{"id":4178,"date":"2024-09-29T21:23:36","date_gmt":"2024-09-30T01:23:36","guid":{"rendered":"https:\/\/cecas.clemson.edu\/ugvaidya\/?page_id=4178"},"modified":"2024-10-09T18:28:47","modified_gmt":"2024-10-09T22:28:47","slug":"cyber-physical-systems","status":"publish","type":"page","link":"https:\/\/cecas.clemson.edu\/ugvaidya\/cyber-physical-systems\/","title":{"rendered":"Cyber-Physical Systems"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"4178\" class=\"elementor elementor-4178\">\n\t\t\t\t<div class=\"elementor-element elementor-element-777fccf e-con-full e-flex e-con e-parent\" data-id=\"777fccf\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-72f0d84 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-heading\" data-id=\"72f0d84\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Cyber-Physical Systems<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-efb5b1a e-flex e-con-boxed e-con e-parent\" data-id=\"efb5b1a\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-69a953b e-con-full e-flex e-con e-child\" data-id=\"69a953b\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-e6b53cf elementor-arrows-position-inside elementor-pagination-position-outside exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-image-carousel\" data-id=\"e6b53cf\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;slides_to_show&quot;:&quot;1&quot;,&quot;navigation&quot;:&quot;both&quot;,&quot;autoplay&quot;:&quot;yes&quot;,&quot;pause_on_hover&quot;:&quot;yes&quot;,&quot;pause_on_interaction&quot;:&quot;yes&quot;,&quot;autoplay_speed&quot;:5000,&quot;infinite&quot;:&quot;yes&quot;,&quot;effect&quot;:&quot;slide&quot;,&quot;speed&quot;:500}\" data-widget_type=\"image-carousel.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-image-carousel-wrapper swiper\" role=\"region\" aria-roledescription=\"carousel\" aria-label=\"Image Carousel\" dir=\"ltr\">\n\t\t\t<div class=\"elementor-image-carousel swiper-wrapper\" aria-live=\"off\">\n\t\t\t\t\t\t\t\t<div class=\"swiper-slide\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"1 of 3\"><figure class=\"swiper-slide-inner\"><img decoding=\"async\" class=\"swiper-slide-image\" src=\"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-content\/uploads\/2024\/10\/RESEARCH_FL_synchronization_region.png\" alt=\"Synchronization-region\" \/><\/figure><\/div><div class=\"swiper-slide\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"2 of 3\"><figure class=\"swiper-slide-inner\"><img decoding=\"async\" class=\"swiper-slide-image\" src=\"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-content\/uploads\/2024\/10\/RESEARCH_FL_non_erasure_porbability.png\" alt=\"Non-erasure-probability\" \/><\/figure><\/div><div class=\"swiper-slide\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"3 of 3\"><figure class=\"swiper-slide-inner\"><img decoding=\"async\" class=\"swiper-slide-image\" src=\"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-content\/uploads\/2024\/10\/RESEARCH_FL_non_erasure_porbability_2.png\" alt=\"Non-erasure-probability-2\" \/><\/figure><\/div>\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"elementor-swiper-button elementor-swiper-button-prev\" role=\"button\" tabindex=\"0\">\n\t\t\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-eicon-chevron-left\" viewBox=\"0 0 1000 1000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M646 125C629 125 613 133 604 142L308 442C296 454 292 471 292 487 292 504 296 521 308 533L604 854C617 867 629 875 646 875 663 875 679 871 692 858 704 846 713 829 713 812 713 796 708 779 692 767L438 487 692 225C700 217 708 204 708 187 708 171 704 154 692 142 675 129 663 125 646 125Z\"><\/path><\/svg>\t\t\t\t\t<\/div>\n\t\t\t\t\t<div class=\"elementor-swiper-button elementor-swiper-button-next\" role=\"button\" tabindex=\"0\">\n\t\t\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-eicon-chevron-right\" viewBox=\"0 0 1000 1000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M696 533C708 521 713 504 713 487 713 471 708 454 696 446L400 146C388 133 375 125 354 125 338 125 325 129 313 142 300 154 292 171 292 187 292 204 296 221 308 233L563 492 304 771C292 783 288 800 288 817 288 833 296 850 308 863 321 871 338 875 354 875 371 875 388 867 400 854L696 533Z\"><\/path><\/svg>\t\t\t\t\t<\/div>\n\t\t\t\t\n\t\t\t\t\t\t\t\t\t<div class=\"swiper-pagination\"><\/div>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-5a703c9 e-con-full e-flex e-con e-child\" data-id=\"5a703c9\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-de18a9b e-con-full e-flex e-con e-child\" data-id=\"de18a9b\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3e696c0 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-heading\" data-id=\"3e696c0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Fundamental limitations for control of dynamical systems over networks<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-448e153 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"448e153\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"margin: 0in; text-align: justify;\"><span style=\"color: #0e101a;\">We have discovered a systematic framework for analyzing and designing network-controlled systems in the presence of uncertainty. This includes discovering fundamental limitation results for estimating and stabilizing nonlinear systems over uncertain communication channels. This research mainly connected fundamental limitations for nonlinear stabilization and estimation with the measure-theoretic entropy of steady-state invariant measure of the open loop system. The positive Lyapunov exponents capture the measure-theoretic entropy for a system with non-equilibrium open loop dynamics such as chaotic attractors or unstable limit cycles. This was the first systematic result to highlight the critical role of non-equilibrium dynamics in nonlinear stabilization and estimation over uncertain channels, and it differs from the existing results based on equilibrium dynamics of local linearization of a nonlinear system.\u00a0<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-caa219d e-con-full e-flex e-con e-child\" data-id=\"caa219d\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d444374 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"d444374\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"margin: 0in; text-align: justify;\"><span style=\"color: #0e101a;\">Our results generalize existing results known in the case of linear systems where Lyapunov exponents emerge as a natural generalization of eigenvalues from linear systems to nonlinear systems.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-9f3aa23 e-flex e-con-boxed e-con e-parent\" data-id=\"9f3aa23\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-7bb6f37 e-con-full e-flex e-con e-child\" data-id=\"7bb6f37\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-22c9874 elementor-arrows-position-inside elementor-pagination-position-outside exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-image-carousel\" data-id=\"22c9874\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;slides_to_show&quot;:&quot;1&quot;,&quot;navigation&quot;:&quot;both&quot;,&quot;autoplay&quot;:&quot;yes&quot;,&quot;pause_on_hover&quot;:&quot;yes&quot;,&quot;pause_on_interaction&quot;:&quot;yes&quot;,&quot;autoplay_speed&quot;:5000,&quot;infinite&quot;:&quot;yes&quot;,&quot;effect&quot;:&quot;slide&quot;,&quot;speed&quot;:500}\" data-widget_type=\"image-carousel.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-image-carousel-wrapper swiper\" role=\"region\" aria-roledescription=\"carousel\" aria-label=\"Image Carousel\" dir=\"ltr\">\n\t\t\t<div class=\"elementor-image-carousel swiper-wrapper\" aria-live=\"off\">\n\t\t\t\t\t\t\t\t<div class=\"swiper-slide\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"1 of 5\"><figure class=\"swiper-slide-inner\"><img decoding=\"async\" class=\"swiper-slide-image\" src=\"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-content\/uploads\/2024\/10\/RESEARCH_COUN_phase_space_partition.png\" alt=\"RESEARCH_COUN_phase_space_partition\" \/><\/figure><\/div><div class=\"swiper-slide\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"2 of 5\"><figure class=\"swiper-slide-inner\"><img decoding=\"async\" class=\"swiper-slide-image\" src=\"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-content\/uploads\/2024\/10\/RESEARCH_COUN_trajectories_fixed_time_dyn_sys-1.png\" alt=\"RESEARCH_COUN_trajectories_fixed_time_dyn_sys\" \/><\/figure><\/div><div class=\"swiper-slide\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"3 of 5\"><figure class=\"swiper-slide-inner\"><img decoding=\"async\" class=\"swiper-slide-image\" src=\"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-content\/uploads\/2024\/10\/RESEARCH_COUN_uncertainty_interconnection.png\" alt=\"RESEARCH_COUN_uncertainty_interconnection\" \/><\/figure><\/div><div class=\"swiper-slide\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"4 of 5\"><figure class=\"swiper-slide-inner\"><img decoding=\"async\" class=\"swiper-slide-image\" src=\"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-content\/uploads\/2024\/10\/RESEARCH_COUN_uncertainty_feedback_loop.png\" alt=\"RESEARCH_COUN_uncertainty_feedback_loop\" \/><\/figure><\/div><div class=\"swiper-slide\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"5 of 5\"><figure class=\"swiper-slide-inner\"><img decoding=\"async\" class=\"swiper-slide-image\" src=\"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-content\/uploads\/2024\/10\/RESEARCH_COUN_uncertainty_io_channel.png\" alt=\"RESEARCH_COUN_uncertainty_io_channel\" \/><\/figure><\/div>\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t\t<div class=\"elementor-swiper-button elementor-swiper-button-prev\" role=\"button\" tabindex=\"0\">\n\t\t\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-eicon-chevron-left\" viewBox=\"0 0 1000 1000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M646 125C629 125 613 133 604 142L308 442C296 454 292 471 292 487 292 504 296 521 308 533L604 854C617 867 629 875 646 875 663 875 679 871 692 858 704 846 713 829 713 812 713 796 708 779 692 767L438 487 692 225C700 217 708 204 708 187 708 171 704 154 692 142 675 129 663 125 646 125Z\"><\/path><\/svg>\t\t\t\t\t<\/div>\n\t\t\t\t\t<div class=\"elementor-swiper-button elementor-swiper-button-next\" role=\"button\" tabindex=\"0\">\n\t\t\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-eicon-chevron-right\" viewBox=\"0 0 1000 1000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M696 533C708 521 713 504 713 487 713 471 708 454 696 446L400 146C388 133 375 125 354 125 338 125 325 129 313 142 300 154 292 171 292 187 292 204 296 221 308 233L563 492 304 771C292 783 288 800 288 817 288 833 296 850 308 863 321 871 338 875 354 875 371 875 388 867 400 854L696 533Z\"><\/path><\/svg>\t\t\t\t\t<\/div>\n\t\t\t\t\n\t\t\t\t\t\t\t\t\t<div class=\"swiper-pagination\"><\/div>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-39b393e e-con-full e-flex e-con e-child\" data-id=\"39b393e\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t<div class=\"elementor-element elementor-element-d9b56aa e-con-full e-flex e-con e-child\" data-id=\"d9b56aa\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-af16c09 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-heading\" data-id=\"af16c09\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Control and optimization over uncertainty networks<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3385468 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"3385468\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"margin: 0in; text-align: justify;\"><span style=\"color: #0e101a;\">The main contribution of this work is to understand fundamental tradeoffs that arise in the control of linear and nonlinear dynamical systems over networks in the presence of uncertainty. For systems with linear dynamics, we have provided a systematic convex optimization-based approach for synthesizing control robust to stochastic network communication uncertainty. For systems with nonlinear dynamics, our results offer tradeoffs that arise between the internal dynamics at the individual nodes of the network, network topology, and the communication uncertainty for robust synchronization over the network. Network dynamical systems are also of interest for solving optimization problems in a distributed manner. The dynamical system viewpoint is employed to solve an optimization problem for distributed optimization over the network.<\/span><\/p>\n<p style=\"margin: 0in; text-align: justify;\">\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-e616aaf e-con-full e-flex e-con e-child\" data-id=\"e616aaf\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-6f58457 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"6f58457\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"margin: 0in; text-align: justify;\"><span style=\"color: #0e101a;\">Our main contributions to this topic include providing a dynamical systems approach for solving robust optimization problems and finite-time convergence proof for solving time-varying optimization problems.\u00a0\u00a0<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-6cbb4dc e-flex e-con-boxed e-con e-parent\" data-id=\"6cbb4dc\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-717f34e exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-heading\" data-id=\"717f34e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Selected publications<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-e52eb3f e-flex e-con-boxed e-con e-parent\" data-id=\"e52eb3f\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-c887107 exad-sticky-section-no exad-glass-effect-no elementor-widget elementor-widget-text-editor\" data-id=\"c887107\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ul>\n<li>A. Diwadkar and U. Vaidya, Limitations, and tradeoffs in synchronizing large-scale networks with uncertain links, Scientific Reports, Nature Publication Group, 2016.<\/li>\n<li>S. Pushpak, A. Diwadkar, and U. Vaidya, Mean Square-Based Stochastic Stability Analysis of Continuous-time Linear Network System, IEEE Transactions of Automatic Control, Volume: 63, Issue: 12, Dec. 2018.<\/li>\n<li>A. Diwadkar and U. Vaidya, Limitations for Nonlinear observation over erasure channels, IEEE Transactions on Automatic Control, Vol. 58, Issue 2, pp-454-459, 2013.<\/li>\n<li>U. Vaidya and N. Elia, Limitations for nonlinear stabilization over erasure channel: Scalar Case, Systems and Control Letters, Volume 61, Issue 9, Pages 959-966, 2012.<\/li>\n<li>A. Diwadkar and U. Vaidya, Control of LTV system with intermittent communication, International Journal of Robust and Nonlinear Control, 2013.<\/li>\n<li>A. Diwadkar and U. Vaidya, Synchronization in large scale nonlinear network with uncertain links, Automatica, Volume 100, February 2019, Pages 194-199.<\/li>\n<li>P. G. Mehta, U. Vaidya and A. Banaszuk, Markov chains, entropy and fundamental limitations in nonlinear stabilization, IEEE Transactions on Automatic Control, Vol 53, pp. 784-791, 2008.<\/li>\n<\/ul>\n<ul>\n<li>Raveendran, A. Mahindrakar, U. Vaidya, <a href=\"https:\/\/scholar.google.com\/citations?view_op=view_citation&amp;hl=en&amp;user=bzUVrKIAAAAJ&amp;cstart=20&amp;pagesize=80&amp;sortby=pubdate&amp;citation_for_view=bzUVrKIAAAAJ:_FM0Bhl9EiAC\">Dynamical System Approach for Time-Varying Constrained Convex Optimization Problems<\/a>, IEEE Transactions on Automatic Control, 2023.<\/li>\n<\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Cyber-Physical Systems Fundamental limitations for control of dynamical systems over networks We have discovered a systematic framework for analyzing and designing network-controlled systems in the presence of uncertainty. This includes discovering fundamental limitation results for estimating and stabilizing nonlinear systems over uncertain communication channels. This research mainly connected fundamental limitations for nonlinear stabilization and estimation &hellip; <a href=\"https:\/\/cecas.clemson.edu\/ugvaidya\/cyber-physical-systems\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Cyber-Physical Systems<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":11,"featured_media":950,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-4178","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-json\/wp\/v2\/pages\/4178","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-json\/wp\/v2\/comments?post=4178"}],"version-history":[{"count":23,"href":"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-json\/wp\/v2\/pages\/4178\/revisions"}],"predecessor-version":[{"id":4476,"href":"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-json\/wp\/v2\/pages\/4178\/revisions\/4476"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-json\/wp\/v2\/media\/950"}],"wp:attachment":[{"href":"https:\/\/cecas.clemson.edu\/ugvaidya\/wp-json\/wp\/v2\/media?parent=4178"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}