Parametric programming: Difference between revisions

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== Applications ==
The connection between parametric programming and [[model predictive control]] established in 2000 has contributed to an increased interest in the topic.<ref>{{cite book |last1=Bemporad |first1=Alberto |last2=Morari |first2=Manfred |last3=Dua |first3=Vivek |last4=Pistikopoulos |first4=Efstratios N. |year=2000 |chapter=The explicit solution of model predictive control via multiparametric quadratic programming |title=Proceedings of the 2000 American Control Conference |pages=872 |doi=10.1109/ACC.2000.876624 |isbn=0-7803-5519-9 |s2cid=1068816 }}</ref><ref>{{cite journal |last1=Bemporad |first1=Alberto |last2=Morari |first2=Manfred |last3=Dua |first3=Vivek |last4=Pistikopoulos |first4=Efstratios N. |title=The explicit linear quadratic regulator for constrained systems |journal=Automatica |date=January 2002 |volume=38 |issue=1 |pages=3–20 |citeseerx=10.1.1.67.2946 |doi=10.1016/S0005-1098(01)00174-1}}</ref> Parametric programming supplies the idea that optimization problems can be parametrized as functions that can be evaluated (similar to a lookup table). This in turns allows the optimization algorithms in optimal controllers to be implemented as pre-computed (off-line) mathematical functions, which may in some cases be simpler and faster to evaluate than solving a full optimization problem on-line. This also opens up the possibility of creating optimal controllers on chips (MPC on chip<ref>[https://www.researchgate.net/publication/223477621_MPC_on_a_chip-Recent_advances_on_the_application_of_multi-parametric_model-based_control MPC on a chip—Recent advances on the application of multi-parametric model-based control | Request PDF<!-- Bot generated title -->]</ref>). However, the off-line parametrization of optimal solutions runs into the curse of dimensionality as the number of possible solutions grows with the dimensionality and number of constraints in the problem.
 
==References==