Necessary Conditions for Free End-Time, Measurably Time Dependent Optimal Control Problems with State Constraints
Vinter, R.B. and Zheng, H. (2000) Necessary Conditions for Free End-Time, Measurably Time Dependent Optimal Control Problems with State Constraints. Set-Valued Analysis, 8, (1-2), 11-29. (doi:10.1023/A:1008762106012).
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Recently, necessary conditions have been derived for fixed-time optimal control problems with state constraints, formulated in terms of a differential inclusion, under very weak hypotheses on the data. These allow the multifunction describing admissible velocities to be unbounded and possibly nonconvex valued. This paper extends the earlier necessary conditions, to allow for free end-times. A notable feature of the new free end-time necessary conditions is that they cover problems with measurably time dependent data. For such problems, standard analytical techniques for deriving free-time necessary conditions, which depend on a transformation of the time variable, no longer work. Instead, we use variational methods based on the calculus of ''essential values".
|Digital Object Identifier (DOI):||doi:10.1023/A:1008762106012|
|Keywords:||Euler Lagrange condition, Hamiltonian inclusion, free time, state constraint, nonconvex differential inclusion, nonsmooth analysis|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||University Structure - Pre August 2011 > School of Mathematics > Operational Research
|Date Deposited:||20 Jul 2006|
|Last Modified:||06 Aug 2015 02:30|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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