The log just shows that the controller was down due to no snmp response, then confirmed down due to no ping, and then when the controller came up, AMP reports that the controller had rebooted due to the change in uptime. This is not the same as AirWave sending a reboot command to the controller. To verify the behavior, check the device logs in /var/log/ap/<id of controller>. There should be an event log that is the same as what you included originally, and then the audit log (used during config audits), and then a telnet_cmds log which would have any reboot command.
For instance, my controller's URL:
http://robs_amp/ap_monitoring?id=1234
this corresponds to CLI directory: /var/log/ap/1234
# cd /var/log/ap/1234
# grep -i reboot *
event.log:Tue Oct 1 12:09:24 2013 Device has rebooted: Device uptime value changed (current: 3 mins 52 secs, calculated: 5 days 14 hrs 18 mins 12 secs) System
This tells me that my controller had rebooted, but it was not initialized by AMP since I didn't see the reboot command in the outgoing telnet_cmds log.