Reducing the Prediction Horizon in NMPC: An Algorithm Based Approach

In order to guarantee stability, known results for MPC without additional terminal costs or endpoint constraints often require rather large prediction horizons. Still, stable behavior of closed loop solutions can often be observed even for shorter horizons. Here, we make use of the recent observation that stability can be guaranteed for smaller prediction horizons via Lyapunov arguments if more than only the first control is implemented. Since such a procedure may be harmful in terms of robustness, we derive conditions which allow to increase the rate at which state measurements are used for feedback while maintaining stability and desired performance specifications. Our main contribution consists in developing two algorithms based on the deduced conditions and a corresponding stability theorem which ensures asymptotic stability for the MPC closed loop for significantly shorter prediction horizons.Comment: 6 pages, 3 figure

Species' responses along environmental gradients on different spatial scales

The abundance of species on Earth varies greatly - while some occur all over the globe, others can only exist in very distinct regions. Trying to explain the reasoning behind the temporal and spatial variation in the commonness and rarity of species has a long history in ecology and yet, many pieces are still missing to complete the puzzle. This thesis investigates species' responses to changing environmental gradients and asks in how far niche characteristics can be used to predict species' range sizes at different spatial scales. We worked with herbaceous species from semi-natural grasslands as well as deciduous forests, focusing especially on their reactions to abiotic conditions (soil pH, nutrients and light). We could show that the breadth of resources used by species (especially regarding soil pH), as well as their tolerance limits, are reliable predictors for their rarity and commonness across different spatial scales. Furthermore, we believe that niche properties can provide guidelines for conservation decisions, especially concerning the selection of suitable habitats for the reintroduction of species. This is a particularly important task to preserve the worldâ s biodiversity in todayâ s ever changing environments

Analysis of unconstrained nonlinear MPC schemes with time varying control horizon

For discrete time nonlinear systems satisfying an exponential or finite time controllability assumption, we present an analytical formula for a suboptimality estimate for model predictive control schemes without stabilizing terminal constraints. Based on our formula, we perform a detailed analysis of the impact of the optimization horizon and the possibly time varying control horizon on stability and performance of the closed loop