Fast oscillating control

The dimension of a system that we try to control is usually much bigger than number of controlled parameters at our disposal. On the other hand, controlled parameters are not constant, we select their values as more or less arbitrary functions of time, and a lack of resources can be compensated by a sophisticated strategy. Moreover, some efficient universal maneuvers, being rescaled and repeated with a high frequency, may serve as additional independent controlled parameters. I'll try to explain how it works in some typical situations including the motion planning under nonholonomic constraints and control of the Navier–Stokes equation by a degenerate external force.