Synthesis and application of optimal strictly negative imaginary controllers
Why this work is in the frame
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Bibliographic record
Abstract
This thesis investigates the synthesis of optimal strictly negative imaginary (SNI) controllers. A recently emerged class of systems called negative imaginary (NI) systems are those characterized by a negative imaginary frequency response. A NI system connected in a positive feedback interconnection with a SNI controller is internally stable if and only if a DC gain condition is satisfied. This can be interpreted as a robust stability result in situations where plant uncertainty does not destroy the NI nature of the plant nor the DC gain condition. Motivated by a desire to realize improved closed-loop performance, this thesis considers the design of optimal SNI controllers. The proposed synthesis methods makes use of convex optimization and linear matrix inequality (LMI) tools. These synthesis methods are then examined in the context of various applications. In particular, this thesis considers tracking control on SO(3) and SE(3) for systems with counter-clockwise input-output dynamics (CCW). CCW input-output maps from torque to attitude, as well as from force and torque to position and attitude, are established for rigid-body motion. Using the properties of CCW systems and NI systems, a stabilizing SNI controller is shown to drive the tracking errors in position and attitude to zero. In addition, a method to synthesize the SNI controller associated with the tracking control problem in an optimal sense is presented. Finally, the control laws are extended to the formation control problem of networks of NI systems and networks of CCW systems. Numerical results are included to demonstrate the effectiveness of the proposed synthesis methods
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it