Controller

An algorithm that computes control actions based on the current state of a system and a defined policy. In control theory, a controller is often represented mathematically as a mapping from the state space to control actions, typically denoted as u(t) = K(x(t)), where K is the control law and x(t) is the state vector at time t. Controllers can be categorized into various types, including open-loop and closed-loop systems, with the latter utilizing feedback to adjust control actions based on the output. In reinforcement learning, controllers are analogous to policies that dictate actions based on observed states, often optimized through techniques such as Q-learning or policy gradients. The design of effective controllers is foundational in fields such as robotics, automation, and systems engineering, where stability and performance are critical metrics.