The paper is structured as follows. First, we propose a novel method that appears to be capable of driving a system near critical points by maintaining certain relational invariants. In our case, these invariants are extracted from the correlation structure of a well-known model operating at a critical point, where correlations scale with distance according to a power law function. Second, we propose a simple learning rule maintaining this correlation invariance, and hypothesize that it could be used for driving systems in different contexts to operate near critical points. We test the model using two classical examples of learning and control: the Mountain Car and a double pendulum. We show evidence suggesting that the general rule proposed here is able to drive adaptive agents with no free parameters towards critical points of operation. At the same time, the agents themselves are poised at points of behavioural transition, where they are able to exploit a broad span of dynamic possibilities available in their environment, suggesting a link between an internal search of critical points and the exploration of external behavioural points of transition. Finally, we suggest further tests of criticality and discuss the limitations and possible generalization of this synthetic approach as a contribution towards understanding deeper principles governing biological and cognitive systems.