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Optimal control of systems determined by strongly nonlinear operator valued measures

100%

Ahmed N.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2008

tom 28

nr 1

165-189

In this paper we consider a class of distributed parameter systems (partial differential equations) determined by strongly nonlinear operator valued measures in the setting of the Gelfand triple V ↪ H ↪ V* with continuous and dense embeddings where H is a separable Hilbert space and V is a reflexive Banach space with dual V*. The system is given by dx + A(dt,x) = f(t,x)γ(dt) + B(t)u(dt), x(0) = ξ, t ∈ I ≡ [0,T] where A is a strongly nonlinear operator valued measure mapping Σ × V to V* with Σ denoting the sigma algebra of subsets of the set I and f is a nonlinear operator mapping I × H to H, γ is a countably additive bounded positive measure and the control u is a suitable vector measure. We present existence, uniqueness and regularity properties of weak solutions and then prove the existence of optimal controls (vector valued measures) for a class of control problems.

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1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Ahmed N.

1 2008

Wyniki wyszukiwania

Optimal control of systems determined by strongly nonlinear operator valued measures