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

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• 作者：Milan Korda^a ; ^{milan.korda@engineering.ucsb.edu} ; Didier Henrion^b ; ^c ; ^d ; ^{henrion@laas.fr} ; Colin N. Jones^e ; ^{colin.jones@epfl.ch}
• 关键词：Optimal control ; Moment relaxations ; Polynomial sums of squares ; Convergence rate ; Semidefinite programming ; Approximation theory
• 刊名：Systems & Control Letters
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：100
• 期：Complete
• 页码：1-5
• 全文大小：414 K
• 卷排序：100

文摘

We study the convergence rate of the moment-sum-of-squares hierarchy of semidefinite programs for optimal control problems with polynomial data. It is known that this hierarchy generates polynomial under-approximations to the value function of the optimal control problem and that these under-approximations converge in the L1L1 norm to the value function as their degree dd tends to infinity. We show that the rate of this convergence is O(1∕loglogd). 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.