Displaying similar documents to “On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradients”

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...

Generalized solutions to hybrid dynamical systems

Ricardo G. Sanfelice, Rafal Goebel, Andrew R. Teel (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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Several recent results in the area of robust asymptotic stability of hybrid systems show that the concept of a generalized solution to a hybrid system is suitable for the analysis and design of hybrid control systems. In this paper, we show that such generalized solutions are exactly the solutions that arise when measurement noise in the system is taken into account.

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.