When Edward Lorentz first described chaos theory, it was heavily misunderstood. Von Neumann famously admitted that he thought what Lorentz was describing would permit global climate control within a decade. It was only much later that realized that such attempts to adjust the climate would be like giving a well shuffled deck of cards an extra shuffle. You can be certain that you changed your odds, but you don't know whether it is for better or for worse.
But what if von Neumann was right? Decades later we learned about mathematical techniques to control chaos. These are clever tricks to perturb chaotic systems to force them into predictable orbits. It's the fancy mathematical version of balancing a broomstick inverted on your hand. If left on its own, the broomstick will fall, but with you constantly observing and correcting, it remains in a steady state.
These approaches can be very low power, though they may take a lot of time to change large systems. Obviously, the faster they can change the system, the more demanding it will be to maintain it. But they do work.
They call for incredible understanding, however. If anything must be modeled stochastically, disorganized complexity rather than organized complexity, then it becomes increasingly hard to combat the random influences. However, if one has modeled everything, including the sun, with sufficient fidelity, one could entrain the entire solar system into doing what you will.
Of course, two of these boxes competing would wreak havoc. One can only assume that they are all in communication with one another and a tremendous amount of skill has gone into deconflicting the effects each individual seeks.