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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K. Maciej Przyłuski (2014)
International Journal of Applied Mathematics and Computer Science
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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 they guarantee the bounded strong quadratic...
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...
L. von-Wolfersdorf (1985)
Banach Center Publications
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Bucci, F. (1998)
Rendiconti del Seminario Matematico
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Baten, Md.Azizul (2005)
Lobachevskii Journal of Mathematics
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J. L. Willems (1985)
Banach Center Publications
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N.P. Osmolovskii, H. Maurer (2005)
Control and Cybernetics
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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...
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...
Andrei Dmitruk (2008)
Control and Cybernetics
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