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A parallel decomposition scheme for solving long-horizon optimal control problems
Publikationstyp
Conference Paper
Date Issued
2019-12-01
Sprache
English
Author(s)
Volume
2019-December
Start Page
5264
End Page
5271
Article Number
9030139
Citation
Proceedings of the 58th IEEE Conference on Decision and Control 2019: 5264-5271 (2019)
Contribution to Conference
Publisher DOI
Scopus ID
Publisher
IEEE
ISSN
07431546
ISBN
9781728113982
We present a temporal decomposition scheme for solving long-horizon optimal control problems. The time domain is decomposed into a set of subdomains with partially overlapping regions. Subproblems associated with the subdomains are solved in parallel to obtain local primal-dual trajectories that are assembled to obtain the global trajectories. We provide a sufficient condition that guarantees convergence of the proposed scheme. This condition states that the effect of perturbations on the boundary conditions (i.e., the initial state and terminal dual/adjoint variable) should decay asymptotically as one moves away from the boundaries. This condition also reveals that the scheme converges if the size of the overlap is sufficiently large and that the convergence rate improves with the size of the overlap. We prove that linear quadratic problems satisfy the asymptotic decay condition, and we discuss numerical strategies to determine if the condition holds in more general cases. We draw upon a non-convex optimal control problem to illustrate the performance of the proposed scheme.
Subjects
Decomposition scheme
Global trajectories
Linear quadratic problem
Non-convex optimal control problems
Numerical strategies
Optimal control problem
Overlapping regions
Temporal decomposition
DDC Class
004: Computer Sciences
510: Mathematics