There are only three ways to control a complex machine (Robot, EV, Rocket).
Two of them are flawed. One of them is the future.
We have compiled a definitive comparison between Non-linear MPC (The Industry Standard), Deep Reinforcement Learning (The Hype), and The Bangsaen Koopman Approach (The Alien Tech).
| Feature / Metric | NMPC (The Ideal) |
Deep MPC (The AI Hype) |
Bangsaen Koopman (The Alien Tech) |
|---|---|---|---|
| The Mathematics | Solves Non-linear Optimization at every single time step. (Iterative Solver) | Uses Neural Networks to approximate the control law. (Black Box) | Transforms Non-linear to Linear Space, then solves simple Matrix Algebra. |
| Computational Load | EXTREME. Requires heavy CPU cycles to converge. | HIGH. Requires GPU/NPU for inference. | NEGLIGIBLE. Just Matrix Multiplication (BLAS). |
| Latency (Speed) | Slow (Milliseconds to Seconds). Risks system instability if solver fails. | Fast, but has Jitter (unpredictable variance). | LIGHT SPEED. Microseconds. Deterministic real-time. |
| Safety Guarantee | High (if hardware keeps up). | ZERO. Cannot prove stability. Susceptible to "Hallucination". | PROVEN. Lyapunov Stable. Mathematically guaranteed bounds. |
| Required Hardware | Industrial PC / FPGA ($1,000+) | NVIDIA Jetson / TPU ($500+) | ESP32 ($2) |
Why NMPC Fails
Non-linear Model Predictive Control (NMPC) is mathematically perfect but practically impossible for low-cost hardware. It tries to solve a complex optimization problem (finding the minimum of a curve) hundreds of times per second.
Result: You need a computer in the trunk just to keep the car on the road.
Why AI Control Fails
"Deep MPC" is popular in research because it's easy to get funding. But Neural Networks are "Black Boxes." You cannot ask them why they made a decision. If they encounter an Edge Case (e.g., snow + rain), they hallucinate.
Result: Unpredictable behavior. Dangerous for human passengers.
The Bangsaen Way
We don't fight the Non-linearity. We Lift it.
By transforming the system states into a higher-dimensional space (Koopman Operator), the chaotic physics become linear.
Result: We can use simple, lightning-fast Linear Algebra (LQR/Kalman) to control complex chaos.
Hardware Cost vs. Control Performance
Graph: Hardware Cost required to achieve < 1ms Loop Time.