Analysis and Solution Methods for Bilevel Optimal Control Problems

Optimality conditions for bilevel optimal control problems with non-convex quasi-variational inequalities

“…Let (𝑥, 𝑢, 𝑦) be a 𝒲-local solution of problem (GBOCP). Theorem 4.2 ensures that there is a constant 𝛽 > 0 such that (𝑥, 𝑢, 𝑦) is a 𝒲-local optimal solution of problem (7). Furthermore, it is clear that (𝑥, 𝑢, 𝑦) is a 𝒲-local optimal solution of problem (11).…”

“…holds for all (𝑥, 𝑢, 𝑦) ∈ Θ 𝐿 × 𝐾 (𝑥 𝑒 , 𝑦) with (𝑥, 𝑦) ∈ B 𝜀 𝒲 (𝑥, 𝑦). Therefore, (𝑥, 𝑢, 𝑦) is a 𝒲-local optimal solution of (7).…”

“…In the realm of bilevel optimization, bilevel optimal control refers to scenarios where at least one of the decision-makers is tasked with solving optimal control problems that involve either ordinary or partial differential equations [7]. In this study, we take up the case when the optimal control mathematical program involves two levels of decision: the upper level, referred to as the 'leader', is an optimal control problem, which incorporates a dynamic system as one of its constraints.…”

Pontryagin optimality conditions for generalized bilevel optimal control problems with pure state inequality constraints

“…In the same vein, bilevel optimal control problems, which are bilevel optimization problems with control at least one level, have been considered because of its numerous applications; see, e.g., [1,2,3,4,5,6,7] and the references therein. Many methods have been used to investigate such problems, including theoretical studies [8,9,10] and numerical studies [4,11,12].…”