How does optimization help select a control action?

In control theory, optimization is the mathematical process used to select the most appropriate control action from a range of available possibilities. This selection is guided by two essential components: a precise mathematical model of the system's behavior and a clearly defined criterion (or purpose) for the control.1

Optimization helps determine the best control action by following these principles:

• Defining Objectives: Optimization requires a specified criterion, such as minimizing total cost or achieving a goal in the minimum possible time.12
• Mathematical Formulation: By using an objective function, the system evaluates potential actions against constraints to identify the one that maximizes or minimizes the desired outcome.3
• Control Laws: Once the optimal action is deduced, it is often expressed as a control law—a function of the system's current state—which allows the controller to determine the necessary action at any given instant.1

In complex systems, this may involve using a Kalman filter to estimate the system's state before applying the optimal control law. Ultimately, optimization ensures that the system operates in the most efficient or effective manner possible according to its defined performance goals.12