Point-to-Point MPC with differnt end time possible?

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I would like to use MPC to realise the transition from one state (incl. position, speed and accleration) to another state with different end time. But I have no reference trajectory, what I know only initial condition and final condition. so my question is: 1. Could MPC help solve this problem? (final state is not equals to zero), add terminal constraint? 2. I would like to use MPC to generate trajectories with different end time, which means I want to reach the desired state with differnt end time. In MPC, $T_{end}=kT_{s}$, $k=N_p$, should I change the value of $T_s$ or change the value of $N_p$?