2019
DOI: 10.1137/18m119121x
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Continuity of Pontryagin Extremals with Respect to Delays in Nonlinear Optimal Control

Abstract: HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des labor… Show more

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Cited by 6 publications
(4 citation statements)
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“…3) Convergence of Pontryagin Variations: Due to the achieved convergences on controls and trajectories, we can now prove that it is possible to pass the limit k → ∞ inside (8), showing that (5) holds. For, we first recall a converging result whose proof comes from a straightforward adaptation to [32,Lemma 3.11], whereby the continuity of the controls is replaced by the weaker assumption (A 4 ).…”
Section: Proof Of the Convergence Resultsmentioning
confidence: 99%
“…3) Convergence of Pontryagin Variations: Due to the achieved convergences on controls and trajectories, we can now prove that it is possible to pass the limit k → ∞ inside (8), showing that (5) holds. For, we first recall a converging result whose proof comes from a straightforward adaptation to [32,Lemma 3.11], whereby the continuity of the controls is replaced by the weaker assumption (A 4 ).…”
Section: Proof Of the Convergence Resultsmentioning
confidence: 99%
“…Motivated by the convergence result established in [54], [55], we could add one further homotopic step on the delay. For computational times, even if many simulations on different missions for (OIP) show that Algorithm 1 can run between 0.5 Hz and 1 Hz, we cannot ensure a real-time processing yet.…”
Section: Discussionmentioning
confidence: 99%
“…Through Lemma 3.7, (A 4 ) becomes crucial to ensure the validity of (AC) in Theorem 3.6. In particular, the works [44][45][46][47], which analyze continuity properties of extremals with respect to appropriate deformations of some deterministic optimal control problems and which inspired our work, show that the timecontinuity of optimal controls u k for each LOCP ∆ k represents a requirement which is not easy to relax (in particular, see the counterexample in [47, Section 2.3]), especially in the presence of trust-region constraints. Importantly, motivated by regularity results in deterministic optimal control settings (see, e.g., [48, Theorem 3.2]), we reckon that more generic mappings G might yield Lemma 3.7, especially when optimizing over deterministic controls, although we leave the investigation of more general sufficient conditions for the time-continuity of optimal controls u k for each LOCP ∆ k as a future research direction, in that it is out of the scope of this work which again focuses on the properties of accumulations points of the sequence generated by SCP.…”
Section: Existence Of Accumulation Points For Scpmentioning
confidence: 99%