A condensed and sparse QP formulation for predictive control

The computational burden that model predictive control (MPC) imposes depends to a large extent on the way the optimal control problem is formulated as an optimization problem. In this paper, we present a new formulation that results in a compact and sparse optimization problem to be solved at each sampling interval. The approach is based on a change of variables that leads to a block banded Hessian when the horizon length is bigger than the controllability index of the plant. In this case the problem can be solved with an interior-point method in time linear in the horizon length. Existing dense approaches grow cubically with the horizon length, whereas existing sparse approaches grow at a significantly greater rate than with the method presented here.