Hidden Factors [From the Editor]

One of the facets of realistic control applications that is not captured by linear models is the asymmetry of control action. Linear springs and quadratic costs give us the impression that all errors of the same magnitude—be they left or right, up or down—are created equal. But this is often not the case. If the goal is to maintain a high temperature, then we need only expend energy to raise the temperature; if we overshoot, then the temperature drops by itself. The saying “you can´t be too rich or too thin” suggests that it´s easy to become poor or obese but difficult to lose weight and earn money—a huge asymmetry in control effort. For an aircraft, we must work to provide lift, but bringing the aircraft to the ground is effortless; we let gravity do the work for us.