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To the best of our knowledge, this is the first attempt to derive necessary conditions of optimality for optimal control problems involving systems with backlash. The case of systems with backlash and elastic impact is covered in a forthcoming and companion paper.<\/jats:p>","DOI":"10.1007\/s11228-025-00780-4","type":"journal-article","created":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T10:34:57Z","timestamp":1760351697000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimal Control of Systems with Backlash: The Case of Inelastic Impact"],"prefix":"10.1007","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9276-2317","authenticated-orcid":false,"given":"M. d. R.","family":"de Pinho","sequence":"first","affiliation":[]},{"given":"M. M. A.","family":"Ferreira","sequence":"additional","affiliation":[]},{"given":"G. 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