Research map / Probabilistic and scientific modeling / Differential equations and PDEs
FESSNC: Fast Exponentially Stable and Safe Neural Controller
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes FESSNC, a neural controller framework for SDEs that learns exponentially stable and safe controllers and then applies closed-form approximate projections to guarantee exponential stability and almost-sure safety, with Hutchinson trace estimation for speed.
Problem
Stabilizing nonlinear SDEs with rigorous exponential stability and almost-sure safety guarantees for learned neural controllers, while keeping training and testing fast in high dimensions.
Approach
Train neural controllers with stability and zeroing-barrier safety losses, then apply closed-form approximate L2 projections (pi_es, pi_sf) that map any candidate controller into the exponentially stable and safe controller spaces; Hutchinson's trace estimator and detach tricks cut Hessian cost.
Key results
- On the kinetic bicycle comparison table, FESSNC reports 100% safety rate and 100% success rate with training time 14 s, versus SYNC 90%/90% at 125 s and RSMC 10% safety at 435 s.
- Average control process time is 10.35 s for FESSNC on double pendulum versus 146.64 s for GP-MPC; BALSA is faster (3.08 s) but performs worse.
- Approximate projection operators are applied to a kernel-based controller on a 3-link pendulum task, improving its stability and safety without further training.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FESSNC instead of SYNC | Kinetic bicycle controller · Kinetic bicycle | training time (sec): 125 -> 14 | Helped |
| Use FESSNC instead of NNDMC | Kinetic bicycle controller · Kinetic bicycle | training time (sec): 209 -> 14 | Helped |
| Use FESSNC instead of RSMC | Kinetic bicycle controller · Kinetic bicycle | training time (sec): 435 -> 14 | Helped |
| Use FESSNC instead of RSMC+ICNN | Kinetic bicycle controller · Kinetic bicycle | training time (sec): 987 -> 14 | Helped |
| Use FESSNC instead of SYNC | Kinetic bicycle controller · Kinetic bicycle | safety rate (%): 90 -> 100 | Helped |
| Use FESSNC instead of RSMC | Kinetic bicycle controller · Kinetic bicycle | safety rate (%): 10 -> 100 | Helped |
| Use FESSNC instead of RSMC+ICNN | Kinetic bicycle controller · Kinetic bicycle | success rate (%): 90 -> 100 | Helped |
| Use FESSNC instead of NNDMC | Kinetic bicycle controller · Kinetic bicycle | success rate (%): 60 -> 100 | Helped |
| Use FESSNC instead of RSMC | Kinetic bicycle controller · Kinetic bicycle | success rate (%): 0 -> 100 | Helped |
| Use FESSNC instead of NNDMC | Kinetic bicycle controller · Kinetic bicycle | control energy: 2.6 -> 1.5 | Helped |
| Use FESSNC instead of RSMC | Kinetic bicycle controller · Kinetic bicycle | control energy: 14.5 -> 1.5 | Helped |
| Use FESSNC instead of GP-MPC | Control controller · Double pendulum | control process time (s): 146.64s -> 10.35s | Helped |
Surprising findings
- Exponential stability does not imply boundedness of the state space (exponential martingale example), so a stable controller may still be unsafe.
- The approximate projection pi_es guarantees membership in the stable space only if the state space is bounded.
Limitations
- Offline, model-based framework requiring known drift and diffusion; not extended to online or model-free settings.
- Restricted to deterministic (fully actuated) control; stochastic control and under-actuated systems left to future work.
- Projection operators require bounded state space for guarantees, which is achieved by first enforcing safety.
Experimental setup
Datasets: simulated SDE trajectories and sampled states from safe regions
Benchmarks: double pendulum swing-up with safety constraint kinematic bicycle with circular safe region synchronization of 50 coupled FitzHugh-Nagumo oscillators
Metrics: success rate safety rate training time control energy computational complexity
Baselines: GP-MPC BALSA SYNC NNDMC RSMC RSMC+ICNN
Builds on: neural Lyapunov control neural stochastic control control barrier functions spectral normalization Hutchinson trace estimator
Closest papers by meaning
- Two‑Stage Learning of Stabilizing Neural Controllers via Zubov Sampling and Iterative Domain Expansion (NeurIPS 2025 · similarity 0.88)
- Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulation (ICML 2024 · similarity 0.86)
- Safely Learning Controlled Stochastic Dynamics (NeurIPS 2025 · similarity 0.86)
- Physics-Informed Neural Network Policy Iteration: Algorithms, Convergence, and Verification (ICML 2024 · similarity 0.85)
- Stability Analysis of Switched Linear Systems with Neural Lyapunov Functions (AAAI 2024 · similarity 0.84)
- Verified Safe Reinforcement Learning for Neural Network Dynamic Models (NeurIPS 2024 · similarity 0.84)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.