Inverse Optimal Control with Convex Features and Box Constraints
Abstract
We study an inverse optimal-control problem for identifying nonnegative weights in a convex-feature lower-level objective. The resulting model is an optimistic bilevel optimal-control problem whose lower level is a strongly convex, linearly constrained control problem with box constraints in L2. For the reduced response map x↦ (yx,ux), we prove global single-valuedness and an explicit Lipschitz estimate, without assuming differentiability of active sets. Exploiting the affine dependence of the lower-level functional on x, we show that the value function is concave and Lipschitz and derive an asymptotically exact optimal-value relaxation. We further establish local identifiability and O(δ) noise stability by a gradient-free argument based on second-order growth. Finally, a KKT reformulation yields a function-space MPCC; Scholtes relaxation gives C-stationarity under uniform multiplier boundedness. A decoupled scalar example provides an explicit strict-complementarity certificate via finiteness of threshold contacts.
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BibTeX
@misc{yu2026inverse,
title = {{Inverse Optimal Control with Convex Features and Box Constraints}},
author = {Jiguang Yu and Louis Shuo Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00033},
eprint = {2610.00033},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00033},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Inverse Optimal Control with Convex Features and Box Constraints
AU - Jiguang Yu
AU - Louis Shuo Wang
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00033
UR - https://arxiv.org/abs/2610.00033
AB - We study an inverse optimal-control problem for identifying nonnegative weights in a convex-feature lower-level objective. The resulting model is an optimistic bilevel optimal-control problem whose lower level is a strongly convex, linearly constrained control problem with box constraints in L^2. For the reduced response map x↦ (y_x,u_x), we prove global single-valuedness and an explicit Lipschitz estimate, without assuming differentiability of active sets. Exploiting the affine dependence of the lower-level functional on x, we show that the value function is concave and Lipschitz and derive an asymptotically exact optimal-value relaxation. We further establish local identifiability and O(δ) noise stability by a gradient-free argument based on second-order growth. Finally, a KKT reformulation yields a function-space MPCC; Scholtes relaxation gives C-stationarity under uniform multiplier boundedness. A decoupled scalar example provides an explicit strict-complementarity certificate via finiteness of threshold contacts.
ER -