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Model predictive control (MPC) is based on perpetually solving optimizationproblems. The solution of the optimization is usually interpreted as theoptimal input for the current state. However, the solution of the optimizationdoes not just provide an optimal input, but an entire optimal affine feedbacklaw and a polytope on which this law is optimal. We recently proposed to usethis feedback law as long as the system remains in its polytope. This can beinterpreted as an event-based approach, where leaving the current polytope isthe event that triggers the next optimization. This approach is especiallyappropriate for a networked control setting since the feedback laws and theirpolytopes 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. Moreprecisely, the optimal polytopes are extended to nonlinearly bounded regions ofvalidity resulting from the intersection of a feasibility and stability region.As a result, fewer quadratic programs need to be solved compared to the optimalapproach. The new validity regions are still suitable for the evaluation on alean local node. Moreover, the regions can be adjusted for a desiredclosed-loop performance.

Regional predictive control with suboptimally extended regions of validity