Displaying similar documents to “Singular trajectories and subanalyticity in optimal control and Hamilton-Jacobi theory.”

Second order optimality conditions in the smooth case and applications in optimal control

Bernard Bonnard, Jean-Baptiste Caillau, Emmanuel Trélat (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical developments of geometric optimal control, and the article contains a review of second order optimality conditions. The computations are related to a test of positivity of the intrinsic second order derivative or a test of singularity of the extremal flow. We derive an algorithm called COTCOT (Conditions...

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,...

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...