Implicit predictors in regularized data-driven predictive control

We introduce the notion of implicit predictors, which characterize the input-(state)-output prediction behavior underlying a predictive control scheme, even if it is not explicitly enforced as an equality constraint (as in traditional model or subspace predictive control). To demonstrate this concept, we derive and analyze implicit predictors for some basic data-driven predictive control (DPC) schemes, which offers a new perspective on this popular approach that may form the basis for modified DPC schemes and further theoretical insights.Comment: This paper is a reprint of a contribution to the IEEE Control Systems Letters. 6 pages, 2 figure

A deterministic view on explicit data-driven (M)PC

We show that the explicit realization of data-driven predictive control (DPC) for linear deterministic systems is more tractable than previously thought. To this end, we compare the optimal control problems (OCP) corresponding to deterministic DPC and classical model predictive control (MPC), specify its close relation, and systematically eliminate ambiguity inherent in DPC. As a central result, we find that the explicit solutions to these types of DPC and MPC are of exactly the same complexity. We illustrate our results with two numerical examples highlighting features of our approach.Comment: 7 pages, 2 figure, submitted to 61st IEE Conference on Decision and Control 202

Site carrying capacity of Norway spruce and Scots pine stands has increased in Germany and northern Europe

The maximum size-density relationship describes site carrying capacity, i.e., the maximum number of trees of a given size that can be stocked per unit area (self-thinning line). We analysed whether the self-thinning lines of Norway spruce (Picea abies (L.) Karst.) and Scots pine (Pinus sylvestris L.) have remained unchanged over time in South Germany, Norway and Finland, i.e., over a wide climatic gradient from Central Europe up to the Arctic circle. The analyses are based on long-term growth and yield experiments measured on individual tree basis over several decades, the oldest experiments established during the early 20th century. The stochastic frontier analysis was used to analyse changes in the species-specific self-thinning lines. The results show that the self-thinning lines have shifted upwards over time in all the regions. Thus, currently stands sustain higher stand densities than in the past. The increase of the maximum density for a given average stem size was more pronounced for pine than for spruce, but similar in all studied geographical regions. In addition, increasing site index was associated with increasing site carrying capacity for spruce and pine in all regions. The results imply that environmental changes have altered site properties in similar fashion across the whole study region. In practical forestry, increased site carrying capacity will reduce mortality and loss of growing stock

Site carrying capacity of Norway spruce and Scots pine stands has increased in Germany and northern Europe

The maximum size-density relationship describes site carrying capacity, i.e., the maximum number of trees of a given size that can be stocked per unit area (self-thinning line). We analysed whether the self-thinning lines of Norway spruce (Picea abies (L.) Karst.) and Scots pine (Pinus sylvestris L.) have remained unchanged over time in South Germany, Norway and Finland, i.e., over a wide climatic gradient from Central Europe up to the Arctic circle. The analyses are based on long-term growth and yield experiments measured on individual tree basis over several decades, the oldest experiments established during the early 20th century. The stochastic frontier analysis was used to analyse changes in the species-specific self-thinning lines. The results show that the self-thinning lines have shifted upwards over time in all the regions. Thus, currently stands sustain higher stand densities than in the past. The increase of the maximum density for a given average stem size was more pronounced for pine than for spruce, but similar in all studied geographical regions. In addition, increasing site index was associated with increasing site carrying capacity for spruce and pine in all regions. The results imply that environmental changes have altered site properties in similar fashion across the whole study region. In practical forestry, increased site carrying capacity will reduce mortality and loss of growing stock.publishedVersio