Interpretable Machine Learning Approach for Nonlinear Control - 22nd EUROPT Conference on Advances in Continuous Optimization

Aug 3, 2026

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Interpretable machine learning is used to derive human-readable control laws for nonlinear dynamical systems while retaining strong control performance. The work addresses the limitations of black-box control and the need for explainable decisions in safety-critical applications. It proposes a three-stage decoupling strategy: open-loop time-parameterized optimization generates optimal state-control trajectories, symbolic regression via genetic programming learns a compact control law from data, and verification validates closed-loop behavior. Key results compare efficiency, scalability, and interpretability against tightly coupled optimization approaches, including nonlinear benchmark simulations such as an inverted pendulum.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages45

Reading Time1 h 53 min

AccessFree to download

Introduction

Motivation and research gap

Genetic programming foundation and limitation

Decoupling optimization and control learning

Symbolic Regression via Genetic Programming

Genetic programming formulation and optimization

Symbolic Regression via Kolmogorov-Arnold Modelling

Model representation and learning

Cases and Models

Inverted pendulum and aircraft response

Results and Discussions

Performance, efficiency, scalability, verification

Summary and Conclusions

Contributions and takeaways

Interpretable Machine Learning Approach for Nonlinear Control Edmondo Minisci*, Giulio Avanzini** *University of Strathclyde (UK), **Universita’ del Salento (Italy) 22nd EUROPT Conference on Advances in Continuous Optimization (EUROPT 2025) 29 June-2 July 2025 University of Southampton, UK Minisci, Avanzini Interpretable ML Approach for NL Control EUROPT 2025 1 / 45 Table of Contents 1 Introduction 2 Symbolic Regression via Genetic Programming 3 Symbolic Regression via Kolmogorov-Arnold Modelling 4 Cases and Models 5 Results and Discussions 6 Summary and Conclusions Minisci, Avanzini Interpretable ML Approach for NL Control EUROPT 2025 2 / 45 Introduction Table of Contents 1 Introduction 2 Symbolic Regression via Genetic Programming 3 Symbolic Regression via Kolmogorov-Arnold Modelling 4 Cases and Models 5 Results and Discussions 6 Summary and Conclusions Minisci, Avanzini Interpretable ML Approach for NL Control EUROPT 2025 3 / 45 Introduction Motivation: The Need for Interpretable Control Systems Black-box AI dominates modern control applications, but lacks transparency Classical control methods require linearisation and gain scheduling for nonlinear systems Gap between AI performance and interpretability limits real-world deployment Safety-critical applications demand explainable control decisions | Key Challenges | | --- | | 1 Maintaining performance while ensuring interpretability
2 Handling nonlinear systems without linearisation approximations
3 Bridging machine learning capabilities with classical control theory
4 Enabling human understanding and verification of control laws

| Research Gap: Need for interpretable ML methods that can discover compact, human-readable control laws for nonlinear systems while maintaining competitive performance Minisci, Avanzini Interpretable ML Approach for NL Control EUROPT 2025 4 / 45 Introduction Foundation: Genetic Programming for Control Systems Our Previous Works: GP for open-loop optimization: Direct trajectory optimization GP for closed-loop design: Direct controller evolution Interpretable control laws: Human-readable expressions Aerospace applications: Reentry vehicle guidance Key Publications: Marchetti et al.”GP guidance control for reentry vehicle” Marchetti et al.”Parametrized GP with adjoint state method” | Previous GP-Control Integration Successes | | --- | | Robustness: GP controllers handle uncertainties effectively
Automation: No need for predefined control structure
Nonlinearity: Direct handling without linearisation
Interpretability: Symbolic expressions enable analysis | Minisci, Avanzini Interpretable ML Approach for NL Control EUROPT 2025 5 / 45 Introduction Critical Limitation: Computational Bottleneck in Previous Work The Coupling Problem Previous Approach: Direct coupling of GP with ODE propagator GP individuals → Control law parameters γ Each fitness evaluation requires full ODE integration Gradient computation via adjoint state method Computationally expensive due to tight coupling Scaling Issues: Large parameter spaces Multiple design variables Complex dynamics Prohibitive for real-time applications Need: Decouple optimization from real-time ODE integration while preserving interpretability and performance Minisci, Avanzini Interpretable ML Approach for NL Control EUROPT 2025 6 / 45 Introduction Innovation: Decoupling Optimization and Control Learning Our Decoupling Approach Three-Stage Process: 1 Open-loop optimization: Time-parametrized control u (t) 2 Data extraction: Optimal trajectory data (x∗ (t), u∗ (t)) 3 Closed-loop learning: GP/ML learns u = f (x,γ) from data Process Flow: Open-loop u∗ (t) → Data (x, u) → GP Learning Control Law u (x) → Verification Minisci, Avanzini Interpretable ML Approach for NL Control EUROPT 2025 7 / 45 Introduction Innovation: De

FAQs

Why is interpretability important for nonlinear control systems?

Modern black-box AI controllers lack transparency, while classical methods often rely on linearisation that can be restrictive for nonlinear dynamics. Safety-critical applications further require explainable and verifiable control decisions.

What computational bottleneck exists in the earlier GP-control coupling approach?

Tightly coupling genetic programming with ODE propagation forces every fitness evaluation to run full ODE integration, making gradient computation expensive and preventing real-time scalability due to large parameter spaces and complex dynamics.

How does the proposed method decouple optimization from control learning?

It first computes optimal open-loop trajectories, extracts state-control data pairs, then trains GP/ML to learn a control law mapping from states to control actions. Finally, it verifies the learned law through closed-loop simulation and trajectory validation.

Aug 3, 2026

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