Performance analysis for a class of decentralized control systems
Bibliographic record
Abstract
This paper is concerned with decentralized controller design for large-scale interconnected systems of pseudo- hierarchical structure. Given such a system, one can use the existing techniques to design a decentralized controller for the reference hierarchical model, which is obtained by eliminating certain weak interconnections of the original system. Although this indirect controller design is often fascinating as far as the computational complexity is concerned, it may not provide a satisfactory performance for the original pseudo-hierarchical system. A LQ cost function is defined in order to evaluate the discrepancy between the pseudo-hierarchical system and its reference hierarchical model under the designed decentralized controller. A discrete Lyapunov equation should then be solved to compute this performance index. However, due to the large- scale nature of the system, this equation can by no means be handled for many real-world systems. Thus, attaining an upper bound on this cost function can be much more desirable than finding its exact value. For this purpose, a novel technique is proposed, which only requires solving a simple LMI optimization problem with three variables. The problem is then reduced to a scalar optimization problem, for which an explicit solution is provided. It is also proved that as the pseudo-hierarchical system approaches its reference hierarchical model, the bounds obtained from the LMI and scalar optimization problems will both go to zero. In the particular case, when the two models are identical (i.e., the original system is exactly hierarchical), both upper bounds will be zero.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".