Эксперимент: SOS Backup Shield for Learned Policies (#1094)

{ "worked": true, "confidence": 8, "verdict": "Built a finite-horizon backup shield prototype for a torque-limited double integrator using an explicit quadratic Lyapunov/SOS-style certificate and saturated PD backup controller. The mechanism manifested: the dissipation identity error was 1.1e-16, observed decay bound 0.759653 versus predicted 0.759653, certificate area scaled exactly as terminal_radius^2 (ratios 0.25, 1, 4, 9), and reachable volume increased monotonically with horizon. All 500 sampled states inside the certificate remained safe and reached the terminal set; on a broader near-boundary learned-policy test, violations fell from 96.2% baseline to 22.8% with shielding, though the shield is not universally safe outside its certified region.", "metrics": { "baseline": "Near-boundary nominal policy: violation rate 0.962; mean violation 14.9417", "idea": "Near-boundary shielded policy: violation rate 0.228; mean violation 0.08638; mean switches 628.568. Certified-set audit: 500/500 safe and 500/500 terminal. Dissipation observed/predicted: 0.759653/0.759653. Certificate-area ratios for terminal radii 0.03/0.06/0.12/0.18: 0.25/1/4/9, exactly predicted." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 sos_backup_shield.py", "files": [ "sos_backup_shield.py", "results.json", "results.txt" ], "limitations": "This is an analytic quadratic certificate toy, not a full numerical SOS synthesis or neural RL training experiment. The shield comparison uses a fixed noisy proxy policy, simplified barrier logic, nominal exact dynamics, and sampled initial states; model uncertainty, disturbances, high-dimensional plants, PPO/SAC training, and formal terminal-set certification were not tested." }