Riccati Equation

The Riccati equation is a type of mathematical formula used to find solutions to problems involving change and optimization, especially in control systems and filtering. It involves a quadratic term (squared variable) alongside linear terms. Essentially, it helps determine the best way to control or predict systems—like guiding a vehicle or managing signals—by balancing current state information with future goals. Solving this equation provides key insights to optimize performance in dynamic environments, making it valuable in engineering, finance, and advanced mathematics.