  In model predictive control (MPC), an optimal control problem (OCP) is solved
for the current state and the first input of the solution, the optimal feedback
law, is applied to the system. This procedure requires to solve the OCP in
every time step. Recently, a new approach was suggested for linear MPC. The
parametric solution of a linear quadratic OCP is a piecewise-affine feedback
law. The solution at a point in state space provides an optimal feedback law
and a domain on which this law is the optimal solution. As long as the system
remains in the domain, the law can be reused and the calculation of an OCP is
avoided. In some domains the optimal feedback laws are identical. By uniting
the corresponding domains, bigger domains are achieved and the optimal feedback
law can be reused more often. In the present paper, we investigate in how far
this approach can be extended from linear to nonlinear MPC, we propose an
algorithm and we illustrate the achieved savings with an example.
