control//controller design//MPC//receding horizon

A receding horizon is the strategy of planning a fixed number of steps ahead, executing only the first step of the plan, observing the result and planning again from the new state, so that the horizon slides forward with time and the plan is never executed whole. It is how MPC turns a finite optimization into feedback, and how planners, chess programs and drivers on a mountain road deal with a future they can only partly see.

A receding horizon is the strategy of planning a fixed number of steps ahead, executing only the first step of the plan, observing the result and planning again from the new state, so that the horizon slides forward with time and the plan is never executed whole. It is how MPC turns a finite optimization into feedback, and how planners, chess programs and drivers on a mountain road deal with a future they can only partly see.

Executing only the first step is what makes it a closed loop. A plan computed once and played out open loop would carry every model error and every gust to the end; replanning from each new measurement corrects them, at the price of solving again every period. The plan computed at time ttt is a proposal for what to do after the current step, overwritten as soon as the next measurement arrives.

1Measure or estimate the state2Plan N steps under the model and limits3Apply the first input4Wait one period

The horizon length is the main tuning knob. Too short and the controller is myopic: it sees the wall when there is no longer force to stop, and the problem can turn infeasible. Long enough to cover the slowest relevant manoeuvre (the braking distance, the settling of a column) and the Riccati terminal cost can stand in for the rest. Each extra step adds decision variables and compute (MPC computation).

The same structure runs at very different timescales. An MPC moves actuators every few milliseconds (a converter) or every minute (a refinery); a task planner on a robot replans the route or the next task about once a second (motion planning); a decision process solved online with tree search does the same with discrete actions (Markov decision process). What differs is the model (continuous dynamics or discrete choices) and how long a plan is allowed to live.

Replanning is not a cure for a bad model. If the model is biased, every new plan inherits the bias and the loop settles off target, which is why process MPC estimates a disturbance term (an offset between prediction and measurement) and feeds it back into the prediction.