Convergence in Nonlinear Optimal Sampled-Data Control Problems

• 成果类型: Article
• 署名作者: Bourdin, Loic; Trelat, Emmanuel
• 署名单位: Universite de Limoges; Inria; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3394650
• 发表日期: 2024
• 页码: 7144-7151
• 关键词: convergence; optimal control; Aerospace electronics; COSTS; vectors; trajectory; STANDARDS; Filippov approach; Pontryagin maximum principle (PMP); sampled-data control

摘要

Consider, on the one part, a general nonlinear finite- dimensional optimal control problem and assume that it has a unique solution x*. On the other part, consider the sampled-data control version of it. Under appropriate assumptions, we prove that the optimal state of the sampled-data problem converges uniformly to x* as the norm of the partition tends to zero. Moreover, applying the Pontryagin maximum principle (PMP) to both problems, we prove that, if x* has a unique weak extremal lift with a costate p that is normal, then the costate of the sampled-data problem converges uniformly to p. In other words, under a normality assumption, control sampling commutes, at the limit of small partitions, with the application of the PMP.