Necessary and sufficient conditions for L1-strong- weak lower semicontinuity of integral functionals

“…on T with aB(t) = \\aB(t, -)\\2 and cB(t) = \\cB(t, -)\\2, while hypothesis if(f) (4) gives us the n-continuity of A -» F(t, x, A). So we have satisfied hypothesis H(F)3.…”

Section: So We Conclude That Indeed Tp(t • X") -► Cp(t ■ X) In L2mentioning

confidence: 99%

On Parametric Evolution Inclusions of the Subdifferential Type with Applications to Optimal Control Problems

Papageorgiou¹

1995

Transactions of the American Mathematical Society

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Abstract. In this paper we study parametric evolution inclusions of the subdifferential type and their applications to the sensitivity analysis of nonlinear, infinite dimensional optimal control problems. The parameter appears in all the data of the problem, including the subdifferential operator. First we establish several continuity results for the solution multifunction of the subdifferential inclusion. Then we study how these results can be used to examine the sensitivity properties (variational stability) of certain broad classes of nonlinear infinite dimensional optimal control problems. Some examples are worked out in detail, illustrating the applicability of our work. These include obstacle problems (with time varying obstacles), optimal control of distributed parameter systems, and differential variational inequalities.

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“…Note that [HL] implies the assumptions of Balder (see Theorem 2.1, [3]). Hence, by Balder's theorem, we can conclude that…”

Section: Existence Of Fractional Optimal Controlmentioning

confidence: 99%

The Solvability and Fractional Optimal Control for Semilinear Stochastic Systems

Kumar

2017

Cubo

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This paper deals with fractional optimal control for a class of semilinear stochastic equation in Hilbert space setting. To ensure the existence and uniqueness of mild solution, a set of sufficient conditions is constructed. The existence of fractional optimal control for semilinear stochastic system is also discussed. Finally, an example is included to show the applications of the developed theory. RESUMENEste artículo estudia el controlóptimo fraccional para una clase de ecuaciones estocásticas semilineales en un contexto de espacios de Hilbert. Para asegurar la existencia y la unicidad de soluciones blandas, construimos un conjunto de condiciones suficientes. La existencia del controlóptimo fraccional para sistemas estocásticos semilineales también es discutido. Finalmente, incluimos un ejemplo para mostrar la aplicabilidad de la teoría desarrollada.

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Necessary and sufficient conditions for L1-strong- weak lower semicontinuity of integral functionals

Cited by 226 publications

References 5 publications

Minimax control of nonlinear evolution equations

Minimax control of nonlinear evolution equations

On Parametric Evolution Inclusions of the Subdifferential Type with Applications to Optimal Control Problems

The Solvability and Fractional Optimal Control for Semilinear Stochastic Systems

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