EMB-145 Captain reported a Rudder Overboost EICAS message on initial climb. The flight crew performed trouble shooting and QRH procedures and determined the #2 Rudder Hydraulic system was inoperative. The flight crew continued to destination airport and swapped aircraft.

Narrative

Upon the initial climb at about 600 ft. MSL the crew received an EICAS message: 'rudder overboost'. The crew identified and cancelled the caution; flew the plane above acceleration altitude; and continued on course with a normal climb profile. The PM ran the QRH for 'rudder overboost'. The Pilot Monitoring (PM) followed the QRH and pushed the Rudder Sys 2 Shutoff PB out; and the EICAS message rudder overboost disappeared. Then; the message 'rudder sys 2 inop' appeared on the EICAS. That was the end of the QRH. The PM sent a message to Dispatch above 10;000 ft. to let them know. The flight continued normally; the crew; aka the pilots; dispatch and maintenance; worked well together and showed CRM. Maintenance was in the know thanks to Dispatch. Upon the plane's arrival to ZZZ1; dispatch notified the pilots that a repo plane was already on it's way to ZZZ1 to replace the broken airplane. As far as threats were involved; there were gusty winds in ZZZ2 upon departure. There were no errors observed; and no Undesirable Aircraft State occurred. The plane landed safely in ZZZ1.