We study linear-quadratic optimal control problems for infinite-dimensional dissipative systems with possibly indefinite cost functionals, subject to the additional requirement that the state converges to zero as time tends to infinity. Assuming the existence of a bounded quadratic storage function and an appropriate state-feedback stabilizability condition, we show that the indefinite optimal control problem is equivalent to a linear-quadratic optimal control problem with a nonnegative cost functional. We establish the relationship between the corresponding value functions and derive the associated operator-node Lur'e equation. Finally, we illustrate the results by several examples. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
This paper develops an intrinsic framework for local solutions to time-varying linear systems with real meromorphic coefficients. Local solutions on compact intervals naturally form a sheaf of vector spaces. We introduce regularity triples to distinguish regularity across singularities, one-sided regularity at singularities, and regularity away from singularities. The local formulation isolates a continuation property implicit in established global frameworks and yields a simple definition of behavioural controllability. We establish an algebraically verifiable sufficient condition for continuation, prove its necessity for controllability, and derive an algebraic characterization of controllability based on the Teichmüller–Nakayama form, recovering and slightly generalizing established results.
This study presents an Exploratory Data Analysis (EDA) of cloud-to-ground (CG) lightning location data from the ALDIS/BLIDS system for 60 ground-mounted photovoltaic (PV) power plants in Germany, covering an observation period from 2005 to 2025. To ensure temporal consistency across this extended dataset, which spans a period of known changes in network performance, a simplified time-based correction factor (CF) was introduced. The CF normalizes annual stroke densities in local reference areas to the stable post-2022 network state. Both negative and positive CG lightning strokes were analyzed, covering event counts and return-stroke peak current amplitudes over five-year periods before and after PV plant installation. Lightning activity within capture areas (CA) encompassing each plant was compared with corresponding local reference areas (RA). A size stratification analysis examines whether plant area modulates the observed response, and a case study compares the local lightning density around a PV plant with that around a tall structure. Across all analyses, no systematic influence of PV plant installation on local lightning frequency or peak current amplitude was detected. The findings also support the use of site-specific lightning data, rather than generalized regional density maps, for the planning and optimization of lightning protection systems at large-scale PV installations.
The shape of the capillary produced during the welding of 1.4301 (X5CrNi18-10, AISI 304) stainless steel at a welding speed of 12 m/min using core-ring-shaped beams delivered through a multi-waveguide fiber was examined by means of synchrotron X-ray imaging. The results show that, under the range of process parameters covered here, ring beams create a temperature field which includes two hot spots which lag behind the center of the beam and are equidistant from the center line of the weld. In the case of small ring diameters these two hot spots can be close enough to the core beam that they can combine with it to create a wide capillary, the shape of which inhibits the formation of pores. When larger diameters are employed, the ring beam hot spots create a separate, secondary capillary (or capillaries) which may sporadically coalesce with the core beam capillary due to surface tension effects. When the capillaries merge, the depth of penetration of the combined capillary is reduced compared with the one created by the core alone. If the coalescence of the capillaries is sporadic then the weld stability is poor from both a porosity and a depth of penetration point of view.
