Necessary Conditions for Free End-Time, Measurably Time Dependent Optimal Control Problems with State Constraints
Necessary Conditions for Free End-Time, Measurably Time Dependent Optimal Control Problems with State Constraints
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"
Euler Lagrange condition, Hamiltonian inclusion, free time, state constraint, nonconvex differential inclusion, nonsmooth analysis
11-29
Vinter, R.B.
bc315999-83a5-4e40-9b6c-ca21382ce81b
Zheng, H.
22605265-1a2f-4a65-b86d-b7f1e73c3fc9
2000
Vinter, R.B.
bc315999-83a5-4e40-9b6c-ca21382ce81b
Zheng, H.
22605265-1a2f-4a65-b86d-b7f1e73c3fc9
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), .
(doi:10.1023/A:1008762106012).
Abstract
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"
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Published date: 2000
Keywords:
Euler Lagrange condition, Hamiltonian inclusion, free time, state constraint, nonconvex differential inclusion, nonsmooth analysis
Organisations:
Operational Research
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Local EPrints ID: 29669
URI: http://eprints.soton.ac.uk/id/eprint/29669
ISSN: 0927-6947
PURE UUID: b4e8b5a9-0bc6-46c4-bc9b-1ad764d321dd
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Date deposited: 20 Jul 2006
Last modified: 15 Mar 2024 07:33
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Author:
R.B. Vinter
Author:
H. Zheng
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