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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Original Publication URL: http://dx.doi.org/10.1023/A:1008762106012

Description/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".

Item Type: Article
ISSNs: 0927-6947 (print)
Related URLs:
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
ePrint ID: 29669
Date Deposited: 20 Jul 2006
Last Modified: 27 Mar 2014 18:18
Contact Email Address: r.vinter@ic.ac.uk
URI: http://eprints.soton.ac.uk/id/eprint/29669

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