A note on minimum time–energy control

Research output: Contribution to journalArticlepeer-review

Abstract

Elementary observations on a free-end-time problem of minimizing a functional of the form u↦∫ 0 t u L(u(t))dt, over controls t↦u(t)∈U, U a convex, compact neighbourhood of 0∈R m, are provided in the context of systems ẋ=f(x,u) with prescribed initial and terminal states: x(0)=ξ and x(t u)=0. Conditions on f and L are identified which are sufficient for existence and continuity of minimizers. For m=1, U=[−1,1] and [Formula presented] (reflecting a twofold performance objective with equal weight placed on transition time and energy expenditure), an exposition of aspects of the problem is given in the case of integrator chains.

Original languageEnglish
Article number105374
JournalSystems & Control Letters
Volume168
Early online date13 Sep 2022
DOIs
Publication statusPublished - 31 Oct 2022

Keywords

  • Existence and continuity of solutions
  • Free-end-time optimal control
  • Integrator chains

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science(all)
  • Mechanical Engineering
  • Electrical and Electronic Engineering

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