{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:14:28Z","timestamp":1760235268636,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,7,31]],"date-time":"2021-07-31T00:00:00Z","timestamp":1627689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Geometrically, the affine connection is the main ingredient that underlies the covariant derivative, the parallel transport, the auto-parallel curves, the torsion tensor field, and the curvature tensor field on a finite-dimensional differentiable manifold. In this paper, we come up with a new idea of controllability and observability of states by using auto-parallel curves, and the minimum time problem controlled by the affine connection. The main contributions refer to the following: (i) auto-parallel curves controlled by a connection, (ii) reachability and controllability on the tangent bundle of a manifold, (iii) examples of equiaffine connections, (iv) minimum time problem controlled by a connection, (v) connectivity by stochastic perturbations of auto-parallel curves, and (vi) computing the optimal time and the optimal striking time. The connections with bounded pull-backs result in bang\u2013bang optimal controls. Some significative examples on bi-dimensional manifolds clarify the intention of our paper and suggest possible applications. At the end, an example of minimum striking time with simulation results is presented.<\/jats:p>","DOI":"10.3390\/sym13081391","type":"journal-article","created":{"date-parts":[[2021,8,1]],"date-time":"2021-08-01T21:46:44Z","timestamp":1627854404000},"page":"1391","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Minimum Time Problem Controlled by Affine Connection"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7132-6900","authenticated-orcid":false,"given":"Constantin","family":"Udriste","sequence":"first","affiliation":[{"name":"Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, 060042 Bucharest, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9160-9185","authenticated-orcid":false,"given":"Ionel","family":"Tevy","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, 060042 Bucharest, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/BF00149271","article-title":"On Completeness in Affine Differential Geometry","volume":"20","author":"Nomizu","year":"1986","journal-title":"Geom. 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