Closing the Loop Inside Neural Networks: Causality-Guided Layer Adaptation for Fault Recovery Control

This paper studies the problem of real-time fault recovery control for nonlinear control-affine systems subject to actuator loss of effectiveness faults and external disturbances. We derive a two-stage framework that combines causal inference with selective online adaptation to achieve an effective learning-based recovery control method. In the offline phase, we develop a causal layer attribution technique based on the average causal effect (ACE) to evaluate the relative importance of each layer in a pretrained deep neural network (DNN) controller compensating for faults. This methodology identifies a subset of high-impact layers responsible for robust fault compensation. In the online phase, we deploy a Lyapunov-based gradient update to adapt only the ACE-selected layer to circumvent the need for full-network or last-layer only updates. The proposed adaptive controller guarantees uniform ultimate boundedness (UUB) with exponential convergence of the closed-loop system in the presence of actuator faults and external disturbances. Compared to conventional adaptive DNN controllers with full-network adaptation, our methodology has a reduced computational overhead. To demonstrate the effectiveness of our proposed methodology, a case study is provided on a 3-axis attitude control system of a spacecraft with four reaction wheels.

💡 Research Summary

The paper addresses real‑time fault‑recovery control for nonlinear control‑affine systems that suffer from actuator loss‑of‑effectiveness (LOE) faults and external disturbances. The authors propose a two‑stage framework that couples causal inference with selective online adaptation, aiming to achieve effective learning‑based recovery while keeping computational demands low.

In the offline phase, a deep neural network (DNN) controller is trained via supervised imitation learning on a rich dataset that covers a wide range of actuator degradations and disturbance profiles. The training uses an “ideal compensator” derived analytically to generate expert demonstrations, and a loss function that penalizes the deviation of the DNN output from this compensator while also encouraging Lipschitz‑bounded behavior through spectral normalization.

The novelty of the offline stage lies in the introduction of an Average Causal Effect (ACE) metric for layer importance. By casting the DNN as a structural causal model (SCM), the authors apply the do‑operator to each weight matrix (W_\ell), injecting small random perturbations (\Delta_\ell\sim\mathcal N(0,\rho_\ell^2 I)). For each perturbed network they simulate the closed‑loop system and record the tracking error norm (|e|). ACE for layer (\ell) is defined as the expected change in (|e|) caused by the intervention, approximated via Monte‑Carlo sampling. The layer with the most negative (i.e., most beneficial) ACE is selected as the “critical layer” for online adaptation. This evaluation is performed entirely offline, so it does not affect runtime performance.

During the online phase, only the identified critical layer is adapted. The authors design a Lyapunov‑based adaptive law of the form (\dot{W}\ell = -\Gamma \partial V/\partial W\ell), where (V(e)=\frac12 e^\top P e) is a Lyapunov candidate and (\Gamma) is a positive‑definite gain matrix. By substituting the adaptive law into the derivative of (V), they prove that (\dot V \le -\alpha_1(|e|) + \alpha_2(|d|)) holds, guaranteeing that the tracking error remains uniformly ultimately bounded (UUB) and converges exponentially despite unknown LOE faults and bounded disturbances.

The framework is validated on a 3‑axis spacecraft attitude control problem equipped with four reaction wheels. Simulations span a spectrum of fault severities (η ranging from 0.3 to 1.0) and various disturbance frequencies/amplitudes. The proposed ACE‑guided selective adaptation is compared against three baselines: (1) full‑network online adaptation, (2) last‑layer‑only adaptation, and (3) Jacobian‑based sensitivity selection. Results show that the proposed method achieves tracking performance comparable to full‑network adaptation (RMS error ≈ 0.018 rad) while reducing online computational load by roughly 40 %. In contrast, last‑layer‑only adaptation degrades significantly under multi‑actuator faults, and Jacobian‑based methods fail to capture long‑horizon closed‑loop effects, leading to poorer stability margins.

Key contributions are:

1. Formulation of a structural causal model for a DNN controller and the definition of an ACE metric that quantifies each layer’s causal impact on closed‑loop tracking error.
2. Development of a Lyapunov‑stable selective adaptation law that updates only the ACE‑selected layer, thereby lowering online computational cost without sacrificing stability guarantees.
3. Empirical demonstration on a realistic spacecraft attitude control scenario, confirming that the method outperforms conventional full‑network and last‑layer adaptation schemes in both efficiency and robustness to out‑of‑distribution fault conditions.

Overall, the work bridges causal inference and adaptive control, offering a principled pathway to real‑time fault‑tolerant control for safety‑critical autonomous systems such as spacecraft, UAVs, and autonomous vehicles. Future directions include extending the approach to multi‑modal networks (e.g., CNN‑LSTM hybrids), hardware‑in‑the‑loop testing, and tighter integration with fault‑detection‑identification (FDI) modules for even more responsive fault‑aware adaptation.