It depends what you mean.
At the basic level they hsve no direct control of the connection between your modem and the modem in the FTTC cabinet. Only Openreach have that. However there are ways an ISP can get Openreach to cause a re-sync but this is not routine.
At the higher level, your ability to access the internet is generally via a PPP session established between your router, (not the modem component), and one of the ISP's routers. That is obviously under their direct control, just as your modem/router is under yours.
Then of course some ISPs have forms of remote control of your modem/router if it is one they have supplied to you. Allowing them to install later versions of its firmware and software, and re-sync it.
My broadband basic info/help site - www.robertos.me.uk.
Domains, site and mail hosting - Tsohost
Connection - AAISP Home::1 80/20. 200GB. Sync 72313/12530Kbps @ 600m. BQMs - IPv4