Time-Domain Sensitivity of the Tracking Error

• Published in: IEEE transactions on automatic control Vol. 69; no. 4; pp. 1 - 12
• Main Authors: O'Neil, S., Schirmer, S. G., Langbein, F. C., Weidner, C. A., Jonckheere, E.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-04-2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic properties; Eigenvalues and eigenfunctions; Error signals; Frequency-domain analysis; Manganese; Optimization; Quantum system; Sensitivity; Steady-state; Time domain analysis; Time measurement; Tracking errors
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2023.3331681

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 <inline-formula><tex-math notation="LaTeX">\mathbf {S(s) + T(s) = I}</tex-math></inline-formula>. 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.