Time Domain Sensitivity of the Tracking Error

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 $\mathbf{S}(\mathbf{s})+\mathbf{T}(\mathbf{s})=\mathbf{I}$. 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.

12 pages, 10 figures, 1 table. in IEEE Transactions on Automatic Control. Scheduled for publication Feb 2024

References in corpus (3)

• Bloch vectors for qudits
• Orbits of quantum states and geometry of Bloch vectors for $N$-level systems
• Robust Control of Quantum Dynamics under Input and Parameter Uncertainty

Cited by in corpus (1)

• Geometric Interpretation of Sensitivity to Structured Uncertainties in Spintronic Networks