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arXiv · 2210.15783

Time Domain Sensitivity of the Tracking Error

S. O'Neil·S. G. Schirmer·F. C. Langbein·C. A. Weidner·E. Jonckheere
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Abstract

A strictly time-domain formulation of the log-sensitivity of the error signal to structured plant uncertainty is presented and analyzed through simple but representative classical and quantum systems. Results demonstrate that across a wide range of physical systems, maximization of performance (minimization of the error signal) asymptotically or at a specific time comes at the cost of increased log-sensitivity, implying a time-domain constraint analogous to the frequency-domain identity $\mathbf{S(s) + T(s) = I}$. While of limited value in classical problems based on asymptotic stabilization or tracking, such a time-domain formulation is valuable in assessing the reduced robustness cost concomitant with high-fidelity quantum control schemes predicated on time-based performance measures.

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S. O'Neil, S. G. Schirmer, F. C. Langbein, C. A. Weidner, E. Jonckheere. 2022-10-27. Time Domain Sensitivity of the Tracking Error. https://doi.org/10.1109/tac.2023.3331681

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