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Neural Event-Triggered Control with Optimal Scheduling
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Proposes Neural ETC, learning neural controllers with Lyapunov-based event-triggering conditions that minimize triggering times, via a path-integral (differentiating through event ODE solver) and a Monte Carlo (Lipschitz-based inter-event-time bound) training approach, plus a projection operator for stability.
Problem
Neural Lyapunov controllers require continuous control updates, which is communication-prohibitive on digital platforms; designing event-triggered controllers that stabilize nonlinear systems while minimizing triggering times (maximizing minimal inter-event time) is an open problem.
Approach
Learn the controller and Lyapunov function jointly with an event-trigger loss: the path-integral variant backpropagates through a neural event ODE solver to get triggering times, while the Monte Carlo variant uses a theoretical lower bound on minimal inter-event time, regularized via Lipschitz constants. An analytical projection onto the stable controller set guarantees stability and schedule opti
Key results
- Neural ETC-MC uses 4 triggers on GRN, 13 on Lorenz and 2 on Cell, versus 23 (NLC) on GRN and 1602 on Lorenz for NLC, per Table 1 averaged over 5 runs.
- Neural ETC-MC attains minimal inter-event time 27.18 on Cell and 15.52 on GRN, versus 6e-6 for NLC on Cell.
- Neural ETC-MC trains in 32 vs 1230 for Neural ETC-PI on GRN, while Neural ETC-PI has lower temporal variance (5e-4 vs 7e-3 on GRN).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Neural ETC-MC instead of Neural ETC-PI | Neural ETC · GRN | Number of triggers: 20($\pm$3) -> 4($\pm$4) | Helped |
| Use Neural ETC-MC instead of Neural ETC-PI | Neural ETC · GRN | MSE under finite triggers: 0.05($\pm$4e-3) -> 0.07($\pm$0.03) | Mixed |
| Use Neural ETC-MC instead of Neural ETC-PI | Neural ETC · Cell | Number of triggers: 11($\pm$0.00) -> 2($\pm$0.00) | Helped |
| Use Neural ETC-PI instead of Neural ETC-MC | Neural ETC · Cell | MSE under finite triggers: 1.66($\pm$0.12) -> 5e-8($\pm$1e-9) | Helped |
| Replace path integral training with Monte Carlo training | Neural ETC · GRN | Training time: 1230 -> 32 | Helped |
| Use Neural ETC-PI instead of Neural ETC-MC | Neural ETC · Lorenz | Temporal variance: 0.09 -> 4e-3 | Helped |
| Set event loss weight $\lambda_2$ to 0.005 rather than the Neural ETC-PI reference 0.05 (ablation) | Neural ETC-PI · Lorenz | Triggering times: {29} -> 114 | Hurt |
| Set event loss weight $\lambda_2$ to 0.5 rather than the Neural ETC-PI reference 0.05 (ablation) | Neural ETC-PI · Lorenz | MSE: 7e-4 -> 0.32 | Hurt |
| Set event loss weight $\lambda_2$ to 0.01 rather than the Neural ETC-MC reference 0.1 (ablation) | Neural ETC-MC · Lorenz | Triggering times: 10 -> 37 | Hurt |
| Set event loss weight $\lambda_2$ to 1.0 rather than the Neural ETC-MC reference 0.1 (ablation) | Neural ETC-MC · Lorenz | MSE: 0.25 -> 0.53 | Hurt |
| Set decay parameter $\sigma=0.8$ (ablation) | Neural ETC variants · Lorenz | Control performance | Helped |
| Use smaller event-loss weight (ablation) | Neural ETC variants · Lorenz | Triggering times | Hurt |
Surprising findings
- Neural ETC-PI has very low temporal variance but much longer training time than Neural ETC-MC, indicating a trade-off rather than uniform dominance.
- Large event-loss weight lambda_2 degrades stabilization performance, so scheduling and stability are in tension.
Limitations
- Relies on fixed-step ODE solvers and may fail for stiff systems.
- Not applicable to SDEs since triggering times are stopping times and cannot be computed with existing event solvers.
- Lipschitz bounds and projection require bounded state space for global guarantees.
Experimental setup
Datasets: simulated dynamical systems (GRN, Lorenz, Cell, FHN)
Benchmarks: GRN Lorenz Cell (100-D)
Metrics: number of triggers minimal inter-event time MSE under finite triggers training time temporal variance
Baselines: BALSA LQR Quad-NLC NLC IRL ETC Critic-Actor ETC ETS PGDNLC
Builds on: neural Lyapunov control neural event ODE input convex neural networks spectral normalization
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