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

Mustapha Serhani; Nadia Raïssi

Displaying similar documents to “Nonconvex Duality and Semicontinuous Proximal Solutions of HJB Equation in Optimal Control”

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.

Nonsmooth optimal regulation and discontinuous stabilization.

Bacciotti, A., Ceragioli, F. (2003)

Abstract and Applied Analysis

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Monotonicity and differential properties of the value functions in optimal control.

Mirică, Ştefan (2004)

International Journal of Mathematics and Mathematical Sciences

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Optimal synthesis via superdifferentials of value function

H. Frankowska (2005)

Control and Cybernetics

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On a system of Hamilton-Jacobi-Bellman inequalities associated to a minimax problem with additive final cost.

Di Marco, Silvia C., González, Roberto L.V. (2003)

International Journal of Mathematics and Mathematical Sciences

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Minima in control problems with constraints

Gianna Stefani, PierLuigi Zezza (1995)

Banach Center Publications

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This paper is devoted to describing second order conditions in the framework of extremal problems, that is, conditions obtained by reducing the optimal control problem to an abstract one in a suitable Banach (or Hilbert) space. The studied problem includes equality constraints both on the end-points and on the state-control trajectory. The second goal is to give a complete description of necessary and sufficient second order conditions for weak local optimality by describing first the...

The maximum principle in optimal control, then and now

Francis Clarke (2005)

Control and Cybernetics

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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...

Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities

Fabio Bagagiolo (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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We study a finite horizon problem for a system whose evolution is governed by a controlled ordinary differential equation, which takes also account of a hysteretic component: namely, the output of a Preisach operator of hysteresis. We derive a discontinuous infinite dimensional Hamilton–Jacobi equation and prove that, under fairly general hypotheses, the value function is the unique bounded and uniformly continuous viscosity solution of the corresponding Cauchy problem.