I use MPC(Model Predictive Control) to regulate a DC motor. Constraints are imposed on inputs u, input difference du and outputs y. When it is infeasible to have all constraints satisfied, the QP in Matlab automatically gives a solution with output y satisfied and input u and du violated. Since the constraints on input cannot be violated in any circumstances, does anyone know how to adjust the solution to have input u satisfying constraints while letting outputs y violating constraints?
http://www-control.eng.cam.ac.uk/Homepage/papers/cued_control_53.pdf
look at the subsection "Slack Variables as Soft Constraints"
...implementation wouldn't be a problem...
Set up input constraints "hard" - define input's lower and upper bound (0 means hard constrained input). Set up output constraints "soft" - define appropriate lower and upper output bound (the larger the value, the softer the constraint).
Consider changing your optimizer. I prefer direct search techniques which are more robust to surface aberrations and can handle constraints (either hard or soft). Consider Leapfrogging. Rhinehart, R. R., M. Su, and U. Manimegalai-Sridhar, “Leapfrogging and Synoptic Leapfrogging: a new optimization approach”, Computers & Chemical Engineering, Vol. 40, 11 May 2012, pp. 67-81.
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