## Pseudospectral Optimal Control

The term for the problem DIDO is solving is optimal control. In calculus, optimal control theory is a mathematical approach to finding the best mechanical response in a given scenario given some set of conditions. Mathematically, optimal control is a set of differential equations that minimize the cost (maximize the payoff) of achieving some desired outcome. Don't worry! We're about to make this concept much simpler.

To understand optimal control, let's freeze time for a moment. Take in the sensations of the world around you: sights, sounds, smells, tastes and physical feelings. Now combine that with everything stored in your brain. The way you respond to any new stimulus around you will be based on all that information. How would you react right now to hearing a doorbell or to smelling freshly baked cookies?

Computers can convert similar sensory information into data in an attempt to imitate our brainpower. The computer can calculate the best response to a given stimulus using all that data. From the computer's perspective, the "best" response would be the action that has the maximum payoff at the minimum cost. That best response concept is what scientists and mathematicians refer to as the optimal control.

Now let's unfreeze time and move forward again. Suddenly, calculating the optimal control is more complicated. As each fraction of a second passes, conditions change, with new sensory data to consider. Thus, the biggest challenge for finding the optimal control is considering these ever-changing conditions and recalculating accordingly. Our brains make these recalculations constantly, but a computer has to have some type of stimulus-response program to do this.

This compounded optimal control problem requires adding another calculus concept: pseudospectral theory. Pseudospectral theory involves using approximate values for optimal control calculations, within some known constraints. DIDO software is known for its pseudospectral approach to optimal control problems. Thus, DIDO helps drive machines that need to constantly re-evaluate their surrounding conditions and respond accordingly, including cars and airplanes.

So far we've determined what optimal control is and the significance of pseudospectral theory. Next, let's zoom in, or rather out, to outer space, where DIDO's had its most prominent application.