Set-Valued Analysis

, Volume 8, Issue 1, pp 11–29

Necessary Conditions for Free End-Time, Measurably Time Dependent Optimal Control Problems with State Constraints

  • R. B. Vinter
  • H. Zheng

DOI: 10.1023/A:1008762106012

Cite this article as:
Vinter, R.B. & Zheng, H. Set-Valued Analysis (2000) 8: 11. doi:10.1023/A:1008762106012


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 conditionHamiltonian inclusionfree timestate constraintnonconvex differential inclusionnonsmooth analysis

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • R. B. Vinter
    • 1
  • H. Zheng
    • 2
  1. 1.Department of Electrical and Electronic Engineering and Centre for Process Systems EngineeringImperial CollegeLondonU.K.
  2. 2.Department of Business StudiesUniversity of EdinburghEdinburghU.K.