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Contingent Cones to Reachable Sets of Control Systems

Frankowska, Halina (1989), Contingent Cones to Reachable Sets of Control Systems, SIAM Journal on Control and Optimization, 27, 1, p. 170-198. http://dx.doi.org/10.1137/0327010

Type
Article accepté pour publication ou publié
Date
1989
Journal name
SIAM Journal on Control and Optimization
Volume
27
Number
1
Publisher
SIAM
Pages
170-198
Publication identifier
Metadata
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Author(s)
Frankowska, Halina
Abstract (EN)
High-order necessary conditions for optimality for an optimal control problem are studied via properties of contingent cones to reachable sets along the optimal trajectory. It is shown that the adjoint vector of Pontryagin’s maximum principle is normal to the set of variations of reachable sets. Results are applied to study optimal control problems for dynamical systems described by: (1) closed-loop control systems; (2) nonlinear implicit systems; (3) differential inclusions; (4) control systems with jumps.
Subjects / Keywords
high-order maximum principles; implicit control system; closed-loop control system; discontinuous trajectory; reachable set; contingent cone