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DOI: 10.23952/cot.2026.5
Received August 31, 2024; Accepted January 25, 2025; Published online January 19, 2026
Abstract. The kinematic model “Dubins car” is considered. A scalar control is constrained by a quadratic integral constraint. A three-dimensional initial phase state is fixed, and a two-dimensional reachable set is constructed “at the instant” on the plane of geometric coordinates. The analysis is based on the Pontryagin maximum principle. Examples of numerical construction of the reachable set are given. A comparison is made with the case of a geometric control constraint.
How to Cite this Article:
V. Patsko, G. Trubnikov, A. Fedotov, Two-dimensional reachable set for dubins car under an integral constraint on control, Commun. Optim. Theory 2026 (2026) 5.