EMB-145 Captain reported multiple systems failures and elected to divert to make a precautionary landing.

Narrative

Climbing through FL315 both RUDDER SYS 1-2 INOP; and AUTOPILOT FAIL messages appeared and the autopilot disconnected. I took controls immediately and leveled at FL320. I told my First Officer to open the Quick Reference Handbook and run the Autopilot fail checklist then the rudder checklist. The rudder checklist did not solve the problem. The messages persisted. I gave the First Officer the flight controls next and asked ATC to descend us out of RVSM airspace. He descended us to FL280. When at FL280 the RUDDER SYS 1-2 INOP message went away. Then RUDDER SYS 1 INOP and RUDDER SYS 2 INOP went on and off and alternated roughly 5 or 6 times. After that the RUDDER SYS 1-2 INOP came back steady. Then the YAW DAMPER FAIL message appeared. I noticed we were approximately 20 miles southeast of ZZZ2. I knew there were Company operations and maintenance there. I told my Flight Attendant to lock up and sit down and I would advise her of the situation in a little while. I sent a message to dispatch of the messages; discussing declaring; and diverting to ZZZ2. He spoke with maintenance and we all agreed for me to request priority handling. I promptly requested priority handling with ZZZ. We got a diversion started and ATC descended us and vectored us to ZZZ2. In the descent around FL180 the RUDDER SYS 1-2 INOP message disappeared. Both AUTOPILOT FAIL and YAW DAMPER FAIL messages persisted. We got through about 12000 ft. at which point we were caught up and finished getting the plane ready for landing. I called the Flight Attendant and informed her of what was happening and did the TEST report. After which I communicated with the passengers of the diversion. They vectored us to left downwind of XXR; at which point I took back flight controls. We landed with no issue. Fire trucks surrounded us and then ATC asked us if we needed their help; to which we informed them no. We parked at the gate. Got a number for ATC. Talked with the fire department; duty manager; maintenance control; and scheduling. People were put into the terminal. I was informed they would go out on the next repo flight. We went to the hotel.