This repository contains implementations and experiments for Koopman-based Robust Model Predictive Control (RMPC) applied to a 2R2C building thermal model. The core idea is to approximate nonlinear thermal dynamics with a linear predictor in a lifted (Koopman) space, enabling the use of linear MPC techniques while retaining nonlinear system fidelity.

The repository includes two complementary implementations:

• A MATLAB implementation based on classical Extended Dynamic Mode Decomposition (EDMD) with handcrafted basis functions.
• A Python implementation using Deep Koopman learning, where the lifting functions are learned via neural networks.

Both implementations follow the same conceptual pipeline and are intended to be compared side-by-side.

The system of interest is a 2R2C thermal building model, commonly used to describe indoor temperature dynamics under heating/cooling inputs and environmental disturbances. The dynamics are nonlinear due to bilinear and quadratic terms arising from heat transfer and control interactions.

The control objective is to:

• Accurately predict thermal states over a finite horizon
• Enable robust MPC design using a linear predictor in lifted space

Koopman operator theory provides the bridge between nonlinear dynamics and linear control.

Both MATLAB and Python solutions follow the same logic:

1. Nonlinear system dynamics ( x_{k+1} = f(x_k, u_k) )

2. Data collection Simulate multiple trajectories under random excitation to collect ( (x_k, u_k, x_{k+1}) ) samples.

3. Lifting to Koopman space Map the original state to a higher-dimensional space: [ z_k = \psi(x_k) ]

4. Linear dynamics in lifted space [ z_{k+1} = A z_k + B u_k ]

5. State reconstruction [ x_k \approx C z_k ]

The key difference lies in how the lifting function ( \psi(\cdot) ) is constructed.

The MATLAB implementation uses explicit basis functions:

• Radial Basis Functions (RBFs)
• Original state components

Key characteristics:

• Deterministic lifting map
• Linear regression to identify (A), (B), and (C)
• Inspired by Koopman MPC formulations by Korda & Mezic

This approach is transparent and interpretable, but requires manual design of basis functions.

The Python implementation replaces handcrafted bases with learned lifting functions:

• A neural network encoder learns ( z = \psi_\theta(x) )
• Linear layers represent the Koopman operator ((A, B))
• A decoder maps lifted states back to physical space

Training objectives include:

• One-step prediction loss in state space
• Koopman consistency loss in lifted space

This formulation preserves the Koopman structure while increasing expressive power and reducing manual feature engineering.

The Deep Koopman model achieves:

• Very low one-step prediction error
• Stable short-horizon rollouts
• Gradual divergence over long horizons, consistent with Koopman eigenvalue sensitivity

A representative rollout comparison between the true nonlinear system and the Koopman predictor is shown below.

Figure: Time-domain comparison of true states and Koopman-predicted states for both state variables.

• Both EDMD (MATLAB) and Deep Koopman (Python) successfully linearize the dynamics in lifted space.
• Deep Koopman provides greater flexibility by learning task-specific basis functions.
• Long-horizon prediction error is primarily driven by small Koopman eigenvalue inaccuracies, a known theoretical limitation.

.
├── data/ # (Optional) datasets or generated simulation data
│
├── results/ # Experimental results and figures
│ └── Koopman_plot1.png # True vs Koopman rollout comparison
│
├── src/ # Source code
│ ├── 2R2C_Lifted_EDMD.m # MATLAB EDMD-based Koopman identification (RBF lifting)
│ └── deep_koopman_2RRC.py # Python Deep Koopman implementation (neural lifting)
├── README.md

• M. Korda, I. Mezic, Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control, Automatica, 2018.
• S. Lusch, J. N. Kutz, S. L. Brunton, Deep learning for universal linear embeddings of nonlinear dynamics, Nature Communications, 2018.

This repository is intended for research and educational purposes, particularly for studying Koopman-based modeling and control in building energy systems and related thermal processes.