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- Title
Discrete Variational Optimal Control.
- Authors
Jiménez, Fernando; Kobilarov, Marin; Martín de Diego, David
- Abstract
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, and underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical examples and a practical one, the control of an underwater vehicle, illustrate the application of the proposed approach.
- Subjects
DISCRETE systems; OPTIMAL control theory; NONHOLONOMIC dynamical systems; ROBUST control; ALGORITHMS; INTEGRATORS; LIE groups
- Publication
Journal of Nonlinear Science, 2013, Vol 23, Issue 3, p393
- ISSN
0938-8974
- Publication type
Article
- DOI
10.1007/s00332-012-9156-z