Optimal Control Theory is a mathematical framework used to determine the best possible control strategies for dynamic systems. It focuses on optimizing a certain performance criterion, such as minimizing costs or maximizing efficiency, while adhering to specific constraints. This theory is widely applied in various fields, including engineering, economics, and robotics. The core idea involves formulating a control problem, defining the system dynamics, and establishing an objective function. Techniques such as the Pontryagin's Maximum Principle and Dynamic Programming are often employed to find the optimal control laws that guide the system's behavior over time.