MPC
Created Freitag 07 Juli 2017
Alberto Bemporad: always not treating the hard constraints, instead moving them to the objective function
Moritz: add an addtional state to capture the offset of the control, treat it as disturbance, it is additive to the control
Mario Zanon: the integrators in Casadi does not have good performance, Rien's integrator in ACADO is 1000 times faster than integrators in Casadi, therefore doing multiple-shooting in Casadi is not efficient. He uses direct collocation, and the author of the solver IPOPT uses collocation, hence that solver has treatment of sparsity from collocation.
Instead of penalizing an inequality like g(x)>=0, add a slack variable so that g(x) - s = 0, s>=0. This way brings some good things for derivatives of the constraint function.
Joachim Ferreau: it's not a strict rule to release or to keep hard constraints, he saw different examples in both ways.
Solvers often solve online MPC optimization problem in approximately the same time, so the limitation in time-to-solve per sampling time could be translated to how many iterations in the solver computation. And the fall-back solution could be used as the last resort.
Moritz (knowledge from Rawlings MPC book):
Need as many integrations as number of measurements
Better put .... in the input than in the output, otherwise it goes through some integrator, then the whole process is slower (Moritz still didn't know the root reason).