You can remote-reboot your Polycom phones from the Asterisk CLI by sending a SIP NOTIFY command. This command instructs the phone to recheck its configuration, and therefore, will reboot when certain parameters have been set in your phone configuration provisioning.

Make sure the following directive is set in your provisioning config:

<specialEvent voIpProt.SIP.specialEvent.checkSync.alwaysReboot="1" />

You find this in sip.cfg, or you can set it in your own configuration (mine's called aaps-settings.cfg, but that's just an arbitrary name).

Notice
When setting this variable in your own configuration, be sure that it's set in the right context, like so:<localcfg> &l  ...