Algebraic Riccati equation

Okay kiddo, let's talk about algebraic riccati equation. This is a math problem that helps us find the solution to a type of equation.

So you know how we have a lot of different ways to solve equations, like addition, subtraction, and multiplication? Well, when it comes to algebraic riccati equations, we use something called matrices.

Do you know what a matrix is? It's like a big square or rectangle made up of rows and columns. Think of it like a Lego puzzle, where each piece is a number and they all fit together to make a bigger picture.

Now, back to the algebraic riccati equation. It's a special kind of equation that's used in a lot of different ways, like in engineering and economics. Basically, it helps us figure out how things change over time.

Think of a car going down a hill. The speed and direction of the car might change as it goes down the hill, right? Well, the algebraic riccati equation helps us figure out what those changes will be.

It's a little bit tricky, but here's the ELI5 version: we use matrices to solve the equation, and the solution helps us understand how things change over time. I hope that makes sense!