Optimal Control Strategies for Robust Certification
We present an optimal control methodology, which we refer to as concentration-of-measure optimal control (COMOC), that seeks to minimize a concentration-of-measure upper bound on the probability of failure of a system. The systems under consideration are characterized by a single performance measure that depends on random inputs through a known response function. For these systems, concentration-of-measure upper bound on the probability of failure of a system can be formulated in terms of the mean performance measure and a system diameter that measures the uncertainty in the operation of the system. COMOC then seeks to determine the optimal controls that maximize the confidence in the safe operation of the system, defined as the ratio of the design margin, which is measured by the difference between the mean performance and the design threshold, to the system uncertainty, which is measured by the system diameter. This strategy has been assessed in the case of a robot-arm maneuver for which the performance measure of interest is assumed to be the placement accuracy of the arm tip. The ability of COMOC to significantly increase the design confidence in that particular example of application is demonstrated.
© 2010 American Society of Mechanical Engineers. 1Submitted to the ASME Journal of Computational and Nonlinear Dynamics, special issue on Multidisciplinary High-Performance Computational Multibody Dynamics, edited by Dan Negrut and Olivier Bauchau, Mar. 15, 2009. Received 16 March 2009; revised 26 October 2009; published 18 May 2010. The authors gratefully acknowledge the support of the U.S. Department of Energy through Caltech's PSAAP Center for the Predictive Modeling and Simulation of High-Energy Density Dynamic Response of Materials. We would also like to thank Sina Ober-Blöbaum for the helpful discussions, and the reviewers for their valuable suggestions in the paper's organization.
Published - Leyendecker2010p10583J_Comput_Nonlin_Dyn.pdf