Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2024

Convergence in nonlinear optimal sampled-data control problems

Résumé

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.

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

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Loïc Bourdin, Emmanuel Trélat. Convergence in nonlinear optimal sampled-data control problems. IEEE Transactions on Automatic Control, 2024, 69 (10), pp.7144--7151. ⟨hal-03975698⟩
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