Higher-order control is contrasted to first-order control. In second- and higher-order control, the way the mechanism is used may change.
It can be said that first-order control is how much something is done, second-order control is what is done, and third-order control is inventing new things to do.
There is no reason to believe a higher-order solution is preferable in all situations; but higher-order solutions should be attempted when first-order solutions have been shown to be ineffectual.