[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82615-en":3,"doc-seo-82615-105":29,"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":13,"seo_description":14,"update_tm":27,"read_time":28},82615,8796095360427,"Lucas Martin","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","Context-Triggered Robust MPC for Temporal Logic Specifications","Synthesis of robust feedback controllers is addressed for discrete-time linear systems under additive bounded disturbances, targeting satisfaction of context-dependent linear temporal logic specifications. Context-triggered temporal-logic synthesis is leveraged through reduction to context-dependent reach-avoid-stay (cRAS) objectives, then certificate-based almost-sure conditions for reach-avoid-stay are developed. A switching architecture combines robust model predictive control with a local invariant controller: MPC provides reachability certificates, while robust constraints ensure avoidance and the local controller enforces staying. Convex duality yields deterministic convex programs. Demonstrations on robot navigation show substantially larger feasible sets than Lyapunov-based approaches, supporting dynamic environments and online task reconfiguration.","Context-Triggered Robust MPC for Temporal Logic Specifications  \nArash Bahari Kordabada,∗ , Satya Prakash Nayakb , Sadegh Soudjania,c and Anne-Kathrin Schmucka  \na Max Planck Institute for Software Systems (MPI-SWS), Kaiserslautern, 67663, Germany b Institute of Science and Technology Austria (ISTA), Klosterneuburg, 3400, Austria c University of Birmingham, Birmingham, B15 2TT, United Kingdom  \narXiv :2607 .01515v1 [ ee ss . SY] 1 Jul 2026  \nARTICLE INFO  \nKeywords:  \nrobust control  \nlinear temporal logic context-triggered control reach-avoid-stay specifications robust model predictive control convex duality  \nAB STRACT  \nWe consider the problem of synthesizing robust feedback controllers for discrete-time linear systems that ensure the satisfaction of context-dependent linear temporal logic specifications in the presence of additive bounded disturbances. Building on existing results that reduce context-triggered temporal logic synthesis to the realization of context-dependent reach-avoid-stay (cRAS) objectives, we focus on the corresponding low-level control synthesis problem. We first employ certificate-based conditions for the almost-sure satisfaction of RAS specifications. Based on these conditions, we propose a switching control architecture that combines robust model predictive control (MPC) with a local invariant controller, and show that the resulting MPC value function serves as a reachability certificate while avoidance is enforced through robust constraints and the stay is enforced via the local controller. To obtain computationally tractable formulations for the resulting robust optimizations, we employ convex duality to reformulate the robust constraints into equivalent deterministic optimization problems, yielding convex quadratic and second-order cone programs for relevant geometric settings. The proposed framework is demonstrated on a robot navigation problem with context-triggered logical switches in both static and moving environments. The results show significantly larger feasible sets than Lyapunov-based approaches, while naturally accommodating dynamic environments and online task reconfiguration.  \n1. Introduction  \nRobust controller synthesis for uncertain systems with continuous state and control spaces under temporal logic specifications is a challenging problem at the intersection of control theory and formal methods [1, 2] . The difficulty stems from the need to simultaneously handle continuous dynamics, state and input constraints, uncertainty, and highlevel logical requirements that describe complex tasks beyond classical objectives such as stabilization, tracking, or regulation [3, 4]. The problem becomes even more challenging when the specification depends on the context, and the context itself may change over time due to external events or because of the evolution of the controlled system [5, 6] . In such settings, the controller must not only satisfy a temporal logic objective, but also react online to context-triggered changes in the active task.  \nTo illustrate this setting, we consider a robot navigating in two rooms connected by a sliding door, illustrated in Figure 1. The robot is required to move among target regions according to a mode requested by the environment. At the same time, it must avoid walls and, depending on the current configuration, also avoid the door region when the door is closed. The logical context changes over time and affects the active objective of the robot. Moreover, the state of the door, namely whether it is open or closed, changes when the robot enters a particular region. Hence, the motion of the robot and  \n∗Corresponding author  \n [arashbk@mpi-sws.org](arashbk@mpi-sws.org) (A.B. Kordabad); [satya.nayak@ist.ac.at](satya.nayak@ist.ac.at)[ ](satya.nayak@ist.ac.at)(S.P. Nayak); [sadegh@mpi-sws.org](sadegh@mpi-sws.org) (S. Soudjani); [akschmuck@mpi-sws.org](akschmuck@mpi-sws.org) (A. Schmuck)  \nORCID(s): 0000-0001-8931-5372 (A.B. Kordabad); 0000-0002-4407-8681 (","cbCait7PX17TkC99","https://ap.wps.com/l/cbCait7PX17TkC99","pdf",969609,1,14,"English","en",105,"# Introduction\n## Context and motivation for context-triggered specifications\n## Reduction to context-dependent reach-avoid-stay objectives\n## Low-level robust MPC synthesis approach","[{\"question\":\"What problem does the paper solve in controller synthesis?\",\"answer\":\"It synthesizes robust feedback controllers for discrete-time linear systems so that context-dependent linear temporal logic specifications are satisfied despite additive bounded disturbances.\"},{\"question\":\"How are temporal-logic objectives handled in the proposed framework?\",\"answer\":\"The work uses known reductions that translate context-triggered temporal logic synthesis into context-dependent reach-avoid-stay (cRAS) objectives, then focuses on low-level control synthesis for these objectives.\"},{\"question\":\"How does the switching control architecture work?\",\"answer\":\"It combines robust MPC with a local invariant controller: the MPC value function acts as a reachability certificate, avoidance is enforced via robust constraints, and the stay behavior is ensured by the local invariant controller.\"}]",1784181829,35,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":27},"context-triggered-robust-mpc-for-temporal-logic-specifications","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/context-triggered-robust-mpc-for-temporal-logic-specifications/82615/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",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},"What problem does the paper solve in controller synthesis?","Question",{"text":75,"@type":76},"It synthesizes robust feedback controllers for discrete-time linear systems so that context-dependent linear temporal logic specifications are satisfied despite additive bounded disturbances.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How are temporal-logic objectives handled in the proposed framework?",{"text":80,"@type":76},"The work uses known reductions that translate context-triggered temporal logic synthesis into context-dependent reach-avoid-stay (cRAS) objectives, then focuses on low-level control synthesis for these objectives.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the switching control architecture work?",{"text":84,"@type":76},"It combines robust MPC with a local invariant controller: the MPC value function acts as a reachability certificate, avoidance is enforced via robust constraints, and the stay behavior is ensured by the local invariant 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