## 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 language | English |
---|---|

Article number | 105374 |

Journal | Systems & Control Letters |

Volume | 168 |

Early online date | 13 Sept 2022 |

DOIs | |

Publication status | Published - 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