[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82588-en":3,"doc-seo-82588-105":29,"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":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82588,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","TERA: A Unified Taylor Model Enabled Reachability Analysis Framework","Reachability analysis for safety-critical systems focuses on computing rigorous enclosures of all possible state trajectories over a finite horizon, enabling bounded-time safety verification. Taylor Model methods reduce the wrapping effect that makes conventional set representations overly conservative. TERA is a Python-native, free and open-source framework providing a single symbolic-numeric workflow for continuous, hybrid, and stochastic systems, leveraging SageMath capabilities and validated Taylor Model integration schemes with probabilistic guarantees.","TERA: A Unified Taylor Model Enabled Reachability Analysis Framework  \nSalma Iraky∗ and Andrew Sogokon  \nJul 2026  \nAbstract—Reachability analysis of safety-critical systems requires computing rigorous enclosures of all possible state trajectories. Taylor Model (TM)-based methods have proved effective at mitigating the so-called wrapping effect which leads to overly conservative enclosures of reachable sets. However, existing tools are often hard to extend or focused on narrow system classes (e.g. deterministic systems modelled by ODEs, or hybrid systems). We develop TERA: a Python-native framework for TM-based reachability analysis of continuous, hybrid and stochastic systems within a single symbolic-numeric workflow. TERA is free and opensource, enabling rapid prototyping of reachability analysis techniques with rigorous enclosures. At present, our im-  \narXiv :2607 .01189v1  \nIn a system, e.g. given by x˙ = f (x, u, w), where u denotes a control input and w represents bounded disturbances or uncertainty, a feedback law u = κ (x) induces the closed-loop dynamics x˙ = f (x,κ(x), w) . If the system is safety-critical, it is important to establish whether, e.g., all closed-loop trajectories remain within prescribed bounds (and perhaps verify other safety requirements) . Given a set of initial states X0 and a finite time horizon T > 0, the forward reachability problem is to compute sets {R (t)} t∈[0,T] that contain all closed-loop trajectories originating in X0 (with probabilistic guarantees when under stochastic disturbances) . In practice, computing these so-called flowpipes exactly is only possible for some special classes of linear systems, so one is forced to resort to set-based over-approximations of system trajectories over a finite time horizon; if these provide a rigorous enclosure of the reachable set, one can perform (bounded time) safety verification of the closed loop system.  \nCommon set representations for over-approximating flowpipes include (hyper-)intervals and zonotopes; however, reachability analysis based on these representations suffers from the wrapping effect, where accumulated overapproximations rapidly yield very conservative enclosures  \n∗ Corresponding author ([s.iraky@lancaster.ac.uk](s.iraky@lancaster.ac.uk)) . Both authors are with the School of Computing and Communications, Lancaster University, UK. This work was presented at CONTROL 2026: 15th United Kingdom Automatic Control Council (UKACC) International Conference on Control, 23–25 June 2026 .  \nof the reachable set. Taylor Models (TMs; see [1]) offer an alternative set representation that mitigates this phenomenon by preserving functional dependencies through high-order polynomial representations with rigorous remainder bounds, making them especially well-suited for reachability analysis of nonlinear systems. Numerous tools have been developed for reachability analysis using TMs, such as Flow∗ (in C++), CORA (in MATLAB) and JuliaReach (in Julia) . However, these are either less suited to rapid prototyping, require a proprietary environment to run, or do not (currently) handle stochastic systems.  \nTERA is a fully Python-native free and open-source reachability framework designed to conveniently integrate with the scientific Python ecosystem and draws on the functionality offered by the SageMath computer algebra system.1 Currently, TERA is capable of computing rigorous TM-based enclosures of reachable sets for continuous systems described by non-linear ODEs (this includes systems with non-polynomial nonlinearities, including transcendental functions such as sin and cos, appearing in the right-hand side), hybrid dynamical systems that combine discrete and continuous behaviour and in which the dynamics of continuous modes may be governed by non-linear ODEs, and stochastic systems (currently support only extends to continuous-time systems) .  \nII. METHODOLOGY  \nWithin TERA, reachable sets are represented using TMs (see [1], [2]) of the form P (x0 ","cbCainuVOqMRWwsL","https://ap.wps.com/l/cbCainuVOqMRWwsL","pdf",1051869,1,2,"English","en",105,"# Methodology\n## Taylor Model representation and validated propagation\n## Hybrid and stochastic extensions\n# Illustrative Examples","[{\"question\":\"What problem does TERA address in reachability analysis?\",\"answer\":\"TERA targets the need to compute rigorous enclosures of reachable sets for safety-critical systems over a time horizon, avoiding overly conservative results.\"},{\"question\":\"How does TERA mitigate the wrapping effect?\",\"answer\":\"TERA uses Taylor Models to preserve functional dependencies via high-order polynomial approximations together with rigorous remainder bounds.\"},{\"question\":\"Which system types can TERA analyze and how does it handle stochasticity?\",\"answer\":\"TERA supports continuous nonlinear ODEs, hybrid dynamical systems, and stochastic systems by combining deterministic TM flowpipes with probabilistic deviation bounds using δ-probabilistic reachable set (δ-PRS) semantics.\"}]",1784181674,5,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"tera-a-unified-taylor-model-enabled-reachability-analysis-framework","",{"@graph":35,"@context":84},[36,52,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,46,49],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":21},"https://docshare.wps.com/document/","Document",{"item":47,"name":12,"@type":42,"position":48},"https://docshare.wps.com/document/research-report/",3,{"item":50,"name":13,"@type":42,"position":51},"https://docshare.wps.com/document/tera-a-unified-taylor-model-enabled-reachability-analysis-framework/82588/",4,{"url":50,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":23,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":40,"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},"What problem does TERA address in reachability analysis?","Question",{"text":74,"@type":75},"TERA targets the need to compute rigorous enclosures of reachable sets for safety-critical systems over a time horizon, avoiding overly conservative results.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does TERA mitigate the wrapping effect?",{"text":79,"@type":75},"TERA uses Taylor Models to preserve functional dependencies via high-order polynomial approximations together with rigorous remainder bounds.",{"name":81,"@type":72,"acceptedAnswer":82},"Which system types can TERA analyze and how does it handle stochasticity?",{"text":83,"@type":75},"TERA supports continuous nonlinear ODEs, hybrid dynamical systems, and stochastic systems by combining deterministic TM flowpipes with probabilistic deviation bounds using δ-probabilistic reachable set (δ-PRS) 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