A parametric LQ approach to multiobjective control system design

The synthesis of a constant parameter output feedback control law of constrained structure is set in a multiple objective linear quadratic regulator (MOLQR) framework. The use of intuitive objective functions such as model-following ability and closed-loop trajectory sensitivity, allow multiple objective decision making techniques, such as the surrogate worth tradeoff method, to be applied. For the continuous-time deterministic problem with an infinite time horizon, dynamic compensators as well as static output feedback controllers can be synthesized using a descent Anderson-Moore algorithm modified to impose linear equality constraints on the feedback gains by moving in feasible directions. Results of three different examples are presented, including a unique reformulation of the sensitivity reduction problem

Examples for the Infinite Dimensional Morse Lemma

Examples are presented which show how to use the Morse lemma in specific infinite dimensional examples and what can go wrong if various hypotheses are dropped. One of the examples shows that the version of the Morse lemma using singularity theory can hold, yet the hypotheses of the Morse–Palais and Morse–Tromba lemmas fail. Another example shows how to obtain a concrete normal form in infinite dimensions using the splitting lemma and hypotheses related to those in the Morse–Tromba lemma. An example of Dancer is given which shows that for the validity of the Morse lemma in Hilbert space, some hypotheses on the higher order terms must be made in addition to smoothness, if the quadratic term is only weakly nondegenerate. A general conjecture along these lines is made

Sitzung vom 10. October 1904

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The relative abundance of wheat Rubisco activase isoforms is post‑transcriptionally regulated

Diurnal rhythms and light availability affect transcription–translation feedback loops that regulate the synthesis of photosynthetic proteins. The CO2-fixing enzyme Rubisco is the most abundant protein in the leaves of major crop species and its activity depends on interaction with the molecular chaperone Rubisco activase (Rca). In Triticum aestivum L. (wheat), three Rca isoforms are present that differ in their regulatory properties. Here, we tested the hypothesis that the relative abundance of the redox-sensitive and redox-insensitive Rca isoforms could be differentially regulated throughout light–dark diel cycle in wheat. While TaRca1-β expression was consistently negligible throughout the day, transcript levels of both TaRca2-β and TaRca2-α were higher and increased at the start of the day, with peak levels occurring at the middle of the photoperiod. Abundance of TaRca-β protein was maximal 1.5 h after the peak in TaRca2-β expression, but the abundance of TaRca-α remained constant during the entire photoperiod. The redox-sensitive TaRca-α isoform was less abundant, representing 85% of the redox-insensitive TaRca-β at the transcript level and 12.5% at the protein level. Expression of Rubisco large and small subunit genes did not show a consistent pattern throughout the diel cycle, but the abundance of Rubisco decreased by up to 20% during the dark period in fully expanded wheat leaves. These results, combined with a lack of correlation between transcript and protein abundance for both Rca isoforms and Rubisco throughout the entire diel cycle, suggest that the abundance of these photosynthetic enzymes is post-transcriptionally regulated

Sitzung vom 22. Februar 1904

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Sitzung vom 12. December 1904

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