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Milan Korda (korda.mgmail.com) Abstract: We study the convergence rate of momentsumofsquares hierarchies of semidefinite programs for optimal control problems with polynomial data. It is known that these hierarchies generate polynomial underapproximations to the value function of the optimal control problem and that these underapproximations converge in the $L^1$ 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 continuoustime infinitehorizon discounted problem and describe in brief how the same rate can be obtained for the finitehorizon continuoustime problem and for the discretetime counterparts of both problems. Keywords: optimal control, moment relaxations, polynomial sums of squares, semidefinite programming, approximation theory Category 1: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Category 2: Applications  Science and Engineering (Control Applications ) Category 3: Nonlinear Optimization (Systems governed by Differential Equations Optimization ) Citation: Download: [PDF] Entry Submitted: 09/08/2016 Modify/Update this entry  
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