Open-loop optimization and closed-loop optimization in synthesis approaches

The basic feature of open-loop model predictive controls (MPC) is "open-loop optimization, closed-loop control." For nominal systems, open-loop prediction and closed-loop prediction are equivalent. For uncertain systems, there is a large difference between the open-loop optimization and the closed-loop optimization. Parameter-dependent open-loop optimization approach is better than feedback MPC with respect to feasibility and optimality. From the side of feasibility, both feedback MPC and single-valued open-loop MPC are special cases of parameter-dependent open-loop MPC. Parameter-dependent open-loop MPC is easier to be feasible than both single-valued open-loop MPC and feedback MPC. Parameter-dependent open-loop MPC and parameter-dependent partial feedback MPC are equivalent, since the vertex state predictions and vertex control moves are all single-valued.