Exact continuous reformulations of logic constraints in nonlinear optimization and optimal control problems
File(s)
Accepted version
Author(s)
Wehbeh, Jad
Kerrigan, Eric
Type
Journal Article
Abstract
Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability challenges and requires specialized solvers. This paper presents an exact reformulation of broad classes of logical constraints as binary-variable-free expressions whose differentiability properties coincide with those of the underlying predicates, enabling their direct integration into nonlinear programming models. Our approach rewrites arbitrary logical propositions into conjunctive normal form, converts them into equivalent max--min constraints, and applies a smoothing procedure that preserves the exact feasible set. The method is evaluated on two benchmark problems, a quadrotor trajectory optimization with obstacle avoidance and a hybrid two-tank system with temporal logic constraints, and is shown to obtain optimal solutions more consistently and efficiently than existing binary variable elimination techniques.
Date Acceptance
2026-08-18
Citation
Automatica
ISSN
0005-1098
Publisher
Elsevier
Journal / Book Title
Automatica
Copyright Statement
Copyright This paper is embargoed until publication. Once published the author’s accepted manuscript will be made available under a CC-BY License in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy).
License URL
Publication Status
Accepted