What is the name of an AI system that learns by trial and error? Imagine a system that controls dampers in a complex vent system that has an objective to perfectly equalize the output from each vent. The system has sensors for damper position, flow at various locations and at each vent. The system is initially implemented using a rather small data set or even a formulaic algorithm to control the dampers. What if that algorithm were programmed to "try" different configurations of dampers to optimize the air flows, guided broadly by either the initial (weak) training or the formula? The system would try different configurations and learn what improved results, and what worsened results, in an effort to reduce error (differential outflow).

What is that kind of AI system called? What is that system of learning called? Are there systems that do that currently?
Near solution to your problem definition is reinforcement learning. You can define some reward using the objective function and define some possible state space for the machine and finally solve the problem by reinforcement learning techniques (near to trial and error by learning the preferences).