ABSTRACT
The elevator must approach the floor slowly enough that when the brakes are ◾ put on the passengers do not bounce. The missile or torpedo must pass close enough to the target that its explosion ◾ can destroy it. The unmanned lunar module must touch down before running out of fuel. ◾ The aircraft must touch down with small vertical velocity, with wings nearly ◾ level, with small sideslip across the runway, pointing straight down the runway, with enough remaining runway to stop safely. We must reach the next gas station before we run out of fuel. ◾
These are not criteria that can be addressed by a transfer function. They require a cost function. This can relate to the end point, such as “fuel remaining,” or can be something integrated throughout the journey. The simplest example of this is arrival time, where we can integrate a constant 1 and also get time as a state variable.
