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.
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e-mail: sleye@zedat.fu-berlin.de
e-mail: lenny.lucas@gmail.com
e-mail: owhadi@caltech.edu
e-mail: ortiz@aero.caltech.edu
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July 2010
Research Papers
Optimal Control Strategies for Robust Certification
Sigrid Leyendecker,
Sigrid Leyendecker
Biocomputing Group, Berlin Mathematical School,
e-mail: sleye@zedat.fu-berlin.de
Free University of Berlin
, Berlin 14195, Germany
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Leonard J. Lucas,
Leonard J. Lucas
Graduate Aeronautical Laboratories,
e-mail: lenny.lucas@gmail.com
California Institute of Technology
, Pasadena, CA 91125
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Houman Owhadi,
Houman Owhadi
Department of Applied and Computational Mathematics and Department of Control and Dynamical Systems,
e-mail: owhadi@caltech.edu
California Institute of Technology
, Pasadena, CA 91125
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Michael Ortiz
Michael Ortiz
Graduate Aeronautical Laboratories,
e-mail: ortiz@aero.caltech.edu
California Institute of Technology
, Pasadena, CA 91125
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Sigrid Leyendecker
Biocomputing Group, Berlin Mathematical School,
Free University of Berlin
, Berlin 14195, Germanye-mail: sleye@zedat.fu-berlin.de
Leonard J. Lucas
Graduate Aeronautical Laboratories,
California Institute of Technology
, Pasadena, CA 91125e-mail: lenny.lucas@gmail.com
Houman Owhadi
Department of Applied and Computational Mathematics and Department of Control and Dynamical Systems,
California Institute of Technology
, Pasadena, CA 91125e-mail: owhadi@caltech.edu
Michael Ortiz
Graduate Aeronautical Laboratories,
California Institute of Technology
, Pasadena, CA 91125e-mail: ortiz@aero.caltech.edu
J. Comput. Nonlinear Dynam. Jul 2010, 5(3): 031008 (10 pages)
Published Online: May 18, 2010
Article history
Received:
March 16, 2009
Revised:
October 26, 2009
Online:
May 18, 2010
Published:
May 18, 2010
Citation
Leyendecker, S., Lucas, L. J., Owhadi, H., and Ortiz, M. (May 18, 2010). "Optimal Control Strategies for Robust Certification." ASME. J. Comput. Nonlinear Dynam. July 2010; 5(3): 031008. https://doi.org/10.1115/1.4001375
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