Control

State Space

A state space is the set of all possible states of a dynamical system, where a state is a variable collection sufficient to determine future evolution given future inputs. State-space control models dynamics as x' = f(x, u), linearized to x' = Ax + Bu for classical design, while in reinforcement learning the state space is one component of the Markov decision process. Robot state spaces are typically continuous and high-dimensional, combining configurations, velocities, and task variables.

Why it matters for physical AI

The size and structure of the state space dictate which methods apply at all — tabular RL, linear control, or deep function approximation — and where the curse of dimensionality bites.