Optimal Control Problems with Symmetry Breaking Cost Functions
dc.contributor.author | Bloch, Anthony M. | |
dc.contributor.author | Colombo, Leonardo J. | |
dc.contributor.author | Gupta, Rohit | |
dc.contributor.author | Ohsawa, Tomoki | |
dc.contributor.utdAuthor | Ohsawa, Tomoki | |
dc.date.accessioned | 2019-06-28T20:40:16Z | |
dc.date.available | 2019-06-28T20:40:16Z | |
dc.date.created | 2017-10-30 | |
dc.description.abstract | We 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.department | School of Natural Sciences and Mathematics | |
dc.identifier.bibliographicCitation | Bloch, 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.issn | 2470-6566 | |
dc.identifier.issue | 1 | |
dc.identifier.uri | https://hdl.handle.net/10735.1/6648 | |
dc.identifier.volume | 1 | |
dc.language.iso | en | |
dc.publisher | SIAM Publications | |
dc.relation.uri | http://dx.doi.org/10.1137/16M1091654 | |
dc.rights | ©2017 Society for Industrial and Applied Mathematics | |
dc.source.journal | SIAM Journal on Applied Algebra and Geometry | |
dc.subject | Euler characteristic | |
dc.subject | Lagrange equations | |
dc.subject | Lie groups | |
dc.title | Optimal Control Problems with Symmetry Breaking Cost Functions | |
dc.type.genre | article |