Nonlinear MPC defines implicit regional optimal control laws

We investigate how to extend the following idea from linear to nonlinear MPC: Solving a linear MPC problem for a fixed initial condition (i.e., a point in the state space), provides an input signal (i.e., a point in input space). The solution at this point, however, actually defines an affine optimal control law (i.e., not just a point) and its domain (not just a point, but a state space polytope) on which this feedback law is the optimal solution. We discuss under which conditions solving a nonlinear MPC problem provides such a regional optimal feedback law and its region of validity.