Stability analysis for optimal control problems governed by semilinear evolution equation

Deng, Hongyong; Wei, Wei

doi:10.1186/s13662-015-0443-5

Cited by 12 publications

(8 citation statements)

References 11 publications

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“…By inspiring of example 5.1 of those by Deng and Wei, we propose the following control functions:

u_{k} false(t, x false) = ({, \begin{matrix} array \sin x & array if t \in [\frac{2 l b}{2 k}, \frac{(2 l + 1) b}{2 k} [, l = 1, ⋯, k - 1 \\ array e^{- \frac{1}{2 k}} \sin x & array otherwise . \end{matrix})

We build

scriptU

U = \{u_{k} (\cdot, x), t \in [0, b], k = 1, ⋯, N\} = \cup_{k = 1}^{N} \{e^{- \frac{1}{2 k}} \sin x\} \cup {\sin x},

where

scriptU

is a bounded closed set in H 1 (0,π).…”

Section: Applicationmentioning

confidence: 99%

“…The converse is false. In fact, if y satisfies Equation 14, then y is not necessarily differentiable.…”

Section: Theorem 1 (Ezzinbi Et Al 17 )mentioning

confidence: 99%

“…However, their main result shows that, in the sense of Baire category, most of the optimal control problems are stable. Deng and Wei studied the existence and stability properties of solutions for the following optimal control problem:

J false(u false) = {(‖‖, y false(b false) - y_{b})}_{E}^{2} + \int_{0}^{b} {(‖‖, y false(t false) - \overset{y}{true} false(t false))}_{E}^{2} d t

subject to

({, \begin{matrix} array y^{'} (t) = A y (t) + f (t, y (t), u (t)) for t \in [0, b], \\ array y (0) = y_{0}, \end{matrix})

where A generates a c 0 ‐semigroup, and u (·) is a function control given in the set of admissible controls

scriptU false[0, b false] \subset L^{1} false(false[0, b false]; X false)

defined in Equation .…”

Section: Introductionmentioning

confidence: 99%

“…In this work, inspired by the work of Deng and Wei, we study the existence and stability of solutions of Problem (P) .…”

Section: Introductionmentioning

confidence: 99%

“…In this work, inspired by the work of Deng and Wei, 14 we study the existence and stability of solutions of Problem (P). The organization of this work is as follows: in Section 2, we give some preliminary results on the set of admissible controls, on the resolvent operator, and on the set-valued mapping theory.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Optimal control problem for some integrodifferential equations in Banach spaces

Diallo

Ezzinbi

Sène

2017

Optim Control Appl Methods

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Summary In this work, we study the existence and stability of solutions for an optimal control problem governed by an integrodifferential equation with compact control set in the space L1([0,b];X). The stability results, in the sense of Baire category theory, for optimal control problems are obtained by the theory of set‐valued mapping and the notion of essential solutions for optimal control problems.

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“…By inspiring of example 5.1 of those by Deng and Wei, we propose the following control functions: