On the smoothness of solutions of linear-quadratic regulator for degenerate diffusions.
Baten, Md.Azizul (2005)
Lobachevskii Journal of Mathematics
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Baten, Md.Azizul (2005)
Lobachevskii Journal of Mathematics
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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...
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...
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.
H. Maurer, N. Osmolovskii (2003)
Control and Cybernetics
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Nikolai Osmolovskii (2009)
Control and Cybernetics
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