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Convergence in nonlinear optimal sampled-data control problems

Loïc Bourdin
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Emmanuel Trélat

Abstract

Consider, on the one part, a general nonlinear finite-dimensional optimal control problem and assume that it has a unique solution whose state is denoted by 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 corresponding partition tends to zero. Moreover, applying the Pontryagin maximum principle 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 nondegeneracy assumption, control sampling commutes, at the limit of small partitions, with the application of the Pontryagin maximum principle.

Dates and versions

hal-03975698 , version 1 (06-02-2023)

Identifiers

• HAL Id : hal-03975698 , version 1
• ARXIV :

Cite

Loïc Bourdin, Emmanuel Trélat. Convergence in nonlinear optimal sampled-data control problems. 2023. ⟨hal-03975698⟩

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