Towards rigorous robust optimal control via generalized high‐order moment expansion

Towards rigorous robust optimal control via generalized high‐order moment expansion This study is concerned with the rigorous solution of worst‐case robust optimal control problems having bounded time‐varying uncertainty and nonlinear dynamics with affine uncertainty dependence. We propose an algorithm that combines existing uncertainty set‐propagation and moment‐expansion approaches. Specifically, we consider a high‐order moment expansion of the time‐varying uncertainty, and we bound the effect of the infinite‐dimensional remainder term on the system state, in a rigorous manner, using ellipsoidal calculus. We prove that the error introduced by the expansion converges to zero as more moments are added. Moreover, we describe a methodology to construct a conservative, yet more computationally tractable, robust optimization problem, whose solution values are also shown to converge to those of the original robust optimal control problem. We illustrate the applicability and accuracy of this approach with the robust time‐optimal control of a motorized robot arm. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Optimal Control Applications and Methods Wiley

Towards rigorous robust optimal control via generalized high‐order moment expansion

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2018 John Wiley & Sons, Ltd.
ISSN
0143-2087
eISSN
1099-1514
D.O.I.
10.1002/oca.2309
Publisher site
See Article on Publisher Site

Abstract

This study is concerned with the rigorous solution of worst‐case robust optimal control problems having bounded time‐varying uncertainty and nonlinear dynamics with affine uncertainty dependence. We propose an algorithm that combines existing uncertainty set‐propagation and moment‐expansion approaches. Specifically, we consider a high‐order moment expansion of the time‐varying uncertainty, and we bound the effect of the infinite‐dimensional remainder term on the system state, in a rigorous manner, using ellipsoidal calculus. We prove that the error introduced by the expansion converges to zero as more moments are added. Moreover, we describe a methodology to construct a conservative, yet more computationally tractable, robust optimization problem, whose solution values are also shown to converge to those of the original robust optimal control problem. We illustrate the applicability and accuracy of this approach with the robust time‐optimal control of a motorized robot arm.

Journal

Optimal Control Applications and MethodsWiley

Published: Jan 1, 2018

Keywords: ; ; ;

References

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