How does dynamic-optimizing control minimize time or total cost?

Dynamic-optimizing control functions by requiring a system to operate in accordance with a specific performance criterion. This approach ensures that the controlled system transitions from an original state to a new position while satisfying defined constraints, typically by minimizing the time required for the transition or by minimizing the total cost associated with the operation.1

To achieve this, control theory relies on the mathematical model of the system, which must precisely describe the plant's internal dynamical state and the effects of potential control actions. The process involves:2

• Optimization: Once the system behavior and the performance criteria are mathematically specified, optimization techniques are used to deduce the appropriate control law.2
• Control Law: This function determines the specific control action to be taken at any instant based on the current state of the system.2
• State Determination: Because exact measurement of all state components is often impossible, systems frequently utilize filters to estimate the state vector before applying the optimal control law.2

By mathematically quantifying these requirements, the controller drives the system to perform at its defined optimum.12