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

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 L-1 norm to the value function as their degree d tends to infinity. We show that the rate of this convergence is 0(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. (C) 2016 Elsevier B.V. All rights reserved.


Published in:
Systems & Control Letters, 100, 1-5
Year:
2017
Publisher:
Amsterdam, Elsevier Science Bv
ISSN:
0167-6911
Keywords:
Laboratories:




 Record created 2017-05-01, last modified 2018-12-03


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