Terminalregion

Terminalregion is a term used in mathematics, control theory, and related computational disciplines to denote a designated region of a space—typically a state space or data space—that satisfies specific terminal conditions or serves as a target for convergence.

In dynamical systems and model predictive control, the terminal region (often denoted as a terminal set) is defined as a subset of the state space that is positively invariant under a prescribed terminal control law. If the system state enters the terminal region, stability and feasibility of the control objective can be guaranteed for the remainder of the horizon. The terminal region is chosen so that every admissible state outside the region can be steered into it within a finite time, after which a simpler stabilizing law can maintain desired performance.

In other contexts, such as automata theory or workflow modeling, the term may refer to the set of terminal or accepting states that mark the completion of a process or the final conditions under which computation or execution terminates.

Terminology and scope vary across disciplines; some authors prefer “terminal set” or “terminal state” instead of “terminal region.” The concept is often linked to related notions such as invariant sets, absorbing states, and attractors, and it frequently appears alongside concepts like terminal cost in optimization formulations.

See also: invariant set, absorbing state, attractor, model predictive control, terminal cost, terminal state.