---
pattern_id: pattern_apmonitor
applicable_symptoms: [apmonitor]
domain: Control_Locomotion
---

# Dynamic optimization and control of differential-algebraic systems is computationally expensive and lacks accessible tools for real-time applications.

**Domain**: `Control_Locomotion`

## Fix

Use APMonitor/Gekko with simultaneous solution of differential and algebraic equations via nonlinear programming (NLP) solvers, enabling real-time optimization and nonlinear model predictive control.

## Anti-pattern

Sequential solution methods that treat differential and algebraic equations separately, leading to slower convergence and higher computational cost.

## Cross-domain analogies

- **Perception_Vision** → Use SLAM-derived trajectories as ground-truth references to supervise reduced-order DAE models for real-time control.
  - related fix: Use SLAM-derived trajectories as ground-truth motion tendency references to supervise or condition video world model predictions.
- **Planning_Decision** → Learn a direct mapping from system state to control actions via offline simulation pre-training.
  - related fix: End-to-end trajectory learning with Vision-Language-Exploration pre-training over a million diverse RGB-D trajectories, directly mapping raw sensor observations to continuous commands.
- **Learning_Training** → Hierarchical decomposition: distill complex dynamics into a medium-fidelity model, then a reduced-order real-time controller.
  - related fix: Two-stage progressive knowledge distillation: first distill from large teacher to medium student, then from medium to small student, achieving 1/7 model size with same accuracy.

## Patch

```diff
--- apmonitor.before.py
+++ apmonitor.after.py
@@ -1,2 +1,4 @@
-# --- BEFORE (vulnerable to the symptom below) ---

+# --- AFTER (ROSCLAW heuristic graft) ---

 # Symptom: Dynamic optimization and control of differential-algebraic systems is computationally expensive and lacks accessible tools for real-time applications.

+# Fix    : Use APMonitor/Gekko with simultaneous solution of differential and algebraic equations via nonlinear programming (NLP) solvers, enabling real-time optimization and nonlinear model predictive control.

+# Avoid  : Sequential solution methods that treat differential and algebraic equations separately, leading to slower convergence and higher computational cost.

```
