[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83706-en":3,"doc-seo-83706-105":28,"detail-sidebar-cat-0-en-105":90},{"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":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":13,"seo_description":14,"update_tm":26,"read_time":27},83706,4398048949847,"Eliana","https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267",8,"Research & Report","Multimodal Nonblocking Supervisory Control Synthesis","Supervisory control synthesis uses nonblocking to guarantee liveness of the supervised system, but standard nonblocking becomes too weak when models include fault behavior, reconfiguration, or multiple control goals. To address this, the paper defines modal and multimodal nonblocking, restricting which states may be visited on paths toward marked states. Synthesis algorithms construct corresponding supervisors, and three intuitive examples—motivated by safety-critical water infrastructure problems—illustrate the approach. The work compares the new variants with established ones and provides implication conditions where possible.","Marijn Minkenberg et al., Multimodal Nonblocking Supervisory Control Synthesis Submitted to CDC 2026, uploaded to arXiv on July 7, 2026 .  \nMultimodal Nonblocking Supervisory Control Synthesis  \nM. Minkenberg 1 , M. A. Reniers 1 , M. A. Goorden 1 , J. M. van de Mortel-Fronczak1 , W. J. Fokkink2  \narXiv :2607 .03263v1 [ ee ss . SY] 3 Jul 2026  \nAbstract—Supervisory control synthesis leverages the nonblocking property to show liveness of the supervised system. This property is particularly weak when system models include fault behavior, reconfiguration, or multiple control goals. To capture a more suitable nonblocking property for such system models, this paper introduces modal and multimodal nonblocking. These novel nonblocking variants impose a restriction on the states visited on the path towards a marked state. Synthesis algorithms are presented to construct modal and multimodal nonblocking supervisors. The novel nonblocking variants are illustrated with three intuitive examples, inspired by real synthesis problems encountered while applying supervisory control synthesis to safety-critical water infrastructures. A comparison is made between the novel nonblocking variants and established nonblocking variants to show that they are distinct. Additionally, where possible, conditions are formulated under which one variant implies the other.  \nI. INTRODUCTION  \nSupervisory control synthesis is a method for the calculation of a correct-by-construction supervisor based on a plant model [1] . It relies on nonblocking to show liveness of the supervised system. A supervised system is called nonblocking if it is always able to reach a marked state, often indicating the ‘rest state’ or ‘safe state’ of a system [2] . However, nonblocking relies on the assumption that the specific path that is used to reach a marked state does not matter. For plants that deal with fault behavior, are reconfigurable, or address multiple control goals, this assumption does not hold.  \nOver the years, several nonblocking variants have been introduced to obtain more suitable nonblocking properties for certain applications. For example, generalized nonblocking [3] defines a subset of states from which a marked state must be reachable. This is relevant for hierarchical supervisory control. Nonblocking with progressive events [4](henceforth progressive nonblocking) restricts the set of events that may be used to reach a marked state. This is particularly useful when the plant contains rare or undesirable behavior. Multitasking nonblocking [5] introduces colored marked states, capturing that multiple rest states must always remain reachable. This is a suitable nonblocking variant for multitasking systems. Quantitative nonblocking [6] places a restriction on the number of events that may be taken to reach a marked state. This is suitable when such a metric must be limited, for example for workpiece-processing plants.  \n*This work was supported as part of STORM SAFE, an Interreg North Sea project co-funded by the European Union.  \n1Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, the Netherlands. {m .minkenberg, m.a.reniers, m.a.goorden, [j.m.v.d.mortel](j.m.v.d.mortel}@tue.nl)[}](j.m.v.d.mortel}@tue.nl)[@tue.nl](j.m.v.d.mortel}@tue.nl)  \n2Department of Computer Science, Vrije Universiteit Amsterdam, Amsterdam, [the Netherlands.](the Netherlands. w.j.fokkink@vu.nl)[ w.j.fokkink@vu.nl](the Netherlands. w.j.fokkink@vu.nl)  \nIn ongoing research [7], supervisory control synthesis is being applied to safety-critical water infrastructures. These systems address various—and often conflicting—control goals, like flood protection, water discharge, fish migration, and ship traffic. Each goal typically has its own set of marked states. The active goals are reconfigured based on environmental parameters such as water levels, the time of year, and the presence of ships.  \nFor these systems, it makes sense to synthesize a supervisor that is alw","cbCailKzKp6ThM86","https://ap.wps.com/l/cbCailKzKp6ThM86","pdf",352205,1,"English","en",105,"# Introduction\n## Why standard nonblocking is insufficient\n## Existing nonblocking variants\n## Motivation from safety-critical water infrastructures\n## Modal and multimodal nonblocking\n## Synthesis algorithms and complexity","[{\"question\":\"Why does standard nonblocking become insufficient for systems with faults or multiple goals?\",\"answer\":\"Standard nonblocking assumes the specific path to a marked state does not matter. When fault behavior, reconfiguration, or multiple control goals are present, this assumption fails because reaching marked states may require passing through undesirable or changing conditions.\"},{\"question\":\"What do modal and multimodal nonblocking require in terms of system paths?\",\"answer\":\"They impose restrictions on the states visited on the path toward a marked state. Modal nonblocking specifies one state set, while multimodal nonblocking generalizes this to one or more state sets that must not be left en route to marked states.\"},{\"question\":\"How are the proposed supervisors constructed and what does the complexity depend on?\",\"answer\":\"The paper presents synthesis algorithms to construct modal and multimodal nonblocking supervisors. The computational complexity scales linearly with the number of defined state sets.\"}]",1784189872,20,{"code":4,"msg":29,"data":30},"ok",{"site_id":23,"language":22,"slug":31,"title":13,"keywords":32,"description":14,"schema_data":33,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":26},"multimodal-nonblocking-supervisory-control-synthesis","",{"@graph":34,"@context":84},[35,52,67],{"@type":36,"itemListElement":37},"BreadcrumbList",[38,42,46,49],{"item":39,"name":40,"@type":41,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":43,"name":44,"@type":41,"position":45},"https://docshare.wps.com/document/","Document",2,{"item":47,"name":12,"@type":41,"position":48},"https://docshare.wps.com/document/research-report/",3,{"item":50,"name":13,"@type":41,"position":51},"https://docshare.wps.com/document/multimodal-nonblocking-supervisory-control-synthesis/83706/",4,{"url":50,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":22,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":39,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":20},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"Why does standard nonblocking become insufficient for systems with faults or multiple goals?","Question",{"text":74,"@type":75},"Standard nonblocking assumes the specific path to a marked state does not matter. When fault behavior, reconfiguration, or multiple control goals are present, this assumption fails because reaching marked states may require passing through undesirable or changing conditions.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What do modal and multimodal nonblocking require in terms of system paths?",{"text":79,"@type":75},"They impose restrictions on the states visited on the path toward a marked state. Modal nonblocking specifies one state set, while multimodal nonblocking generalizes this to one or more state sets that must not be left en route to marked states.",{"name":81,"@type":72,"acceptedAnswer":82},"How are the proposed supervisors constructed and what does the complexity depend on?",{"text":83,"@type":75},"The paper presents synthesis algorithms to construct modal and multimodal nonblocking supervisors. 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