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Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures

Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Kobilarov, Marin (2012) Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures. Journal of Nonlinear Science, 22 (4). pp. 599-629. ISSN 0938-8974. doi:10.1007/s00332-012-9140-7.

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Computing globally efficient solutions is a major challenge in optimal control of nonlinear dynamical systems. This work proposes a method combining local optimization and motion planning techniques based on exploiting inherent dynamical systems structures, such as symmetries and invariant manifolds. Prior to the optimal control, the dynamical system is analyzed for structural properties that can be used to compute pieces of trajectories that are stored in a motion planning library. In the context of mechanical systems, these motion planning candidates, termed primitives, are given by relative equilibria induced by symmetries and motions on stable or unstable manifolds of e.g. fixed points in the natural dynamics. The existence of controlled relative equilibria is studied through Lagrangian mechanics and symmetry reduction techniques. The proposed framework can be used to solve boundary value problems by performing a search in the space of sequences of motion primitives connected using optimized maneuvers. The optimal sequence can be used as an admissible initial guess for a post-optimization. The approach is illustrated by two numerical examples, the single and the double spherical pendula, which demonstrates its benefit compared to standard local optimization techniques.

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Additional Information:© 2012 Springer Science+Business Media, LLC. Received: 31 October 2011; Accepted: 23 June 2012; Published online: 13 July 2012. Jerry Marsden has been a great inspiration to us to work on this topic. We thank him for fruitful discussions and collaborations during the last years. This contribution was partly developed and published in the course of the Collaborative Research Centre 614 “Self-Optimizing Concepts and Structures in Mechanical Engineering” funded by the German Research Foundation (DFG) under grant number SFB 614. M. Kobilarov was supported by the Keck Institute for Space Studies, Caltech.
Group:Keck Institute for Space Studies
Funding AgencyGrant Number
Keck Institute for Space Studies (KISS)UNSPECIFIED
German Research Foundation (DFG)SFB 614
Subject Keywords:Lagrangian mechanics; Optimal control; Symmetries; Invariant manifolds
Issue or Number:4
Classification Code:Mathematics Subject Classification: 37J15; 49M37; 70Q05
Record Number:CaltechAUTHORS:20121008-084841949
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:34737
Deposited By: Tony Diaz
Deposited On:09 Oct 2012 21:55
Last Modified:09 Nov 2021 23:10

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