A branch and bound algorithm for the bilevel programming problem
SIAM Journal on Scientific and Statistical Computing
A polyhedral branch-and-cut approach to global optimization
Mathematical Programming: Series A and B
Survey paper: Set invariance in control
Automatica (Journal of IFAC)
Survey Constrained model predictive control: Stability and optimality
Automatica (Journal of IFAC)
Hi-index | 22.14 |
One of the most fundamental problems in model predictive control (MPC) is the lack of guaranteed stability and feasibility. It is shown how Farkas' Lemma in combination with bilevel programming and disjoint bilinear programming can be used to search for problematic initial states which lack recursive feasibility, thus invalidating a particular MPC controller. Alternatively, the method can be used to derive a certificate that the problem is recursively feasible. The results are initially derived for nominal linear MPC, and thereafter extended to the additive disturbance case.