Question

In the context of MPC, why is the control horizon typically shorter than the prediction horizon when calculating optimal actuator commands?

Accepted Answer

In Model Predictive Control, the prediction horizon is the window of time into the future over which the controller simulates the system&#x27;s behavior to anticipate how current actions affect future states. The control horizon is the number of time steps into the future over which the controller is allowed to calculate and apply distinct actuator commands. Setting the control horizon shorter than the prediction horizon provides two primary benefits: computational efficiency and system stability. By restricting the number of future control inputs the algorithm must solve for, the size of the underlying mathematical optimization problem is reduced, allowing the controller to compute solutions faster, which is critical for real-time applications. Furthermore, forcing the control inputs to remain constant after the control horizon ends acts as a form of regularization. This prevents the controller from attempting to make aggressive, high-frequency adjustments at the very end of the prediction window, where the model&#x27;s accuracy is naturally lower due to cumulative uncertainty. For example, if a vehicle navigates a curve, a long prediction horizon allows the controller to see the entire turn to plan a smooth path, while a shorter control horizon ensures the steering input changes gradually rather than oscillating rapidly to satisfy every minor prediction error at the edge of the planning window.

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In the context of MPC, why is the control horizon typically shorter than the prediction horizon when calculating optimal actuator commands?