Does Model Predictive Control update the input trajectories for every iteration?

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According to Model Predictive Control, it finds the best input trajectories (input signals) for the open loop control system, or MPC can also be closed loop too.

My question is a open loop MPC updates the input trajectories for every iteration the computer do?

For exampel. If the open loop MPC have the control horizon 10 and predict horizon 15. Does it mean that the MPC controller finds the best input trajectories for the control horizon, which are 10 iterations for the computer.

Or does it mean that the open loop MPC have the setup control horizon 10 and predict horizon 15 and finds the best input trajectories for the 10 next inputs. But the next iteration/reading the computer do, the MPC controller, once again, do the same thing. Find the next optimal input trajectories for the 10 next input? In this case, the MPC controller will add another new input trajectory and remove the first trajectory.

Is this how MPC works, or does MPC uses that whole 10 input trajectories before it find the next 10?

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