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dc.contributor.authorKang, Wei
dc.contributor.authorWilcox, Lucas C.
dc.date8 April 2017
dc.date.accessioned2018-08-28T16:34:32Z
dc.date.available2018-08-28T16:34:32Z
dc.date.issued2017-04-08
dc.identifier.citationKang, Wei, and Lucas C. Wilcox. "Mitigating the curse of dimensionality: sparse grid characteristics method for optimal feedback control and HJB equations." Computational Optimization and Applications 68.2 (2017): 289-315.en_US
dc.identifier.urihttp://hdl.handle.net/10945/59728
dc.descriptionThe article of record as published may be found at http://dx.doi.org/10.1007/s10589-017-9910-0en_US
dc.description.abstractWe address finding the semi-global solutions to optimal feedback control and the Hamilton–Jacobi–Bellman (HJB) equation. Using the solution of an HJB equation, a feedback optimal control law can be implemented in real-time with minimum computational load. However, except for systems with two or three state variables, using traditional techniques for numerically finding a semi-global solution to an HJB equation for general nonlinear systems is infeasible due to the curse of dimensionality. Here we present a new computational method for finding feedback optimal control and solving HJB equations which is able to mitigate the curse of dimensionality. We do not discretize the HJB equation directly, instead we introduce a sparse grid in the state space and use the Pontryagin’s maximum principle to derive a set of necessary conditions in the form of a boundary value problem, also known as the characteristic equations, for each grid point. Using this approach, the method is spatially causality free, which enjoys the advantage of perfect parallelism on a sparse grid. Compared with dense grids, a sparse grid has a significantly reduced size which is feasible for systems with relatively high dimensions, such as the 6-D system shown in the examples. Once the solution obtained at each grid point, high-order accurate polynomial interpolation is used to approximate the feedback control at arbitrary points. We prove an upper bound for the approximation error and approximate it numerically. This sparse grid characteristics method is demonstrated with three examples of rigid body attitude control using momentum wheels.en_US
dc.description.sponsorshipAFOSR, NRL, DARPA, and CRUSERen_US
dc.format.extent27 p.en_US
dc.publisherSpringeren_US
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.titleMitigating the curse of dimensionality: sparse grid characteristics method for optimal feedback control and HJB equationsen_US
dc.typeArticleen_US
dc.contributor.corporateNaval Postgraduate School (U.S.)en_US
dc.contributor.departmentApplied Mathematicsen_US
dc.subject.authorOptimal feedback controlen_US
dc.subject.authorHamilton–Jacobi–Bellman equationen_US
dc.subject.authorSparse griden_US
dc.subject.authorMethod of characteristicsen_US
dc.subject.authorRigid body attitude controlen_US
dc.description.distributionstatementApproved for public release; distribution is unlimited.


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