Existence and stability analysis for nonlinear optimal control problems with $1$-mean equicontinuous controls

Optimal control problem for some integrodifferential equations in Banach spaces

“…Thus, (H 3 ) is satisfied. Then, by Theorem 4, we deduce that Equation25 has an admissible control on [0, b]. By inspiring of example 5.1 of those by Deng and Wei,14 we propose the following control functions:u k (t, x) build  by  = {u k (·, x), t ∈ [0, b], k = 1, · · · , N} = ∪ N k=1 { e − 1 2k sin x } ∪ {sin x},…”

“…2 z 2 y(s, z)ds +α(t)ϕ (y(t, z)) + u(t) for t ∈ [0, b] and z ∈]0, π[, y(t, 0) = u(t, π) = 0, y(0, z) = y 0 (z), (25) whereȳ(·) ∈ L 2 (0, b; L 2 (0, π)), y 0 ∈ L 2 (0, π) and y b ∈ L 2 (0, π), γ ∈  1 ([0, b]…”

“…We want to bring an additional temperature (control u(t)) so that at time b, the configuration of the material is close to a given desired state. To rewrite Equation 25 in the abstract form, we introduce the space E = L 2 (0, π).…”

Stability and solvability for a class of optimal control problems described by non-instantaneous impulsive differential equations

“…In [37], Deng and Wei considered the existence and stability analysis for the above nonlinear optimal control problems with 1-mean equicontinuous controls. Different from [30], Deng and Wei got the existence and stability results by weakening the condition of the control.…”

Higher-order sensitivity analysis in set-valued optimization under Henig efficiency

“…It is well known that stability and sensitivity analysis [4,13] is not only theoretically interesting but also practically important in optimization theory. A number of useful results have been obtained in usual scalar optimization (see Refs.…”