Collective Steering in Finite Time: Controllability on GL+(n, R)

• 成果类型: Article
• 署名作者: Abdelgalil, Mahmoud; Georgiou, Tryphon T.
• 署名单位: University of California System; University of California San Diego; University of California System; University of California Irvine
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3574186
• 发表日期: 2025
• 关键词: products

摘要

We consider the problem of steering a collection of n particles that obey identical n-dimensional linear dynamics via a common state feedback law toward a rearrangement of their positions, cast as a controllability problem for a dynamical system evolving on the space of matrices with positive determinant. We show that such a task is always feasible and, moreover, that it can be achieved arbitrarily fast. We also show that an optimal feedback control policy to achieve a similar feat, may not exist. Furthermore, we show that there is no universal formula for a linear feedback control law to achieve a rearrangement, optimal or not, that is everywhere continuous with respect to the specifications. We conclude with partial results on the broader question of controllability of dynamics on orientation-preserving diffeomorphisms.