{"613960":{"#nid":"613960","#data":{"type":"event","title":"PhD Defense by Kaivalya Bakshi","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003EPh.D. Thesis Announcement\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EBy\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EKaivalya Bakshi\u003C\/p\u003E\r\n\r\n\u003Cp\u003E(Advisor: Prof. Evangelos Theodorou)\u003C\/p\u003E\r\n\r\n\u003Cp\u003E2:00 PM, Thursday 12 Nov 2018\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cem\u003EKlaus Building, Conference room 2108\u003C\/em\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ELARGE SCALE STOCHASTIC CONTROL: ALGORITHMS, OPTIMALITY\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EAND STABILITY\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ESummary: \u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Optimal control of large-scale multi-agent networked systems which describe social\u003C\/p\u003E\r\n\r\n\u003Cp\u003Enetworks, macro-economies, traffic and robot swarms is a topic of interest in engineer-\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eing, biophysics and economics. A central issue is constructing scalable control-theoretic\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eframeworks when the number of agents is infinite.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; In this work, we exploit PDE representations of the optimality laws in order to provide\u003C\/p\u003E\r\n\r\n\u003Cp\u003Ea tractable approach to ensemble (open loop) and closed loop control of such systems. A\u003C\/p\u003E\r\n\r\n\u003Cp\u003Ecentralized open loop optimal control problem of an ensemble of agents driven by jump\u003C\/p\u003E\r\n\r\n\u003Cp\u003Enoise is solved by a sampling algorithm based on the infinite dimensional minimum prin-\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eciple to solve it. The relationship between the infinite dimensional minimum principle and\u003C\/p\u003E\r\n\r\n\u003Cp\u003Edynamic programming principles is established for this problem.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; Mean field game (MFG) models expressed as PDE systems are used to describe emer-\u003C\/p\u003E\r\n\r\n\u003Cp\u003Egent phenomenon in decentralized feedback optimal control models of a continuum of\u003C\/p\u003E\r\n\r\n\u003Cp\u003Einteracting agents with stochastic dynamics. However, stability analysis of MFG models\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eremains a challenging problem, since they exhibit non-unique solutions in the absence of a\u003C\/p\u003E\r\n\r\n\u003Cp\u003Emonotonicity assumption on the cost function. This thesis addresses the key issue of sta-\u003C\/p\u003E\r\n\r\n\u003Cp\u003Ebility and control design in MFGs. Specifically, we present detailed results on a models for\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eflocking and population evolution.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp; An interesting connection between MFG models and the imaginary-time Schr\u0026ouml;dinger\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eequation is used to obtain explicit stability constraints on the control design in the case\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eof non-interacting agents. Compared to prior works on this topic which apply only to\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eagents obeying very simple integrator dynamics, we treat nonlinear agent dynamics and\u003C\/p\u003E\r\n\r\n\u003Cp\u003Ealso provide analytical design constraints.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ECommittee Members:\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003EProf. Evangelos Theodorou (Advisor)\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Piyush Grover (Principal Research Scientist, MERL)\u003C\/p\u003E\r\n\r\n\u003Cp\u003EProf. Eric Feron (AE)\u003C\/p\u003E\r\n\r\n\u003Cp\u003EProf. Yongxin Chen (AE)\u003C\/p\u003E\r\n\r\n\u003Cp\u003EProf. Ionel Popescu (MATH)\u003C\/p\u003E\r\n\r\n\u003Cp\u003EProf. Paul Bogdan (EE, USC Viterbi)\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"LARGE SCALE STOCHASTIC CONTROL: ALGORITHMS, OPTIMALITY AND STABILITY "}],"uid":"27707","created_gmt":"2018-11-07 17:58:53","changed_gmt":"2018-11-07 17:58:53","author":"Tatianna Richardson","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2018-11-12T14:00:00-05:00","event_time_end":"2018-11-12T16:00:00-05:00","event_time_end_last":"2018-11-12T16:00:00-05:00","gmt_time_start":"2018-11-12 19:00:00","gmt_time_end":"2018-11-12 21:00:00","gmt_time_end_last":"2018-11-12 21:00:00","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":"174045","name":"Graduate students"},{"id":"78751","name":"Undergraduate students"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}