Model Predictive Control with Stabilizing Prediction Horizon of Systems Described by Time-Discretized ODEs and DAEs

In this thesis, model predictive control (MPC) of linear time-invariant inhomogeneous explicit and implicit difference equations is considered. Closed-loop stability via a sufficiently long prediction horizon is addressed.
A stabilizing prediction horizon can be determined via an optimization problem that is dependent on a comparison function sufficing a controllability condition. Methods for the determination of such a comparison function are developed. Here, quadratic level costs with symmetric state-input weighting matrices are considered. Methods for the inclusion of linear inequality state and input constraints are developed. Considering the comparison function, a maximal singular value is wanted to be minimal. A solution can be obtained by mainly computing an inverse or a QR decomposition. Methods for the systematic determination of a stabilizing prediction horizon are contributed. The existing theory is extended in, for example, the possibility to consider state and input constraints. The benefits of the developed methods are shown via two examples. It is shown how to implement MPC algorithms by transforming the optimal control problem into a quadratic program.