability for convex multivalued functions,Math. Op. Res., 1, 130–143
ROBINSON S.M. (1976) Stability theory for systems of inequalities, part ii: differentiable nonlinear systems,SIAM J. on Numerical Analysis,13, 497–513
URSESCU C. (1975) Multifunctions with closed convex graph,Czechoslovakia Mathematics J.,25, 438–441
AUBIN J.-P. Si WETS R. (1988) Stable approximations of set-valued maps, Ann.Inst. Henri Poincaré, Analyse non linéaire, 5, 519–535
AUBIN J.-P., EKELAND I. (1984) APPLIED NONLINEAR ANALYSIS, Wiley-Interscience
FRANKOWSKA H. (1990) On controllability and observability of implicit systems,Systems and Control Letters, 14, 219–225
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media New York
About this chapter
Cite this chapter
Aubin, JP. (2009). Outline of the Book. In: Viability Theory. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4910-4_2
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4910-4_2
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4909-8
Online ISBN: 978-0-8176-4910-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)