The flight crew reported that they observed a LOW AIRSPEED advisoryon the aircraft’s Engine Indication and Crew Alerting System (EICAS), whenclimbing through flight level (FL) 380. They also reported that, at the same time, the aircraft’s slip/skid indication2 deflected to the full right position on the Primary Flight Display (PFD)3. The PFD speed tape4 then indicated that the aircraft was approaching the overspeed limit and the stall speed limit5 simultaneously. The aircraft nose then pitched up, with the aircraft climbing to approximately FL410. The indicated airspeed then decreased from 270 to 158 kts, and the stall warningand stick shaker devices activated. The pilot in command reported that he then disconnected the autopilot and lowered the nose of the aircraft.
.....The pilot in command later reported that the PFD indications appeared normal
when descending through FL200. He then reportedly selected the LEFT6 autopilot‘ON’, but the aircraft banked to the right and the nose pitched down, so the autopilot was disengaged. A similar result occurred when the RIGHT autopilot was selected, so the pilot in command left the autopilot disengaged and manually flew the aircraft. The pilot in command reported that, with the autopilot disengaged, there were no further control difficulties experienced. The pilot in command reported that he attempted to disconnect the autothrottle by pressing the thrust lever autothrottle disconnect switches and pushing the autothrottle engage switch. The autothrottle arm switches had remained in the ‘ARMED’ position during the occurrence.
... The flight crew later reported that the aircraft’s autobrake system was selected to AUTOBRAKE 3 before landing, but that after landing the autobrakes were not able to be cancelled by using the brake pedals. The AUTOBRAKE switch was then selected to OFF and normal operation resumed.