[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120421-en":3,"doc-seo-120421-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},120421,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Interpretable Machine Learning Approach for Nonlinear Control - 22nd EUROPT Conference on Advances in Continuous Optimization","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.","Interpretable Machine Learning Approach for Nonlinear  \nControl  \nEdmondo Minisci*, Giulio Avanzini**  \n*University of Strathclyde (UK), **Universita’ del Salento (Italy)  \n22nd EUROPT Conference on Advances in Continuous Optimization  \n(EUROPT 2025)  \n29 June-2 July 2025  \nUniversity of Southampton, UK  \nMinisci, Avanzini Interpretable ML Approach for NL Control EUROPT 2025 1 / 45  \nTable of Contents  \n1 Introduction  \n2 Symbolic Regression via Genetic Programming  \n3 Symbolic Regression via Kolmogorov-Arnold Modelling  \n4 Cases and Models  \n5 Results and Discussions  \n6 Summary and Conclusions  \nMinisci, Avanzini Interpretable ML Approach for NL Control EUROPT 2025 2 / 45  \nIntroduction  \nTable of Contents  \n1 Introduction  \n2 Symbolic Regression via Genetic Programming  \n3 Symbolic Regression via Kolmogorov-Arnold Modelling  \n4 Cases and Models  \n5 Results and Discussions  \n6 Summary and Conclusions  \nMinisci, Avanzini Interpretable ML Approach for NL Control EUROPT 2025 3 / 45  \nIntroduction  \nMotivation: The Need for Interpretable Control Systems  \n Black-box AI dominates modern control applications, but lacks transparency  \n Classical control methods require linearisation and gain scheduling for nonlinear systems  \n Gap between AI performance and interpretability limits real-world deployment  \n Safety-critical applications demand explainable control decisions  \n\n| Key Challenges |\n| --- |\n| 1 Maintaining performance while ensuring interpretability\u003Cbr>2 Handling nonlinear systems without linearisation approximations\u003Cbr>3 Bridging machine learning capabilities with classical control theory\u003Cbr>4 Enabling human understanding and verification of control laws\u003Cbr>\u003Cbr>\u003Cbr>\u003Cbr> |\n\nResearch Gap: Need for interpretable ML methods that can discover compact, human-readable control laws for nonlinear systems while maintaining competitive performance  \nMinisci, Avanzini Interpretable ML Approach for NL Control EUROPT 2025 4 / 45  \nIntroduction  \nFoundation: Genetic Programming for Control Systems  \nOur Previous Works:  \n GP for open-loop optimization: Direct trajectory optimization  \n GP for closed-loop design: Direct controller evolution  \n Interpretable control laws: Human-readable expressions  \n Aerospace applications: Reentry vehicle guidance  \nKey Publications:  \n Marchetti et al.”GP guidance control for reentry vehicle”  \n Marchetti et al.”Parametrized GP with adjoint state method”  \n\n| Previous GP-Control Integration Successes |\n| --- |\n|  Robustness: GP controllers handle uncertainties effectively\u003Cbr> Automation: No need for predefined control structure\u003Cbr> Nonlinearity: Direct handling without linearisation\u003Cbr> Interpretability: Symbolic expressions enable analysis |\n\nMinisci, Avanzini Interpretable ML Approach for NL Control EUROPT 2025 5 / 45  \nIntroduction  \nCritical Limitation: Computational Bottleneck in Previous Work  \nThe Coupling Problem  Previous Approach: Direct coupling of GP with ODE propagator  \n GP individuals → Control law parameters γ  \n Each fitness evaluation requires full ODE integration  \n Gradient computation via adjoint state method  \n Computationally expensive due to tight coupling  \nScaling Issues:  \n Large parameter spaces  Multiple design variables  Complex dynamics  \n Prohibitive for real-time applications  \nNeed: Decouple optimization from real-time ODE integration while preserving interpretability and performance  \nMinisci, Avanzini Interpretable ML Approach for NL Control EUROPT 2025 6 / 45  \nIntroduction  \nInnovation: Decoupling Optimization and Control Learning  \nOur Decoupling Approach   \nThree-Stage Process:  \n1 Open-loop optimization: Time-parametrized control u (t)  \n2 Data extraction: Optimal trajectory data (x∗ (t), u∗ (t))  \n3 Closed-loop learning: GP/ML learns u = f (x,γ) from data  \nProcess Flow:  \nOpen-loop u∗ (t) → Data (x, u) → GP Learning  \nControl Law u (x) → Verification  \nMinisci, Avanzini Interpretable ML Approach for NL Control EUROPT 2025 7 / 45  \nIntroduction  \nInnovation: De","cbCaiah0AyGNHRYQ","https://ap.wps.com/l/cbCaiah0AyGNHRYQ","pdf",999314,1,45,"English","en",105,"# Introduction\n## Motivation and research gap\n## Genetic programming foundation and limitation\n## Decoupling optimization and control learning\n# Symbolic Regression via Genetic Programming\n## Genetic programming formulation and optimization\n# Symbolic Regression via Kolmogorov-Arnold Modelling\n## Model representation and learning\n# Cases and Models\n## Inverted pendulum and aircraft response\n# Results and Discussions\n## Performance, efficiency, scalability, verification\n# Summary and Conclusions\n## Contributions and takeaways","[{\"question\":\"Why is interpretability important for nonlinear control systems?\",\"answer\":\"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.\"},{\"question\":\"What computational bottleneck exists in the earlier GP-control coupling approach?\",\"answer\":\"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.\"},{\"question\":\"How does the proposed method decouple optimization from control learning?\",\"answer\":\"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.\"}]","Interpretable Machine Learning Approach for Nonlinear Control - 22nd EUROPT Conference on Advances in Continuous Optimization | PDF",1785729957,113,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"interpretable-machine-learning-approach-for-nonlinear-control-22nd-europt-conference-on-advances-in-continuous-optimization","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/interpretable-machine-learning-approach-for-nonlinear-control-22nd-europt-conference-on-advances-in-continuous-optimization/120421/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why is interpretability important for nonlinear control systems?","Question",{"text":75,"@type":76},"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.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What computational bottleneck exists in the earlier GP-control coupling approach?",{"text":80,"@type":76},"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.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the proposed method decouple optimization from control learning?",{"text":84,"@type":76},"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. 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