Lear 60 Captain reported autopilot malfunctions caused an uncommanded pitch trim action. The Captain disconnected the autopilot and returned to cleared altitude.

Narrative

We were level at 10;000 feet MSL with Departure Control. We were initially on an RNAV departure but given a vector to turn northward and to delete the speed restriction. This is what they normally do. Nothing unusual so far but as I initiated the left turn to the assigned heading and increased power the aircraft pitched upward rather aggressively. The autopilot was already engaged. It was working normally but for some reason the aircraft pitched upward. We both noticed this and by time I reacted the aircraft pitch attitude was continuing to increase to about 10 degrees nose high before I was able to disconnect the autopilot and take control manually. I pushed forward; trimmed downward; throttled back but by then we were at least 500 feet above our assigned altitude. In the whole process I noticed the amber trim warning light was on momentarily.I'm experienced; have flown for over X years; with approximately 29;000 hours and flew military aircraft for X years with the military and airlines for X years and have not experienced this before. I informed Departure that I had a trim control problem and they asked if I needed any further assistance to which I said I did not. The aircraft was back under control. We had a team of doctors on board; a transplant team. All were okay.I guardedly reengaged the autopilot and there were no additional occurrences and the trim light had already gone out. It was a stand alone occurrence with no forewarning. During the rest of the flight I disengaged the autopilot and ran the pitch trim and reengaged it two or three more times with no unusual occurrences. I'm not sure what caused the issue. In my airline career I was a functional check flight Captain so I am very aware familiar with flight control and trim systems. All I can figure is that possibly the automated trim system rate of response during the turn and thrust increase for some unknown reason could not keep up.