Publications

We consider an input-constrained differential-drive robot with actuator dynamics. For this system, we establish asymptotic stability of the origin on arbitrary compact, convex sets using Model Predictive Control (MPC) without stabilizing terminal conditions despite the presence of state constraints and actuator dynamics. We note that the problem without those two additional ingredients was essentially solved beforehand, despite the fact that the linearization is not stabilizable. We propose an approach successfully solving the task at hand by combining the theory of barriers to characterize the viability kernel and an MPC framework based on so-called cost controllability. Moreover, we present a numerical case study to derive quantitative bounds on the required length of the prediction horizon. To this end, we investigate the boundary of the viability kernel and a neighbourhood of the origin, i.e. the most interesting areas.

Microfluidic techniques allow for the tailored construction of specific microparticles, which are becoming increasingly interesting and relevant. Here, using a microfluidic hole-plate-device and thermal-initiated free radical polymerization, submicrometer polymer particles with a highly textured surface were synthesized. Two types of monomers were applied: (1) methylmethacrylate (MMA) combined with crosslinkers and (2) divinylbenzene (DVB). Surface texture and morphology can be influenced by a series of parameters such as the monomer-crosslinker-solvent composition, surfactants, and additives. Generally, the most structured surfaces with the simultaneously most uniform particles were obtained in the DVB-toluene-nonionic-tensides system. In a second approach, poly-MMA (PMMA) particles were used to build aggregates with bigger polymer particles. For this purpose, tripropyleneglycolediacrylate (TPGDA) particles were synthesized in a microfluidic co-flow arrangement and polymerized by light- irradiation. Then, PMMA particles were assembled at their surface. In a third step, these composites were dispersed in an aqueous acrylamide-methylenebisacrylamide solution, which again was run through a co-flow-device and photopolymerized. As such, entities consisting of particles of three different size ranges - typically 0.7/30/600 [my]m - were obtained. The particles synthesized by both approaches are potentially suitable for loading with or incorporation of analytic probes or catalysts such as dyes or metals.

Microbatteries (MBs) and microsupercapacitors (MSCs) are primary on-chip micropower sources that drive autonomous and stand-alone microelectronic devices for implementation of the Internet of Things (IoT). However, the performance of conventional MBs and MSCs is restricted by their 2D thin-film electrode design, and these devices struggle to satisfy the increasing IoT energy demands for high energy density, high power density, and long lifespan. The energy densities of MBs and MSCs can be improved significantly through adoption of a 2D thick-film electrode design; however, their power densities and lifespans deteriorate with increased electrode thickness. In contrast, 3D architecture electrodes offer remarkable opportunities to simultaneously improve MB and MSC energy density, power density, and lifespan. To date, various 3D architecture electrodes have been designed, fabricated, and investigated for MBs and MSCs. This review provides an update on the principal superiorities of 3D architecture electrodes over 2D thick-film electrodes in the context of improved MB and MSC energy density, power density, and lifespan. In addition, the most recent and representative progress in 3D architecture electrode development for MBs and MSCs is highlighted. Finally, present challenges are discussed and key perspectives for future research in this field are outlined.

We investigate optimal control of linear port-Hamiltonian systems with control constraints, in which one aims to perform a state transition with minimal energy supply. Decomposing the state space into dissipative and non-dissipative (i.e. conservative) subspaces, we show that the set of reachable states is bounded w.r.t. the dissipative subspace. We prove that the optimal control problem exhibits the turnpike property with respect to the non-dissipative subspace, i.e., for varying initial conditions and time horizons optimal state trajectories evolve close to the conservative subspace most of the time. We analyze the corresponding steady-state optimization problem and prove that all optimal steady states lie in the non-dissipative subspace. We conclude this paper by illustrating these results by a numerical example from mechanics.

The theory of randomly perturbed graphs deals with the properties of graphs obtained as the union of a deterministic graph H and a random graph G. We study Hamiltonicity in two distinct settings. In both of them, we assume H is some deterministic graph with minimum degree at least αn, for some α (possibly depending on n). We first consider the case when G is a random geometric graph, and obtain an asymptotically optimal result. We then consider the case when G is a random regular graph, and obtain different results depending on the regularity.