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Problems involving functional differential equations with terminal conditions in function space are considered. Their application to mechanical and electrical systems is discussed. Investigations of controllability, existence of optimal controls, and necessary and sufficient conditions for optimality are reported.
Optimal control of systems governed by functional differential equations of retarded and neutral type is considered. Problems with function space initial and terminal manifolds are investigated. Existence of optimal controls, regularity, and bang-bang properties are discussed. Necessary and sufficient conditions are derived and several solved examples which illustrate the theory are presented.
The results of various authors dealing with problems involving functional differential equations with terminal conditions in function space are reviewed. The review includes not only very recent results, but also some little known results of Soviet mathematicians prior to 1970. Particular attention is given to results concerning controllability, existence of optimal controls, and necessary and sufficient conditions for optimality.
Asymptotic fixed point theorems and periodic systems of functional-differential equations
Describing functions to analyze feedback control systems containing nonlinearities of dead zone and backlash
The expansion of shrubs in the Arctic tundra fundamentally modifies land-atmosphere interactions. However, it remains unclear how shrub distribution and expansion differ across key species due to challenges with discriminating tundra plant species at regional scales. Here, we combined multi-scale, multi-platform remote sensing and in situ trait measurements to elucidate the distribution patterns and primary controls of two representative deciduous-tall-shrub (DTS) genera, Alnus and Salix, in low-Arctic tundra. We show that topographic features were a key control on DTSs, creating heterogeneous, but predictable distributions of Alnus and Salix fractional cover (fCover). Alnus was more tolerant of elevation and slope and was found on hilly uplands (slope >10°) within a specific elevational band (200–400 m above sea level [MSL]). In contrast, Salix occurred at lower elevations (50–300 m MSL) on gentler slopes (3-10°) and required adequate soil moisture associated with its profligate water use. We also show that niche differentiation between Alnus and Salix changed with patch size, where larger patches were more specialized in resource requirements than individual plants of Alnus and Salix. To understand what constrains the growth of DTSs at locations with low fCover, we developed environmental limiting factor models, which showed that topography limits the upper bound of Alnus and Salix fCover in 69.2% and 48.7% of the landscape, respectively. These findings highlight a critical need to better understand and represent topography-controlled processes and functional traits in regulating shrub distribution, as well as a need for more detailed species classification to predict shrubification in the Arctic.
Multivariate function approximation forms the basis of adaptive control systems for space flight
Saturn I /SA-8/ launch vehicle - environmental control systems, functional description, index of finding numbers, and schematics of launch complex
Saturn I /SA-10/ - launch pad accessories functional description, finding numbers, and schematics
Saturn I /SA-10/ launch vehicle and Launch Complex 37B functional systems description - environmental conditioning, index of finding numbers, and mechanical schematics
Saturn I /SA-8/ launch vehicle - launch pad accessories functional description, index of finding numbers, and mechanical schematics
Saturn launch vehicle and launch complex functional description - RP-1 fuel system, finding numbers, and schematics
E. coli ribosomes structure, molecular components, function and protein synthesis with artificial ribosome derivatives deficient in one component
Saturn I /SA-8/ launch vehicle and Launch Complex 37B - pneumatic distribution system
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Saturn I /SA-10/ launch vehicle and Launch Complex 37B - liquid hydrogen fuel system
Saturn I /SA-10/ launch vehicle and Launch Complex 37B - H- 1 rocket engine and hydraulic systems
Saturn I /SA-8/ launch vehicle and launch complex systems - H- 1 rocket engine, and hydraulic systems