Control

Cost Function

A cost function is a scalar objective that quantifies the undesirability of states, actions, or trajectories, which optimization-based planners and controllers minimize, the mirror image of a reward function being maximized. In optimal control, costs typically penalize state error, control effort, and constraint proximity, as in the quadratic costs of LQR and MPC; in motion planning, costs encode path length, smoothness, and obstacle clearance.

Why it matters for physical AI

Cost design encodes intent for model-based layers just as reward design does for RL, and mis-specified costs produce confidently wrong behavior, motivating learned costs from demonstrations via inverse optimal control.