Optimal Control Problems with Symmetry Breaking Cost Functions

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dc.contributor.authorBloch, Anthony M.
dc.contributor.authorColombo, Leonardo J.
dc.contributor.authorGupta, Rohit
dc.contributor.authorOhsawa, Tomoki
dc.contributor.utdAuthorOhsawa, Tomoki
dc.date.accessioned2019-06-28T20:40:16Z
dc.date.available2019-06-28T20:40:16Z
dc.date.created2017-10-30
dc.description.abstractWe investigate symmetry reduction of optimal control problems for left-invariant control affine systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a discrete-time setting as well as the standard continuous time formulation. Specifically, we recast the optimal control problem as a constrained variational problem with a partial symmetry breaking Lagrangian and obtain the Euler-Poincare equations from a variational principle. By using a Legendre transformation, we recover the Lie Poisson equations obtained by Borum and Bretl [IEEE Trans. Automat. Control, 62 (2017), pp. 3209-3224] in the same context. We also discretize the variational principle in time and obtain the discrete-time Lie Poisson equations. We illustrate the theory with some practical examples including a motion planning problem in the presence of an obstacle.
dc.description.departmentSchool of Natural Sciences and Mathematics
dc.identifier.bibliographicCitationBloch, Anthony M., Leonardo J. Colombo, Rohit Gupta, and Tomoki Ohsawa. 2017. "Optimal control problems with symmetry breaking cost functions." SIAM Journal on Applied Algebra and Geometry 1(1): 626-646, doi:10.1137/16M1091654
dc.identifier.issn2470-6566
dc.identifier.issue1
dc.identifier.urihttps://hdl.handle.net/10735.1/6648
dc.identifier.volume1
dc.language.isoen
dc.publisherSIAM Publications
dc.relation.urihttp://dx.doi.org/10.1137/16M1091654
dc.rights©2017 Society for Industrial and Applied Mathematics
dc.source.journalSIAM Journal on Applied Algebra and Geometry
dc.subjectEuler characteristic
dc.subjectLagrange equations
dc.subjectLie groups
dc.titleOptimal Control Problems with Symmetry Breaking Cost Functions
dc.type.genrearticle

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