Christian Kirches develops a fast numerical algorithm of wide applicability that efficiently solves mixed-integer nonlinear optimal control problems. He uses convexification and relaxation techniques to obtain computationally tractable reformulations for which feasibility and optimality certificates can be given even after discretization and rounding.
Christian Kirches develops a fast numerical algorithm of wide applicability that efficiently solves mixed-integer nonlinear optimal control problems. He uses convexification and relaxation techniques to obtain computationally tractable reformulations for which feasibility and optimality certificates can be given even after discretization and rounding.
In this thesis, we introduce the novel concept of relaxed barrier function based model predictive control and present a comprehensive theoretical and algorithmic framework for the design, analysis, and implementation of relaxed barrier function based MPC approaches. Instead of treating the underlying optimization as an idealized static map, a key motive of the MPC results and algorithms presented in this thesis is to study the interconnected dynamics of controlled plant and iterative optimization algorithm in an integrated barrier function based framework and to analyze the resulting overall closed-loop system both from a systems theoretic and algorithmic perspective. One of the presented main results is a novel class of barrier function based anytime MPC algorithms that guarantee important properties of the closed-loop system independently of the number of optimization algorithm iterations that are performed at each sampling step. The obtained theoretical results are illustrated by various numerical examples and benchmark tests as well as by an experimental case study in which the proposed class of barrier function based MPC algorithms is applied to the predictive control of a self-driving car.
Modern complementary metal oxide semiconductor (CMOS) digital-to-analog converters (DACs) are limited in their bandwidth due to technological constraints. These limitations can be overcome by parallel DAC architectures, which are called interleaving concepts. Christian Schmidt analyzes the limitations and the potential of two innovative DAC interleaving concepts to provide the basis for a practical implementation: the analog multiplexing DAC (AMUX-DAC) and the frequency interleaving DAC (FI-DAC). He presents analytical and discrete-time models as a theoretical foundation and develops digital signal processing (DSP) algorithms to compensate the analog impairments. Further, he quantifies the impact of various limiting parameters with numerical simulations and verifies both concepts in laboratory experiments. About the Author: Christian Schmidt works at the Fraunhofer Heinrich-Hertz-Institute, Berlin, Germany, on innovative solutions for broadband signal generation in the field of optical communications. The studies for his dissertation were carried out at the Technische Universität Berlin and at the Fraunhofer Heinrich-Hertz-Institute, both Berlin, Germany.
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