ExAMPC: the Data-Driven Explainable and Approximate NMPC with Physical Insights

2025-03-01

AI Summary

Nonlinear model predictive control (NMPC) deployment faces challenges of high computational complexity, lack of closed-loop performance guarantees, and poor physical interpretability. Method: This paper proposes ExAMPC—a physics-informed, explainable AI-enhanced framework for constructing high-fidelity, low-overhead, and interpretable approximate NMPC. It employs low-order spline embedding for >95% state dimensionality reduction, integrates SHAP-based sensitivity analysis with symbolic regression to expose optimization solution dependencies on physical variables and parameters, and introduces a physics-driven continuous-time constraint penalization mechanism to enhance trajectory feasibility. Contributions/Results: ExAMPC reduces trajectory constraint violations by 93%, enables accurate prediction of computational load and worst-case execution time, and demonstrates real-world efficacy in automated valet parking and autonomous racing lap-time optimization.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Amidst the surge in the use of Artificial Intelligence (AI) for control purposes, classical and model-based control methods maintain their popularity due to their transparency and deterministic nature. However, advanced controllers like Nonlinear Model Predictive Control (NMPC), despite proven capabilities, face adoption challenges due to their computational complexity and unpredictable closed-loop performance in complex validation systems. This paper introduces ExAMPC, a methodology bridging classical control and explainable AI by augmenting the NMPC with data-driven insights to improve the trustworthiness and reveal the optimization solution and closed-loop performance's sensitivities to physical variables and system parameters. By employing a low-order spline embedding to reduce the open-loop trajectory dimensionality by over 95%, and integrating it with SHAP and Symbolic Regression from eXplainable AI (XAI) for an approximate NMPC, we enable intuitive physical insights into the NMPC's optimization routine. The prediction accuracy of the approximate NMPC is enhanced through physics-inspired continuous-time constraints penalties, reducing the predicted continuous trajectory violations by 93%. ExAMPC enables accurate forecasting of the NMPC's computational requirements with explainable insights on worst-case scenarios. Experimental validation on automated valet parking and autonomous racing with lap-time optimization NMPC, demonstrates the methodology's practical effectiveness in real-world applications.

Problem

• Bridges classical control and explainable AI for NMPC
• Reduces computational complexity of NMPC using data-driven insights
• Enhances trustworthiness and predictability of NMPC in real-world applications

Innovation

• Data-driven insights enhance NMPC trustworthiness
• Low-order spline embedding reduces trajectory dimensionality
• Physics-inspired constraints improve prediction accuracy