Predictive-optimal control is able to deal with many practical control issu
es, such as guarantees of nominal stability, nominal performance optimizati
on and constraint handling. It is also particularly easy to apply to a syst
em that is well approximated by a linear model such as with this benchmark
problem. Here the aim is to illustrate the efficacy of two novel approaches
to predictive control. In the first approach the system is first stabilize
d with a simple control law. The predictive control is then added as an out
er-loop optimization for constraint handling. The second approach is comput
ationally more efficient; here constraints are handled by a systematic mixi
ng of two stabilizing control laws.