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.

arXiv comment12 pages, 10 figures, 1 table. in IEEE Transactions on Automatic Control. Scheduled for publication Feb 2024

References in corpus (17)

• Perfect state transfer in quantum spin networks
• Training Schrödinger's cat: quantum optimal control
• Quantum control theory and applications: A survey
• Bloch vectors for qudits
• Realizing Rapid, High-Fidelity, Single-Shot Dispersive Readout of Superconducting Qubits
• Stabilizing Open Quantum Systems by Markovian Reservoir Engineering
• Robust quantum gates for systems subject to decoherence via optimal control: Markovian vs non-Markovian dynamics
• Orbits of quantum states and geometry of Bloch vectors for $N$-level systems
• A Spin Chain Primer
• Backaction driven, robust, steady-state long-distance qubit entanglement over lossy channels
• Time optimal information transfer in spintronics networks
• Design of Feedback Control Laws for Information Transfer in Spintronics Networks
• Robust Control Performance for Open Quantum Systems
• Robust Control of Quantum Dynamics under Input and Parameter Uncertainty
• Flag-Based Control of Quantum Purity for $n=2$ Systems
• Robustness of energy landscape control for spin networks under decoherence
• Prediction of short time qubit readout via measurement of the next quantum jump of a coupled damped driven harmonic oscillator

Cited by in corpus (1)

• Geometric Interpretation of Sensitivity to Structured Uncertainties in Spintronic Networks