Improved state dependent parametrizations including a piecewise linear feedback for constrained linear MPC

A new class of state dependent parametrizations is introduced which can be used in linear model predictive control (MPC) to approximate the optimal predicted input trajectories and thereby speed up the online optimization. The parametrizations are piecewise constant over the state space and also contain, in addition to previous results, a piecewise linear state feedback term. A new data mining algorithm is presented, tailored to determine such parametrizations offline. A refinement step for the parametrizations is formulated which guarantees constraint satisfaction and thereby enables application of the parametrizations in an asymptotically stabilizing overall MPC scheme online. In an example, superior performance of the new results is demonstrated.