High-order variations and small-time local attainability
Mikhail Krastanov (2009)
Control and Cybernetics
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Mikhail Krastanov (2009)
Control and Cybernetics
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Rosa Maria Bianchini Tiberio, Roberto Conti (1986)
Časopis pro pěstování matematiky
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Ludovic Rifford (2001)
ESAIM: Control, Optimisation and Calculus of Variations
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Let be a general control system; the existence of a smooth control-Lyapunov function does not imply the existence of a continuous stabilizing feedback. However, we show that it allows us to design a stabilizing feedback in the Krasovskii (or Filippov) sense. Moreover, we recall a definition of a control-Lyapunov function in the case of a nonsmooth function; it is based on Clarke’s generalized gradient. Finally, with an inedite proof we prove that the existence of this type of control-Lyapunov...
Francis H. Clarke, Ludovic Rifford, R. J. Stern (2002)
ESAIM: Control, Optimisation and Calculus of Variations
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An optimal control problem is studied, in which the state is required to remain in a compact set . A control feedback law is constructed which, for given , produces -optimal trajectories that satisfy the state constraint universally with respect to all initial conditions in . The construction relies upon a constraint removal technique which utilizes geometric properties of inner approximations of and a related trajectory tracking result. The control feedback is shown to possess...
Marco Castelpietra (2009)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider an optimal control problem for a system of the form = , with a running cost . We prove an interior sphere property for the level sets of the corresponding value function . From such a property we obtain a semiconcavity result for , as well as perimeter estimates for the attainable sets of a symmetric control system.
P. Cannarsa, L. Rifford (2008)
Annales de l'I.H.P. Analyse non linéaire
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