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标题：Bifurcation preserving discretisations of optimal control problems
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作者：Christian Offen ; Sina Ober-Blöbaum
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2021
卷号：54
期号：19
页码：334-339
DOI：10.1016/j.ifacol.2021.11.099
语种：English
出版社：Elsevier
摘要：AbstractThe first order optimality conditions of optimal control problems (OCPs) can be regarded as boundary value problems for Hamiltonian systems. Variational or symplectic discretisation methods are classically known for their excellent long term behaviour. As boundary value problems are posed on intervals of fixed, moderate length, it is not immediately clear whether methods can profit from structure preservation in this context. When parameters are present, solutions can undergo bifurcations, for instance, two solutions can merge and annihilate one another as parameters are varied. We will show that generic bifurcations of an OCP are preserved under discretisation when the OCP is either directly discretised to a discrete OCP (direct method) or translated into a Hamiltonian boundary value problem using first order necessary conditions of optimality which is then solved using a symplectic integrator (indirect method). Moreover, certain bifurcations break when a non-symplectic scheme is used. The general phenomenon is illustrated on the example of a cut locus of an ellipsoid.
关键词：Keywordscatastrophe theorybifurcationsvariational methodssymplectic integrators