Recovery Limits After Disturbance or Model Changes

Derive lower bounds and complete recovery guarantees for the peak deviation and recovery time after abrupt changes in disturbances, reference signals, actuator effectiveness, or plant models when corrective inputs, adaptive gains, and actuator states have bounded rates.

Background

Most designer-assigned-time formulations analyze convergence from an initial condition under a fixed disturbance model. Operational systems instead experience abrupt disturbances, faults, reference changes, and actuator degradation. Bounded actuator and adaptation rates impose unavoidable transient deviations and may prevent immediate restoration of a deadline.

A recovery theory should relate disturbance changes and internal-controller rates to unavoidable peak error, recovery time, actuator reserve, and dwell-time requirements for repeated events.

References

A recovery theory for designer-assigned-time control should state which changes can be rejected within a recovery horizon, what actuator reserve this requires, what transient error is unavoidable, and whether repeated events require a minimum dwell time.

— From Asymptotic to Designer-Assigned-Time Control: A Review of Stability Notions, Design Mechanisms, and Controller Architectures  (2610.11964 - Bingöl, 8 Oct 2026) in Section 5.1, paragraph “Recovery limits after disturbances, faults, and model changes”