LESC-ODE: Lyapunov-Enhanced Neural ODE Controller for Stochastic Source Seeking

Source seeking for mobile robots in unknown signal fields is a fundamental yet challenging problem in robotics, with applications ranging from environmental monitoring to hazardous material detection. Traditional stochastic controllers, such as those based on Ornstein-Uhlenbeck (OU) noise or Extremum Seeking (ES), offer robustness but often suffer from slow convergence, large oscillations, and lack theoretical stability guarantees in complex, non-linear environments. While recent learning-based controllers (e.g., neural ODEs, NN controllers with Lyapunov certificates) have improved adaptation and performance, they 1) often neglect explicit stability constraints, leading to unpredictable behaviors, and 2) struggle to balance exploration-exploitation under noise. To address these gaps, we present LESC-ODE (Lyapunov-Enhanced Stochastic Controller with Neural ODE), a novel neural ODE-based control framework that integrates a Lyapunov stability network, residual ODE dynamics module, and OU-driven stochastic perturbations. LESC-ODE enforces formal stability via Lyapunov constraints, captures control intentions from historical signals, and maintains exploration capability. Extensive experiments in noisy signal fields show that LESC-ODE outperforms OU-based and baseline strategies in convergence speed, trajectory smoothness, and peak signal intensity, while preserving stability and interpretability. These results highlight the promise of combining theoretical guarantees with learned dynamics for robust robotic source seeking.

Recommended citation: G. Li, J. Shen, Q. Sun, and R. Ding, ‘LESC-ODE: Lyapunov-Enhanced Neural ODE Controller for Stochastic Source Seeking’, in 2025 IEEE International Conference on Data Mining Workshops (ICDMW), 2025, pp. 1748–1752.
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