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Assessing the speed-up achievable by online constraint removal in MPC

We recently proposed to accelerate online MPC calculations by detecting and removing inactive constraints from the online optimization problems as a function of the current initial state. A number of variants of constraint removal (CR) have been explored, ranging from detecting inactive constraints based on precomputed regions of activity or approximations thereof to online methods that do not require any offline preparation. In typical applications CR can reduce the computing times required for the calculation of the model predictive control laws by 15% to 90%. Since CR is very easy to implement, does not require any additional assumptions to be fulfilled beyond the usual ones for stability, and can be combined with all optimization algorithms, it is very easy to cash in the described acceleration. Moreover, CR may prove useful if an existing, established MPC implementation needs to be accelerated, e.g., in order to use it on an embedded processor, but replacing it altogether is not an option.