Behavioral Measures and their Correlation with IPM Iteration Counts on Semi-Definite Programming Problems

We study four measures of problem instance behavior that might account for the observed differences in interior-point method (IPM) iterations when these methods are used to solve semidefinite programming (SDP) problem instances: (i) an aggregate geometry measure related to the primal and dual feasible regions (aspect ratios) and norms of the optimal solutions, (ii) the (Renegar-) condition measure C(d) of the data instance, (iii) a measure of the near-absence of strict complementarity of the optimal solution, and (iv) the level of degeneracy of the optimal solution. We compute these measures for the SDPLIB suite problem instances and measure the correlation between these measures and IPM iteration counts (solved using the software SDPT3) when the measures have finite values. Our conclusions are roughly as follows: the aggregate geometry measure is highly correlated with IPM iterations (CORR = 0.896), and is a very good predictor of IPM iterations, particularly for problem instances with solutions of small norm and aspect ratio. The condition measure C(d) is also correlated with IPM iterations, but less so than the aggregate geometry measure (CORR = 0.630). The near-absence of strict complementarity is weakly correlated with IPM iterations (CORR = 0.423). The level of degeneracy of the optimal solution is essentially uncorrelated with IPM iterations

Anwendung von Prädiktivreglern in Verbrennungsmotorsteuerungen

Das Ziel dieser Arbeit ist die Anwendbarkeit des numerisch anspruchsvollen modellprädiktiven Regelungskonzeptes innerhalb moderner Verbrennungsmotorsteuerungen zu erreichen. Durch simulative Untersuchungen wird die Eignung der modellprädiktiven Regelung zur Führungs- und Störungsregelung des Motordrehmoments und der Motordrehzahl belegt. Die praktische Anwendbarkeit wird anhand einer Implementierung in einem serienmäßigen Motorsteuergerät und einer anschließenden Fahrt im Fahrzeug auf einer Teststrecke gezeigt und diskutiert.This thesis focusses on usability of the numerically sophisticated model predictive control concept within modern engine control. The effectiveness of model predictive control for tracking and disturbance rejection regarding engine torque and engine speed is proved by simulation. The field of application is evaluated, proven and reflected on the basis of an implementation in an standard electronic control unit and a subsequent drive on a test track