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Displaying similar documents to “Local small time controllability and attainability of a set for nonlinear control system”

On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradients

Ludovic Rifford (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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Let x ˙ = f ( x , u ) 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...

Feedback in state constrained optimal control

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 S . A control feedback law is constructed which, for given ε > 0 , produces ε -optimal trajectories that satisfy the state constraint universally with respect to all initial conditions in S . The construction relies upon a constraint removal technique which utilizes geometric properties of inner approximations of S and a related trajectory tracking result. The control feedback is shown to possess...

Interior sphere property for level sets of the value function of an exit time problem

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 x ˙ = , 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.