NN-ADRC

NN-ADRC (Neural Network - Active Disturbance Rejection Control) is an advanced control architecture that combines:

• ADRC — A model-free control approach that estimates and rejects disturbances in real-time
• Neural Network — A learned compensator that predicts optimal counter-actions for known disturbance patterns

Active Disturbance Rejection Control (ADRC)

ADRC treats all disturbances (unknown dynamics, external forces, actuator failures) as a single “total disturbance” and estimates it in real-time using an Extended State Observer (ESO).

Extended State Observer (ESO)

The ESO extends the system state with an additional state representing the total disturbance:

ẋ = Ax + Bu + Bd*d

Where d is the total disturbance. The ESO estimates distant and its derivatives, allowing the controller to cancel it.

fal() Nonlinearity

The ESO uses a nonlinear function fal() (fast function) instead of a simple linear observer:

fal(e, α, δ) = e / δ^(1-α)    if |e| ≤ δ
               sign(e)|e|^α    if |e| > δ

This provides faster convergence for large errors while maintaining smoothness near zero.

Neural Network Compensator

The NN is trained to predict the compensatory acceleration Δr̈ needed for specific failure patterns:

• Input: [position, velocity, acceleration]
• Output: Δr̈ (6-DOF compensatory acceleration)
• Training: Levenberg-Marquardt backpropagation on data from “Gremlin” script (random engine kills)

In AEGIS (Planned)

Phase 1 ✓ (Complete)

Quaternion PD attitude control with inertia-scaled torque. ESO scaffolding with fal() and parameter stubs.

Phase 2 (Planned)

• Transient Profile Generator (TG): Smooths target-state jumps into dynamically feasible trajectories
• WSEF: Computes u₀ = k₁(v₁ − z₁) + k₂(v₂ − z₂), u = (u₀ − z₃)/b₀
• NN Compensator: Feedforward NN for failure compensation
• Fallback: NN clamped to [-clamp, +clamp]; triggers zero NN → pure ADRC

Phase 3-5

• Control Allocator integration
• FDI adaptation to monitor ESO disturbance and NN output
• NN training via automated “Gremlin” failures

Key Risk

The source paper (gimbal system) validated on smooth, continuous disturbances (cable drag, friction). AEGIS failures are discrete step-functions (instant engine death) — an out-of-distribution case requiring fallback mechanisms.

Related Concepts

• Active Disturbance Rejection Control — The broader ADRC field
• Extended State Observer — Core ADRC component
• Neural Network — The learning component
• Control Allocation — Where NN output is integrated
• Fault Detection and Isolation — Monitors NN and ESO signals
• Extended Kalman Filter — The current state estimator (to be augmented)
• Optuna Hyperparameter Tuning — Tuning ADRC parameters
• State Machine — Mission phases for NN training

Sources

• AEGIS Project (docs/NN-ADRC/, src/guidance/adrc.py)
• Leblebicioglu, K. et al. NN Based Active Disturbance Rejection Controller for a Multi-Axis Gimbal System.