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 |
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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
- General Computer Science
- Mechanical Engineering
- Electrical and Electronic Engineering