Time-varying constraint optimization for sensorless adaptive optics systems driven by deep PSF-Zernike estimation.

Sensorless adaptive optics avoids a dedicated wavefront sensor, but closed-loop correction then depends on inferring aberrations from noisy focal-plane point-spread functions (PSFs) under finite latency and deformable-mirror (DM) constraints. This difficulty becomes acute in time-varying turbulence, where the commanded correction can be applied to a wavefront state that is already outdated. We present a closed-loop sensorless adaptive optics framework that combines single-frame PSF-to-modal estimation with delay-aware constrained control. A hybrid CNN-Transformer regresses 28 residual Zernike coefficients from noisy PSFs, and an autoregressive predictor with online parameter adaptation and fractional-step forecasting aligns the estimate with the effective actuation instant. The delay-aligned residual is then embedded in a constrained model predictive controller that enforces DM amplitude and slew-rate limits. Simulations over multiple turbulence strengths show that the learned estimator provides informative single-frame modal estimates, while the proposed NN+AR+MPC scheme improves loop stability, reduces residual phase RMS, and maintains higher Strehl ratio than both direct control and non-predictive MPC. The advantage grows with turbulence strength, indicating that temporal misalignment, rather than static estimation error alone, is the dominant limiter in the strong-turbulence regime. These results position delay-aware constrained optimization as a practical ingredient for robust high-speed sensorless adaptive optics.