Model reference adaptive iterative learning control for linear systems
Bibliographic record
Abstract
Abstract In this paper, we propose a model reference adaptive control (MRAC) strategy for continuous‐time single‐input single‐output (SISO) linear time‐invariant (LTI) systems with unknown parameters, performing repetitive tasks. This is achieved through the introduction of a discrete‐type parametric adaptation law in the ‘iteration domain’, which is directly obtained from the continuous‐time parametric adaptation law used in standard MRAC schemes. In fact, at the first iteration, we apply a standard MRAC to the system under consideration, while for the subsequent iterations, the parameters are appropriately updated along the iteration‐axis, in order to enhance the tracking performance from iteration to iteration. This approach is referred to as the model reference adaptive iterative learning control (MRAILC). In the case of systems with relative degree one, we obtain a pointwise convergence of the tracking error to zero, over the whole finite time interval, when the number of iterations tends to infinity. In the general case, i.e. systems with arbitrary relative degree, we show that the tracking error converges to a prescribed small domain around zero, over the whole finite time interval, when the number of iterations tends to infinity. It is worth noting that this approach allows: (1) to extend existing MRAC schemes, in a straightforward manner, to repetitive systems; (2) to avoid the use of the output time derivatives, which are generally required in traditional iterative learning control (ILC) strategies dealing with systems with high relative degree; (3) to handle systems with multiple tracking objectives (i.e. the desired trajectory can be iteration‐varying). Finally, simulation results are carried out to support the theoretical development. Copyright © 2006 John Wiley & Sons, Ltd.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".