Optimal switching between collective motion states for two agents
✍ Scribed by Allison Kolpas; Jeff Moehlis
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 420 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
✦ Synopsis
We show that steering control can be chosen to give bistability between parallel and antiparallel collective motion states for a continuous-time kinetic model of two agents moving in the plane with unit speed. Variational methods are used to determine the optimal input to the steering control of one of the agents which leads to switching between these collective states. For any given time interval of switching, such an optimal input is shown to exist and to be unique. The properties of optimal inputs are interpreted by considering the phase space geometry of the Euler-Lagrange equations associated with the optimization.