A Neural Network Architecture to Learn Explicit MPC Controllers from Data (1911.10789v1)

Abstract: We present a methodology to learn explicit Model Predictive Control (eMPC) laws from sample data points with tunable complexity. The learning process is cast in a special Neural Network setting where the coefficients of two linear layers and a parametric quadratic program (pQP) implicit layer are optimized to fit the training data. Thanks to this formulation, powerful tools from the machine learning community can be exploited to speed up the off-line computations through high parallelization. The final controller can be deployed via low-complexity eMPC and the resulting closed-loop system can be certified for stability using existing tools available in the literature. A numerical example on the voltage-current regulation of a multicell DC-DC converter is provided, where the storage and on-line computational demands of the initial controller are drastically reduced with negligible performance impact.

Essay on Learning Explicit MPC Controllers Using Neural Networks

The paper "A Neural Network Architecture to Learn Explicit MPC Controllers from Data" presents a novel methodology for constructing explicit Model Predictive Control (eMPC) laws from sample data, leveraging neural networks' computational capabilities. The proposed approach integrates the flexibility and performance of neural networks with the robustness of eMPC to reduce computational demands while providing stability certifications.

Key Methodological Components

In this paper, eMPC laws are derived using a neural network framework that includes two linear layers followed by an implicit parametric quadratic programming (pQP) layer. This structure offers several advantages:

• High Parallelization: The neural network setup enhances computational efficiency through high parallelization, speeding up off-line calculations.
• Low-Complexity Deployment: The resultant controller is deployable via low-complexity eMPC, which drastically reduces storage and online computational demands, as demonstrated in the power electronics case paper.
• Stability Certification: Post-training, the approximation allows for closed-loop stability certification using existing methods, ensuring reliability and safety in practical implementations.

Numerical Example and Results

In the case paper, the method was applied to voltage-current regulation in a multicell DC-DC converter. The initial eMPC controller was highly complex, requiring significant storage memory. In contrast, the neural network-based approach reduced storage requirements by over 90% with negligible performance degradation. Two viable learned controllers distinguished themselves by achieving a remarkable decrease in worst-case computation time while maintaining steady-state errors under specified thresholds.

Implications

The paper's findings have several implications for the field of control systems:

1. Reduction of Complexity: By optimizing the parameters of a minimalistic neuron layer setup, the learning process enables the reduction of complexity in controllers, broadening the application scope of eMPC in resource-constrained environments.
2. Flexible Complexity Tuning: The ability to incrementally adjust complexity allows practitioners to tailor controllers according to specific application needs, balancing between the fidelity of the control law approximation and computational resources.
3. Practical Deployment Advantages: This approach aligns with real-world requirements where computational efficiency and storage constraints often limit the adoption of complex control strategies.

Future Perspectives

The robust methodology proposed in this paper opens several avenues for future research:

• Further Reduction of Complexity: Exploration of additional techniques to further streamline storage and computational needs without compromising performance could be pursued.
• Application to Nonlinear Systems: Extending the setup to predict and learn controllers for nonlinear systems would enhance its utility across a broader range of applications.
• Enhanced Learning Algorithms: Integrating advanced learning algorithms may offer improved efficiency in training, promoting faster convergence and better accuracy.

Overall, the intersection of machine learning and control system methodologies demonstrates a promising blend of techniques that achieve high-performance control strategies with reduced operational burdens. This work accentuates the potential of neural networks to optimize traditional control practices, presenting a compelling case for adoption in scenarios restricting conventional eMPC implementations.