{"id":698,"date":"2021-09-30T20:45:39","date_gmt":"2021-09-30T20:45:39","guid":{"rendered":"https:\/\/elo-x.eu\/?p=698"},"modified":"2024-07-01T09:45:33","modified_gmt":"2024-07-01T09:45:33","slug":"jean-pierre-allamaa-2","status":"publish","type":"post","link":"https:\/\/elo-x.eu\/?p=698","title":{"rendered":"Ramin Abbasi"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"698\" class=\"elementor elementor-698\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-11ad091 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"11ad091\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4645320\" data-id=\"4645320\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9a05e75 elementor-widget elementor-widget-page-title\" data-id=\"9a05e75\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"page-title.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\n\t\t<div class=\"hfe-page-title hfe-page-title-wrapper elementor-widget-heading\">\n\n\t\t\t\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">\n\t\t\t\t\t\t\t\t\n\t\t\t\tRamin Abbasi  \n\t\t\t<\/h2 > \n\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 class=\"elementor-element elementor-element-ca86f70 my-divider elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"ca86f70\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bf21411 elementor-widget elementor-widget-text-editor\" data-id=\"bf21411\" 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><span style=\"color: #352a87;\"><span style=\"font-size: 24px;\">PhD Candidate in Engineering Science at KU Leuven<\/span><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d04271b elementor-widget elementor-widget-text-editor\" data-id=\"d04271b\" 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<div style=\"width: 1120px; margin-bottom: 5px;\" data-id=\"571d48f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\"><p><span style=\"color: #333333;\"><b>Atlas Copco Airpower<\/b><\/span><\/p><\/div>\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<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9fe98ef elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9fe98ef\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-6f52f17\" data-id=\"6f52f17\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2ca30c2 elementor-widget elementor-widget-image\" data-id=\"2ca30c2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"525\" height=\"350\" src=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2021\/09\/Profile-1024x682.png\" class=\"attachment-large size-large wp-image-2767\" alt=\"\" srcset=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2021\/09\/Profile-1024x682.png 1024w, https:\/\/elo-x.eu\/wp-content\/uploads\/2021\/09\/Profile-300x200.png 300w, https:\/\/elo-x.eu\/wp-content\/uploads\/2021\/09\/Profile-768x512.png 768w, https:\/\/elo-x.eu\/wp-content\/uploads\/2021\/09\/Profile-1536x1024.png 1536w, https:\/\/elo-x.eu\/wp-content\/uploads\/2021\/09\/Profile-2048x1365.png 2048w\" sizes=\"(max-width: 767px) 89vw, (max-width: 1000px) 54vw, (max-width: 1071px) 543px, 580px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2e751dc elementor-widget elementor-widget-video\" data-id=\"2e751dc\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/www.youtube.com\\\/watch?v=hcBXppOYzbQ&amp;ab_channel=ProjectELO-X&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-4b93b98\" data-id=\"4b93b98\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8d2ff49 elementor-widget elementor-widget-text-editor\" data-id=\"8d2ff49\" 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>Ramin Abbasi graduated from KU Leuven as a mechanical engineer with a focus on systems and control theory in 2017. His interest in mathematical optimization led him to research in the field of optimal control theory. His thesis focused on an optimal co-design of controllers (Linear Feedback and Model Predictive Controller) and trajectory for systems using nonlinear programming. He is investigating model predictive algorithms for compressor room control at Atlas Copco.<\/p>\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<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6009267 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6009267\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9156808\" data-id=\"9156808\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-67e3347 my-divider elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"67e3347\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bcef1d3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bcef1d3\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-668d476\" data-id=\"668d476\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0d3490a elementor-widget elementor-widget-heading\" data-id=\"0d3490a\" 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\">Project description<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6887ee1 elementor-widget elementor-widget-text-editor\" data-id=\"6887ee1\" 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>The aim of this project is the design and development of tailored model predictive algorithms for compressor room control, executable on constraint CPUs. A compressor room ecosystem consists of compressors, auxiliary devices, buffer vessels, and complex networks of pipes. Every compressor and the auxiliary device (dryers and air separators) that leave the production area are steered via a so-called local controller that adjusts the required pressure, sets alarms, monitors sensors, and controls the different actuators. In many cases, however, customers require air demand that cannot be provided by a single compressor, while air demand can vary throughout time. In both cases, multiple compressors are typically used in parallel. A group of compressors is termed a compressor room and is typically regulated by a central controller whose main purpose is to regulate the compressors in such a way so that they provide pressurized air in the most energy-efficient way and\/or ensure an equal number of running hours for all involved compressors. Lately, new applications are emerging with a strong focus on high-quality pressurized airflows (marginal oil and particle contamination, extremely low humidity, etc.). However, current control algorithms do not have the flexibility to support these new applications. Providing control algorithms that have the flexibility to deal with a wide range of requirements (e.g., flow, pressure, air quality) puts serious constraints on the type of control technologies and requires new control algorithms and control concepts. A significantly improved control algorithm will open new opportunities, and it is expected to provide solutions with a further reduction of the energy consumption in the compressor room. MPC is believed to offer a good answer to the latter challenges.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e0d869a elementor-align-center elementor-widget elementor-widget-button\" data-id=\"e0d869a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/elo-x.eu\/?p=2751\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Read more about this project<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\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<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-853fa6e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"853fa6e\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f04ac7c\" data-id=\"f04ac7c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-db1d977 my-divider elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"db1d977\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-775bb4b elementor-widget elementor-widget-heading\" data-id=\"775bb4b\" 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\">Publications<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3356973 elementor-widget elementor-widget-shortcode\" data-id=\"3356973\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-shortcode\"><div class=\"teachpress_pub_list\"><form name=\"tppublistform\" method=\"get\"><a name=\"tppubs\" id=\"tppubs\"><\/a><div class=\"tp_search_input\"><input type=\"hidden\" name=\"p\" id=\"page_id\" value=\"698\"\/><input name=\"tsr\" id=\"tp_search_input_field\" type=\"search\" placeholder=\"Enter search word\" value=\"\" tabindex=\"1\"\/><div class=\"teachpress_search_button\"><input name=\"tps_button\" class=\"tp_search_button\" type=\"submit\" tabindex=\"10\" value=\"Search\"\/><\/div><\/div><\/form><div class=\"teachpress_publication_list\"><div class=\"tp_publication tp_publication_workingpaper\"><div class=\"tp_pub_number\">1.<\/div><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Abbasi-Esfeden, Ramin;  Nurkanovic, Armin;  Diehl, Moritz;  Patrinos, Panagiotis;  Swevers, Jan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('99','tp_links')\" style=\"cursor:pointer;\">An Efficient Mixed-Integer Formulation and an Iterative Method for Optimal Control of Switched Systems Under Dwell Time Constraints<\/a> <span class=\"tp_pub_type tp_  workingpaper\">Working paper<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_year\">2025<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_99\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('99','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_99\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('99','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_99\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('99','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_99\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@workingpaper{abbasiesfeden2025efficientmixedintegerformulationiterative,<br \/>\r\ntitle = {An Efficient Mixed-Integer Formulation and an Iterative Method for Optimal Control of Switched Systems Under Dwell Time Constraints},<br \/>\r\nauthor = {Ramin Abbasi-Esfeden and Armin Nurkanovic and Moritz Diehl and Panagiotis Patrinos and Jan Swevers},<br \/>\r\nurl = {https:\/\/arxiv.org\/abs\/2501.05158},<br \/>\r\nyear  = {2025},<br \/>\r\ndate = {2025-01-09},<br \/>\r\nabstract = {This paper presents an efficient Mixed-Integer Nonlinear Programming (MINLP) formulation for systems with discrete control inputs under dwell time constraints. By viewing such systems as a switched system, the problem is decomposed into a Sequence Optimization (SO) and a Switching Time Optimization (STO) -- the former providing the sequence of the switched system, and the latter calculating the optimal switching times. By limiting the feasible set of SO to subsequences of a master sequence, this formulation requires a small number of binary variables, independent of the number of time discretization nodes. This enables the proposed formulation to provide solutions efficiently, even for large numbers of time discretization nodes. To provide even faster solutions, an iterative algorithm is introduced to heuristically solve STO and SO. The proposed approaches are then showcased on four different switched systems and results demonstrate the efficiency of the MINLP formulation and the iterative algorithm.},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {workingpaper}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('99','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_99\" style=\"display:none;\"><div class=\"tp_abstract_entry\">This paper presents an efficient Mixed-Integer Nonlinear Programming (MINLP) formulation for systems with discrete control inputs under dwell time constraints. By viewing such systems as a switched system, the problem is decomposed into a Sequence Optimization (SO) and a Switching Time Optimization (STO) -- the former providing the sequence of the switched system, and the latter calculating the optimal switching times. By limiting the feasible set of SO to subsequences of a master sequence, this formulation requires a small number of binary variables, independent of the number of time discretization nodes. This enables the proposed formulation to provide solutions efficiently, even for large numbers of time discretization nodes. To provide even faster solutions, an iterative algorithm is introduced to heuristically solve STO and SO. The proposed approaches are then showcased on four different switched systems and results demonstrate the efficiency of the MINLP formulation and the iterative algorithm.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('99','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_99\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-arxiv\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/arxiv.org\/abs\/2501.05158\" title=\"https:\/\/arxiv.org\/abs\/2501.05158\" target=\"_blank\">https:\/\/arxiv.org\/abs\/2501.05158<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('99','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_workingpaper\"><div class=\"tp_pub_number\">2.<\/div><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Abbasi-Esfeden, Ramin;  Plate, Christoph;  Sager, Sebastian;  Swevers, Jan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('93','tp_links')\" style=\"cursor:pointer;\">Dynamic Programming for Mixed Integer Optimal Control Problems with Dwell Time Constraints<\/a> <span class=\"tp_pub_type tp_  workingpaper\">Working paper<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_year\">2024<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_93\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('93','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_93\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('93','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_93\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('93','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_93\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@workingpaper{AbbasiEsfeden2024,<br \/>\r\ntitle = {Dynamic Programming for Mixed Integer Optimal Control Problems with Dwell Time Constraints},<br \/>\r\nauthor = {Ramin Abbasi-Esfeden and Christoph Plate and Sebastian Sager and Jan Swevers},<br \/>\r\nurl = {http:\/\/dx.doi.org\/10.2139\/ssrn.5043263},<br \/>\r\ndoi = {10.2139\/ssrn.5043263},<br \/>\r\nyear  = {2024},<br \/>\r\ndate = {2024-12-17},<br \/>\r\njournal = {Elsevier BV},<br \/>\r\nabstract = {This paper introduces Dynamic Programming (DP) as a method for solving the Combinatorial Integral Approximation (CIA) problem within the CIA decomposition approach for Mixed-Integer Optimal Control Problems (MIOCPs). Additionally, we incorporate general dwell time constraints into the DP framework. The proposed method is tested on three MIOCPs with a minimum dwell time constraint, and its performance is compared to the usage of the state-of-the-art general purpose solver GuRoBi (MILP) and to the tailored branch-and-bound (BnB) solver from the pycombina package. The results show that DP is more computationally efficient, and its flexible cost-to-go function formulation makes it suitable for handling cases where simple approximations of the relaxed solution are insufficient.},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {workingpaper}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('93','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_93\" style=\"display:none;\"><div class=\"tp_abstract_entry\">This paper introduces Dynamic Programming (DP) as a method for solving the Combinatorial Integral Approximation (CIA) problem within the CIA decomposition approach for Mixed-Integer Optimal Control Problems (MIOCPs). Additionally, we incorporate general dwell time constraints into the DP framework. The proposed method is tested on three MIOCPs with a minimum dwell time constraint, and its performance is compared to the usage of the state-of-the-art general purpose solver GuRoBi (MILP) and to the tailored branch-and-bound (BnB) solver from the pycombina package. The results show that DP is more computationally efficient, and its flexible cost-to-go function formulation makes it suitable for handling cases where simple approximations of the relaxed solution are insufficient.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('93','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_93\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"http:\/\/dx.doi.org\/10.2139\/ssrn.5043263\" title=\"http:\/\/dx.doi.org\/10.2139\/ssrn.5043263\" target=\"_blank\">http:\/\/dx.doi.org\/10.2139\/ssrn.5043263<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.2139\/ssrn.5043263\" title=\"Follow DOI:10.2139\/ssrn.5043263\" target=\"_blank\">doi:10.2139\/ssrn.5043263<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('93','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_number\">3.<\/div><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Roy, Wim Van;  Nurkanovic, Armin;  Abbasi-Esfeden, Ramin;  Frey, Jonathan;  Pozharskiy, Anton;  Swevers, Jan;  Diehl, Moritz<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('48','tp_links')\" style=\"cursor:pointer;\">Continuous Optimization for Control of Finite-State Machines with Cascaded Hysteresis Via Time-Freezing<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">2023 62nd IEEE Conference on Decision and Control (CDC), <\/span><span class=\"tp_pub_additional_pages\">pp. 6261-6266, <\/span><span class=\"tp_pub_additional_publisher\">IEEE, <\/span><span class=\"tp_pub_additional_address\">Singapore, Singapore, <\/span><span class=\"tp_pub_additional_year\">2024<\/span>, <span class=\"tp_pub_additional_isbn\">ISBN: 979-8-3503-0124-3<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_48\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('48','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_48\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('48','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_48\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('48','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_48\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{VanRoy2023CDC,<br \/>\r\ntitle = {Continuous Optimization for Control of Finite-State Machines with Cascaded Hysteresis Via Time-Freezing},<br \/>\r\nauthor = {Wim Van Roy and Armin Nurkanovic and Ramin Abbasi-Esfeden and Jonathan Frey and Anton Pozharskiy and Jan Swevers and Moritz Diehl},<br \/>\r\ndoi = {10.1109\/CDC49753.2023.10384083},<br \/>\r\nisbn = {979-8-3503-0124-3},<br \/>\r\nyear  = {2024},<br \/>\r\ndate = {2024-01-19},<br \/>\r\nurldate = {2023-12-01},<br \/>\r\nbooktitle = {2023 62nd IEEE Conference on Decision and Control (CDC)},<br \/>\r\npages = {6261-6266},<br \/>\r\npublisher = {IEEE},<br \/>\r\naddress = {Singapore, Singapore},<br \/>\r\nabstract = {Control problems with Finite-State Machines (FSM) are often solved using integer variables, leading to a mixed-integer optimal control problem (MIOCP). This paper proposes an alternative method to describe a subclass of FSMs using complementarity constraints and time-freezing. The FSM from this subclass is built up by a sequence of states where a transition between the states is triggered by a single switching function. This can be looked at as a cascade of hysteresis loops where a memory effect is used to maintain the active state of the state machine. Based on the reformulation for hybrid systems with a hysteresis loop [13], a method is developed to reformulate this subclass in a similar fashion. The approach transforms the original problem into a Piecewise Smooth System (PSS), which can be discretized using the recently developed Finite Elements with Switch Detection [15], allowing for high-accuracy solutions. The reformulation is compared to a mixed-integer formulation from the literature on a time-optimal control problem. This work is a first step towards the general reformulation of FSMs into nonsmooth systems without integer states.},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('48','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_48\" style=\"display:none;\"><div class=\"tp_abstract_entry\">Control problems with Finite-State Machines (FSM) are often solved using integer variables, leading to a mixed-integer optimal control problem (MIOCP). This paper proposes an alternative method to describe a subclass of FSMs using complementarity constraints and time-freezing. The FSM from this subclass is built up by a sequence of states where a transition between the states is triggered by a single switching function. This can be looked at as a cascade of hysteresis loops where a memory effect is used to maintain the active state of the state machine. Based on the reformulation for hybrid systems with a hysteresis loop [13], a method is developed to reformulate this subclass in a similar fashion. The approach transforms the original problem into a Piecewise Smooth System (PSS), which can be discretized using the recently developed Finite Elements with Switch Detection [15], allowing for high-accuracy solutions. The reformulation is compared to a mixed-integer formulation from the literature on a time-optimal control problem. This work is a first step towards the general reformulation of FSMs into nonsmooth systems without integer states.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('48','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_48\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/10.1109\/CDC49753.2023.10384083\" title=\"Follow DOI:10.1109\/CDC49753.2023.10384083\" target=\"_blank\">doi:10.1109\/CDC49753.2023.10384083<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('48','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_number\">4.<\/div><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Roy, Wim Van;  Abbasi-Esfeden, Ramin;  Swevers, Jan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('39','tp_links')\" style=\"cursor:pointer;\">A Dynamic Programming-based Heuristic Approach for Unit Commitment Problems<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">2023 European Control Conference (ECC), <\/span><span class=\"tp_pub_additional_pages\">pp. 1-8, <\/span><span class=\"tp_pub_additional_publisher\">IEEE, <\/span><span class=\"tp_pub_additional_address\">Bucharest, Romania, <\/span><span class=\"tp_pub_additional_year\">2023<\/span>, <span class=\"tp_pub_additional_isbn\">ISBN: 978-3-907144-08-4<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_39\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('39','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_39\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('39','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_39\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('39','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_39\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{vanRoy2023ADP,<br \/>\r\ntitle = {A Dynamic Programming-based Heuristic Approach for Unit Commitment Problems},<br \/>\r\nauthor = {Wim Van Roy and Ramin Abbasi-Esfeden and Jan Swevers},<br \/>\r\nurl = {https:\/\/ieeexplore.ieee.org\/document\/10178216},<br \/>\r\ndoi = {https:\/\/doi.org\/10.23919\/ECC57647.2023.10178216},<br \/>\r\nisbn = {978-3-907144-08-4},<br \/>\r\nyear  = {2023},<br \/>\r\ndate = {2023-07-17},<br \/>\r\nurldate = {2023-07-17},<br \/>\r\nbooktitle = {2023 European Control Conference (ECC)},<br \/>\r\npages = {1-8},<br \/>\r\npublisher = {IEEE},<br \/>\r\naddress = {Bucharest, Romania},<br \/>\r\nabstract = {Unit Commitment (UC) problems are an essential set of problems in the power industry with applications in energy grid or heating systems management and control. The engineering goal is to balance the demand with the production of a network of production units, called generators, by providing a schedule and operating points for each generator cost-effectively while considering constraints. The constraints are caused by the dynamics of the system, the limits on the reserves, and possible robustness requirements. Due to the appearance of the on\/off states from the generators, the resulting problems are NP-hard to solve. Thus, existing techniques to achieve a cost-efficient solution are computationally expensive. This paper proposes a dynamic programming-based heuristic to solve a UC problem. The heuristic focuses on finding a feasible and cost-effective solution for systems with a limited number of generators where a long time horizon is important. This method is compared to a Mixed Integer Linear Program (MILP) implementation for a micro-grid where it achieves a computation time that is an order of magnitude smaller than MILP programs for problems with a limited number of generators but a long time horizon.},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('39','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_39\" style=\"display:none;\"><div class=\"tp_abstract_entry\">Unit Commitment (UC) problems are an essential set of problems in the power industry with applications in energy grid or heating systems management and control. The engineering goal is to balance the demand with the production of a network of production units, called generators, by providing a schedule and operating points for each generator cost-effectively while considering constraints. The constraints are caused by the dynamics of the system, the limits on the reserves, and possible robustness requirements. Due to the appearance of the on\/off states from the generators, the resulting problems are NP-hard to solve. Thus, existing techniques to achieve a cost-efficient solution are computationally expensive. This paper proposes a dynamic programming-based heuristic to solve a UC problem. The heuristic focuses on finding a feasible and cost-effective solution for systems with a limited number of generators where a long time horizon is important. This method is compared to a Mixed Integer Linear Program (MILP) implementation for a micro-grid where it achieves a computation time that is an order of magnitude smaller than MILP programs for problems with a limited number of generators but a long time horizon.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('39','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_39\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/ieeexplore.ieee.org\/document\/10178216\" title=\"https:\/\/ieeexplore.ieee.org\/document\/10178216\" target=\"_blank\">https:\/\/ieeexplore.ieee.org\/document\/10178216<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.23919\/ECC57647.2023.10178216\" title=\"Follow DOI:https:\/\/doi.org\/10.23919\/ECC57647.2023.10178216\" target=\"_blank\">doi:https:\/\/doi.org\/10.23919\/ECC57647.2023.10178216<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('39','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_inproceedings\"><div class=\"tp_pub_number\">5.<\/div><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Abbasi-Esfeden, Ramin;  Roy, Wim Van;  Swevers, Jan<\/p><p class=\"tp_pub_title\"><a class=\"tp_title_link\" onclick=\"teachpress_pub_showhide('41','tp_links')\" style=\"cursor:pointer;\">Iterative Switching Time Optimization for Mixed-integer Optimal Control Problems<\/a> <span class=\"tp_pub_type tp_  inproceedings\">Proceedings Article<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_in\">In: <\/span><span class=\"tp_pub_additional_booktitle\">2023 European Control Conference (ECC), <\/span><span class=\"tp_pub_additional_pages\">pp. 1-6, <\/span><span class=\"tp_pub_additional_publisher\">IEEE, <\/span><span class=\"tp_pub_additional_address\">Bucharest, Romania, <\/span><span class=\"tp_pub_additional_year\">2023<\/span>, <span class=\"tp_pub_additional_isbn\">ISBN: 978-3-907144-08-4<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_abstract_link\"><a id=\"tp_abstract_sh_41\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('41','tp_abstract')\" title=\"Show abstract\" style=\"cursor:pointer;\">Abstract<\/a><\/span> | <span class=\"tp_resource_link\"><a id=\"tp_links_sh_41\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('41','tp_links')\" title=\"Show links and resources\" style=\"cursor:pointer;\">Links<\/a><\/span> | <span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_41\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('41','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_41\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@inproceedings{AbbasiEsfeden2023STO,<br \/>\r\ntitle = {Iterative Switching Time Optimization for Mixed-integer Optimal Control Problems},<br \/>\r\nauthor = {Ramin Abbasi-Esfeden and Wim Van Roy and Jan Swevers},<br \/>\r\nurl = {https:\/\/ieeexplore.ieee.org\/document\/10178419},<br \/>\r\ndoi = {https:\/\/doi.org\/10.23919\/ECC57647.2023.10178419},<br \/>\r\nisbn = {978-3-907144-08-4},<br \/>\r\nyear  = {2023},<br \/>\r\ndate = {2023-07-17},<br \/>\r\nurldate = {2023-07-17},<br \/>\r\nbooktitle = {2023 European Control Conference (ECC)},<br \/>\r\npages = {1-6},<br \/>\r\npublisher = {IEEE},<br \/>\r\naddress = {Bucharest, Romania},<br \/>\r\nabstract = {This paper proposes an iterative method to solve Mixed-Integer Optimal Control Problems arising from systems with switched dynamics. The so-called relaxed problem plays a central role within this context. Through a numerical example, it is shown why relying on the relaxed problem can lead the solution astray. As an alternative, an iterative Switching Time optimization method is proposed. The method consists of two components that iteratively interact: a Switching Time optimization (STO) problem and a sequence optimization. Each component is explained in detail, and the numerical example is resolved, the results of which shows the efficiency of the proposed algorithm. Finally, the advantages and disadvantages of the method are discussed and future lines of research are sketched.},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {inproceedings}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('41','tp_bibtex')\">Close<\/a><\/p><\/div><div class=\"tp_abstract\" id=\"tp_abstract_41\" style=\"display:none;\"><div class=\"tp_abstract_entry\">This paper proposes an iterative method to solve Mixed-Integer Optimal Control Problems arising from systems with switched dynamics. The so-called relaxed problem plays a central role within this context. Through a numerical example, it is shown why relying on the relaxed problem can lead the solution astray. As an alternative, an iterative Switching Time optimization method is proposed. The method consists of two components that iteratively interact: a Switching Time optimization (STO) problem and a sequence optimization. Each component is explained in detail, and the numerical example is resolved, the results of which shows the efficiency of the proposed algorithm. Finally, the advantages and disadvantages of the method are discussed and future lines of research are sketched.<\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('41','tp_abstract')\">Close<\/a><\/p><\/div><div class=\"tp_links\" id=\"tp_links_41\" style=\"display:none;\"><div class=\"tp_links_entry\"><ul class=\"tp_pub_list\"><li><i class=\"fas fa-globe\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/ieeexplore.ieee.org\/document\/10178419\" title=\"https:\/\/ieeexplore.ieee.org\/document\/10178419\" target=\"_blank\">https:\/\/ieeexplore.ieee.org\/document\/10178419<\/a><\/li><li><i class=\"ai ai-doi\"><\/i><a class=\"tp_pub_list\" href=\"https:\/\/dx.doi.org\/https:\/\/doi.org\/10.23919\/ECC57647.2023.10178419\" title=\"Follow DOI:https:\/\/doi.org\/10.23919\/ECC57647.2023.10178419\" target=\"_blank\">doi:https:\/\/doi.org\/10.23919\/ECC57647.2023.10178419<\/a><\/li><\/ul><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('41','tp_links')\">Close<\/a><\/p><\/div><\/div><\/div><div class=\"tp_publication tp_publication_presentation\"><div class=\"tp_pub_number\">6.<\/div><div class=\"tp_pub_info\"><p class=\"tp_pub_author\"> Roy, Wim Van;  Abbasi-Esfeden, Ramin;  Swevers, Jan<\/p><p class=\"tp_pub_title\">Online Unit Commitment Problem Solving using Extended Dynamic Programming <span class=\"tp_pub_type tp_  presentation\">Presentation<\/span> <\/p><p class=\"tp_pub_additional\"><span class=\"tp_pub_additional_date\">22.03.2023<\/span>.<\/p><p class=\"tp_pub_menu\"><span class=\"tp_bibtex_link\"><a id=\"tp_bibtex_sh_40\" class=\"tp_show\" onclick=\"teachpress_pub_showhide('40','tp_bibtex')\" title=\"Show BibTeX entry\" style=\"cursor:pointer;\">BibTeX<\/a><\/span><\/p><div class=\"tp_bibtex\" id=\"tp_bibtex_40\" style=\"display:none;\"><div class=\"tp_bibtex_entry\"><pre>@misc{vanRoy2023EDP,<br \/>\r\ntitle = {Online Unit Commitment Problem Solving using Extended Dynamic Programming},<br \/>\r\nauthor = {Wim Van Roy and Ramin Abbasi-Esfeden and Jan Swevers},<br \/>\r\nyear  = {2023},<br \/>\r\ndate = {2023-03-22},<br \/>\r\nurldate = {2023-03-22},<br \/>\r\nkeywords = {},<br \/>\r\npubstate = {published},<br \/>\r\ntppubtype = {presentation}<br \/>\r\n}<br \/>\r\n<\/pre><\/div><p class=\"tp_close_menu\"><a class=\"tp_close\" onclick=\"teachpress_pub_showhide('40','tp_bibtex')\">Close<\/a><\/p><\/div><\/div><\/div><\/div><\/div><\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Department of Mechanical Engineering, PMA division, KU Leuven<\/p>\n","protected":false},"author":2,"featured_media":2767,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[9,8],"tags":[],"class_list":["post-698","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-esr","category-people"],"_links":{"self":[{"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/posts\/698","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/elo-x.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=698"}],"version-history":[{"count":30,"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/posts\/698\/revisions"}],"predecessor-version":[{"id":2795,"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/posts\/698\/revisions\/2795"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/media\/2767"}],"wp:attachment":[{"href":"https:\/\/elo-x.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=698"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/elo-x.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=698"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/elo-x.eu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=698"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}