How are state estimation and optimal control combined in a controller?

In control theory, the combination of state estimation and optimal control is achieved through a two-step process that allows a controller to manage systems where the full state vector cannot be measured directly or instantaneously.1

The integration follows this systematic approach:

• State Estimation: Because it is often unrealistic to measure every component of a system's state, the first step involves building an optimal filter, such as a Kalman filter, to determine the best possible estimate of the current state vector.1
• Optimal Control: The second step involves determining an optimal control law. This law defines the control action as a function of the system's state.1
• Implementation: The controller, functioning as a special-purpose computer, mechanizes this process by substituting the estimated state vector obtained from the filter directly into the optimal control law.1

By combining these steps, the controller can effectively regulate the system based on the best available information, even in the presence of measurement limitations.1