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Article Dans Une Revue Systems and Control Letters Année : 2017

Convergence rates of moment-sum-of-squares hierarchies for optimal control problems

Résumé

We study the convergence rate of moment-sum-of-squares hierarchies of semidefinite programs for optimal control problems with polynomial data. It is known that these hierarchies generate polynomial under-approximations to the value function of the optimal control problem and that these under-approximations converge in the L1 norm to the value function as their degree d tends to infinity. We show that the rate of this convergence is O(1/ log log d). We treat in detail the continuous-time infinite-horizon discounted problem and describe in brief how the same rate can be obtained for the finite-horizon continuous-time problem and for the discrete-time counterparts of both problems.
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Dates et versions

hal-01362456 , version 1 (08-09-2016)

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Milan Korda, Didier Henrion, Colin N. Jones. Convergence rates of moment-sum-of-squares hierarchies for optimal control problems. Systems and Control Letters, 2017, 100, pp.1-5. ⟨hal-01362456⟩
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