Displaying similar documents to “Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints”

Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints

Nikolai P. Osmolovskii (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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Second-order sufficient conditions of a bounded strong minimum are derived for optimal control problems of ordinary differential equations with initial-final state constraints of equality and inequality type and control constraints of inequality type. The conditions are stated in terms of quadratic forms associated with certain tuples of Lagrange multipliers. Under the assumption of linear independence of gradients of active control constraints...

Second-order sufficient conditions for strong solutions to optimal control problems

J. Frédéric Bonnans, Xavier Dupuis, Laurent Pfeiffer (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this article, given a reference feasible trajectory of an optimal control problem, we say that the quadratic growth property for bounded strong solutions holds if the cost function of the problem has a quadratic growth over the set of feasible trajectories with a bounded control and with a state variable sufficiently close to the reference state variable. Our sufficient second-order optimality conditions in Pontryagin form ensure this property and ensure that the reference trajectory...

On an infinite dimensional linear-quadratic problem with fixed endpoints: the continuity question

K. Maciej Przyłuski (2014)

International Journal of Applied Mathematics and Computer Science

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In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.

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...