recedinghorizon

Receding horizon refers to a control and planning approach in which decisions are made by optimizing over a finite future horizon that moves forward in time. At each decision step, an optimization problem is solved to determine a sequence of control actions, but only the first action is implemented. The horizon then recedes forward, the current state is updated, and the optimization is solved again. This approach is a core idea behind model predictive control (MPC), though the term can also describe rolling-horizon planning in other domains.

Typically, the method solves an optimization problem of the form: minimize a cost function over a horizon N, subject to system dynamics and any state and input constraints. The cost often aggregates stage costs that penalize deviation from targets, effort, or other performance criteria, plus a terminal cost or constraint. The optimization yields a control sequence, of which the first element is applied, after which the process state is measured or estimated and the problem is resolved at the next time step. The horizon length N and the frequency of updates are design choices that balance performance, robustness, and computational resources.

Receding horizon methods can handle multivariable systems, nonlinear dynamics, and a variety of constraints. They can be deterministic or incorporate uncertainty, leading to robust or stochastic variants. Stability and feasibility are important considerations and may be ensured with terminal constraints or costs, or through theoretical guarantees under specific conditions.

Common applications include chemical process control, aerospace, autonomous and robotic systems, automotive control, and energy management. The approach is valued for its ability to integrate optimization with feedback, enabling constraint handling and adaptive responses to changing conditions.