Fault-Tolerant Adaptive Switching Control of Deformable Mirrors under Actuator Failures and Saturation Limits

This paper presents an adaptive switching fault-tolerant control (FTC) framework for deformable mirrors to ensure reliable surface shape tracking under actuator faults and constraints. A finite-dimensional sensor-actuator model is established that operates directly in actuator-sensor coordinates while preserving both the resonant characteristics and static gain of the original mirror dynamics. The model is then decomposed into localized one-sensor, multiple-actuator subsystems, enabling decentralized control and reducing computational complexity. Each subsystem integrates an adaptive control law with an online switching mechanism that autonomously reconfigures actuator excitation subsets. Rather than relying on explicit fault detection, the switching is driven by a performance index that deactivates faulty actuators and reallocates effort to backups when saturation occurs. An adaptive disturbance compensation law further addresses modeling uncertainties and neglected actuator couplings. A Lyapunov-based analysis establishes closed-loop stability for all subsystems and the overall system. Simulation results demonstrate that the proposed method achieves accurate wavefront shaping, efficient actuator utilization, and robust fault tolerance.