A note on minimum time–energy control

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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
Early online date13 Sept 2022
Publication statusPublished - 31 Oct 2022


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

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Computer Science
  • Mechanical Engineering
  • Electrical and Electronic Engineering


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