  Model predictive control (MPC) is based on perpetually solving optimization
problems. The solution of the optimization is usually interpreted as the
optimal input for the current state. However, the solution of the optimization
does not just provide an optimal input, but an entire optimal affine feedback
law and a polytope on which this law is optimal. We recently proposed to use
this feedback law as long as the system remains in its polytope. This can be
interpreted as an event-based approach, where leaving the current polytope is
the event that triggers the next optimization. This approach is especially
appropriate for a networked control setting since the feedback laws and their
polytopes can be evaluated with a low computational effort on lean local nodes.
In this article the region of validity for a feedback law is extended. More
precisely, the optimal polytopes are extended to nonlinearly bounded regions of
validity resulting from the intersection of a feasibility and stability region.
As a result, fewer quadratic programs need to be solved compared to the optimal
approach. The new validity regions are still suitable for the evaluation on a
lean local node. Moreover, the regions can be adjusted for a desired
closed-loop performance.
