Generalized Semi-Infinite Programming for Robust Optimal Control with Decision-Dependent Uncertainty
Abstract
Generalized semi-infinite programs (GSIPs) arise in robust optimal control whenever the admissible uncertainty depends on the state or controls. Existing GSIP methods either impose restrictive structural assumptions or require global optimization that scales poorly to control problems. We present a general framework that reformulates any GSIP with mild regularity as an existence-constrained semi-infinite program, smoothing its disjunctive feasibility condition into differentiable existence constraints over a fixed index superset. The resulting program is solved by established adaptive discretization (cutting-plane) methods using only off-the-shelf nonlinear-programming solvers, and converges under standard assumptions. Treating the state trajectory as part of the uncertainty extends the framework to robust nonlinear optimal control with state-dependent uncertainty. We demonstrate it on a nonconvex benchmark GSIP and a satellite de-tumbling problem with dynamically varying inertia.
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BibTeX
@misc{wehbeh2026generalized,
title = {{Generalized Semi-Infinite Programming for Robust Optimal Control with Decision-Dependent Uncertainty}},
author = {J. Wehbeh and E. C. Kerrigan and E. Scaccia},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01538},
eprint = {2609.01538},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01538},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Generalized Semi-Infinite Programming for Robust Optimal Control with Decision-Dependent Uncertainty
AU - J. Wehbeh
AU - E. C. Kerrigan
AU - E. Scaccia
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01538
UR - https://arxiv.org/abs/2609.01538
AB - Generalized semi-infinite programs (GSIPs) arise in robust optimal control whenever the admissible uncertainty depends on the state or controls. Existing GSIP methods either impose restrictive structural assumptions or require global optimization that scales poorly to control problems. We present a general framework that reformulates any GSIP with mild regularity as an existence-constrained semi-infinite program, smoothing its disjunctive feasibility condition into differentiable existence constraints over a fixed index superset. The resulting program is solved by established adaptive discretization (cutting-plane) methods using only off-the-shelf nonlinear-programming solvers, and converges under standard assumptions. Treating the state trajectory as part of the uncertainty extends the framework to robust nonlinear optimal control with state-dependent uncertainty. We demonstrate it on a nonconvex benchmark GSIP and a satellite de-tumbling problem with dynamically varying inertia.
ER -