Displaying similar documents to “Nonsmooth optimal regulation and discontinuous stabilization.”

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...

Nonconvex Duality and Semicontinuous Proximal Solutions of HJB Equation in Optimal Control

Mustapha Serhani, Nadia Raïssi (2009)

RAIRO - Operations Research

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In this work, we study an optimal control problem dealing with differential inclusion. Without requiring Lipschitz condition of the set valued map, it is very hard to look for a solution of the control problem. Our aim is to find estimations of the minimal value, (), of the cost function of the control problem. For this, we construct an intermediary dual problem leading to a weak duality result, and then, thanks to additional assumptions of monotonicity of proximal subdifferential,...

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.

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...

Regularity along optimal trajectories of the value function of a Mayer problem

Carlo Sinestrari (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider an optimal control problem of Mayer type and prove that, under suitable conditions on the system, the value function is differentiable along optimal trajectories, except possibly at the endpoints. We provide counterexamples to show that this property may fail to hold if some of our conditions are violated. We then apply our regularity result to derive optimality conditions for the trajectories of the system.