Displaying similar documents to “Filippov approach in stochastic maximum principle without differentiability assumptions.”

An optimal control problem for a fourth-order variational inequality

A. Khludnev (1992)

Banach Center Publications

Similarity:

An optimal control problem is considered where the state of the system is described by a variational inequality for the operator w → εΔ²w - φ(‖∇w‖²)Δw. A set of nonnegative functions φ is used as a control region. The problem is shown to have a solution for every fixed ε > 0. Moreover, the solvability of the limit optimal control problem corresponding to ε = 0 is proved. A compactness property of the solutions of the optimal control problems for ε > 0 and their relation with the...

Optimality Conditions for a Nonlinear Boundary Value Problem Using Nonsmooth Analysis

Mohamed Akkouchi, Abdellah Bounabat, Manfred Goebel (2003)

Annales mathématiques Blaise Pascal

Similarity:

We study in this paper a Lipschitz control problem associated to a semilinear second order ordinary differential equation with pointwise state constraints. The control acts as a coefficient of the state equation. The nonlinear part of the equation is governed by a Nemytskij operator defined by a Lipschitzian but possibly nonsmooth function. We prove the existence of optimal controls and obtain a necessary optimality conditions looking somehow to the Pontryagin’s maximum principle. These...

Convergence of optimal solutions in control problems for hyperbolic equations

S. Migórski (1995)

Annales Polonici Mathematici

Similarity:

A sequence of optimal control problems for systems governed by linear hyperbolic equations with the nonhomogeneous Neumann boundary conditions is considered. The integral cost functionals and the differential operators in the equations depend on the parameter k. We deal with the limit behaviour, as k → ∞, of the sequence of optimal solutions using the notions of G- and Γ-convergences. The conditions under which this sequence converges to an optimal solution for the limit problem are...