{"659297":{"#nid":"659297","#data":{"type":"event","title":"PhD Defense by Matthew Abate","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ETitle:\u003C\/strong\u003E\u0026nbsp;Efficient Prediction for Dynamical Systems with Applications to Robust Safe Autonomy\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EDate:\u003C\/strong\u003E Tuesday July 19th 2022\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ETime:\u003C\/strong\u003E 1:30 - 3:30 pm ET\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ELocation:\u003C\/strong\u003E TSRB 523\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EMatthew Abate\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003ERobotics PhD Candidate\u003C\/p\u003E\r\n\r\n\u003Cp\u003ESchool of Mechanical Engineering\u003C\/p\u003E\r\n\r\n\u003Cp\u003EGeorgia Institute of Technology\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ECommittee\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Samuel Coogan (Advisor) - Department of Eletrical and Computer Engineering, Georgia Tech\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Eric Feron (Advisor) -\u0026nbsp;Division of\u0026nbsp;Computer, Electrical and Mathematical Sciences and Engineering, KAUST\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr.\u0026nbsp;Matthieu Bloch - Department of Eletrical and Computer Engineering, Georgia Tech\u003Cbr \/\u003E\r\nDr.\u0026nbsp;Panagiotis Tsiotras - Department of Aerospace Engineering, Georgia Tech\u003Cbr \/\u003E\r\nDr. Yorai Wardi - Department of Eletrical and Computer Engineering, Georgia Tech\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ESummary\u0026nbsp;\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003EReachability analysis of control systems plays a crucial role in system verification and controller synthesis. However, many reachability techniques fall short, being only applicable to certain classes of systems or too computationally burdensome for real-time applications. The subject of this thesis is the mixed monotonicity property of dynamical systems which is known to be a general property and which provides a computationally efficient technique for over-approximating reachable sets using hyperrectangles. Specifically, the mixed monotonicity of a dynamical system is tied to the existence of a related decomposition function that separates the system\u0026#39;s vector field into cooperative and competitive state interactions. Reachable sets for the mixed monotone system can then be computed simply using a decomposition function and foundational results from monotone dynamical systems theory.\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EIn this thesis, we establish that all continuous-time dynamical systems bearing a locally Lipschitz continuous vector field are mixed monotone and we provide a construction for the unique tight decomposition function of a dynamical system that attains the tightest possible over-approximations of reachable sets. We then provide a suite of new analysis tools for mixed monotone systems that can be applied to attain, for example, over- and under-approximations of both forward- and backward-time reachable sets, and also robustly forward invariant sets. \u0026nbsp;As a final point, we study conservatism in mixed monotone reachable set approximations, and we provide new tools for reducing conservatism using, for example, the decomposition function of a separate dynamical system, formed via a transformation of the initial system\u0026#39;s vector field. \u0026nbsp;We conclude with a case study of a seven-dimensional spacecraft system and a hardware demonstration of in-the-loop reachability analysis and enforced system safety. \u0026nbsp;Numerous illustrative numerical examples are also provided.\u003C\/p\u003E\r\n","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Efficient Prediction for Dynamical Systems with Applications to Robust Safe Autonomy "}],"uid":"27707","created_gmt":"2022-07-07 15:29:27","changed_gmt":"2022-07-07 15:29:27","author":"Tatianna Richardson","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2022-07-19T14:30:00-04:00","event_time_end":"2022-07-19T16:30:00-04:00","event_time_end_last":"2022-07-19T16:30:00-04:00","gmt_time_start":"2022-07-19 18:30:00","gmt_time_end":"2022-07-19 20:30:00","gmt_time_end_last":"2022-07-19 20:30:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"221981","name":"Graduate Studies"}],"categories":[],"keywords":[{"id":"100811","name":"Phd Defense"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1788","name":"Other\/Miscellaneous"}],"invited_audience":[{"id":"78761","name":"Faculty\/Staff"},{"id":"78771","name":"Public"},{"id":"78751","name":"Undergraduate students"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}