How does a control law determine the action taken by a control system?

In control theory, a control law is a mathematical function that determines the specific action a system should take at any given instant based on its current state.1

The system to be controlled, often called the plant, is described by its internal dynamical state—a set of numbers known as the state vector that quantifies the effects of all past external influences. By expressing the control action as a function of this state, the control law dictates how the system responds to achieve a desired objective or optimization.1

Because it is often impossible to measure every component of the state vector perfectly, the process typically involves two steps:
* State Determination: Using an optimal filter (such as a Kalman filter) to calculate the best estimate of the current state vector.1
* Implementation: Substituting this estimate into the control law to determine the necessary action, which is then executed by a controller.1

This approach is more general than traditional feedback or feedforward methods, as a single control law can incorporate both strategies to manage complex system dynamics.1