Online Active Learning Architecture for Safety-Critical Control Systems

Online Active Learning (OAL) aims to extend deep learning from static inference after offline training to continuous adaptation during real-time interaction with a changing physical environment. This transition is essential for safety-critical applications, but it raises a central theoretical question: whether the online parameter update process remains stable when scaled to multilayer neural architectures. This paper develops a stability-focused OAL framework. The framework uses prediction error as a feedback signal to update a structured deep model, thereby linking online learning with Lyapunov-based energy minimization. We show that prediction error convergence alone is insufficient for global parameter convergence because multilayer networks may admit high-dimensional manifolds of equivalent output solutions. The analysis therefore separates output error regulation, internal zero dynamics, interlayer coupling, and parameter convergence. Persistency of excitation and active damping are then used to remove the residual null-space modes that remain after output error convergence. A cascaded Lyapunov analysis establishes asymptotic stability of the overall OAL learning process, while monotonic activation functions and diffeomorphic layer mappings provide the uniqueness condition for the target parameter trajectory. The resulting proof provides a theoretical basis for applying online adaptive learning to large-scale neural systems in nonstationary and safety-critical settings.

Neural networks offer critical adaptability for controlling complex systems where nominal modeling proves intractable. However, when offline-trained neural networks are deployed within closed-loop control systems, their actions fundamentally alter the state distribution upon which they were trained. This paper introduces a unified taxonomy to categorize these sequential failure modes: the initial Closed-Loop Identification Error, the deployment-induced Action Error, and the continuous Tracking Error. Through discrete-time sensitivity analysis, this work formalizes how offline-learned parameters locally guarantee a trajectory divergence upon deployment, degrading performance due to local loss geometry. To mitigate this distribution shift, we propose actionable design policies centered on time-scale separated online adaptation. These mechanisms are validated through ablation studies on a nonlinear Duffing oscillator, demonstrating that bounded continuous learning successfully mitigates trajectory divergence whereas static deployments fail, offering concrete guidelines for practitioners deploying machine learning components in safety-critical feedback systems.

Online residual learning can reduce model mismatch in predictive control, but passive data collection may fail to adequately cover states that become important later in the task. Task-agnostic active learning targets uncertain or informative regions, but information acquired in such regions does not necessarily improve task performance. This paper introduces Task-Oriented Information Acquisition (ToIA), an active-learning criterion for model predictive path integral control (MPPI) with online Gaussian process (GP) residual learning. For each sampled control sequence, ToIA estimates how much an observation obtained early in the rollout would reduce predictive uncertainty at later states on the same rollout, and weights this reduction by the rollout's relevance to the task. The score is evaluated over the existing MPPI rollout batch without sampling future observations or re-optimizing control under hypothetical posterior updates. In simulated off-road navigation across held-out maps with heterogeneous terrain, ToIA improved the goal-reaching success rate over passive GP learning by 19.3 and 27.4 percentage points and outperformed task-agnostic active-learning baselines across dense and sparse online-learning intervals. An ablation study indicates that task relevance is particularly important under sparse model updates. The implementation supports online control at 20 Hz on an NVIDIA RTX 2080 Ti.