{
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        "rendered": "<div data-elementor-type=\"wp-post\" data-elementor-id=\"744\" class=\"elementor elementor-744\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4e1822f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4e1822f\" 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-c4d9f97\" data-id=\"c4d9f97\" 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-7f4489a elementor-widget elementor-widget-page-title\" data-id=\"7f4489a\" 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\tHierarchical Control Systems  \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\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-21539e6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"21539e6\" 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-b8a70cd\" data-id=\"b8a70cd\" 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\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-9895bec elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9895bec\" 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-66 elementor-top-column elementor-element elementor-element-6d1e23d\" data-id=\"6d1e23d\" 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-c5cfc37 elementor-widget elementor-widget-text-editor\" data-id=\"c5cfc37\" 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>In a world of automation, performance of control systems can make or break a product. More automation and advanced functionalities generally imply a larger number of control algorithms that interact with each other, in layered structures, and with the environment.\u00a0<\/p><p><span style=\"word-spacing: normal;\">Hierarchical structures are widespread since they allow the designers to break the problem complexity and employ established design approaches, either model-based or data-driven, at smaller scale on individual sub-problems. However, in this way the performance and safety of the overall system depends on the teamwork of its subsystems. For highly autonomous systems operating in presence of large uncertainty, it becomes very difficult to analyze and predict the overall behavior. Indeed, hierarchical layouts pose challenges regarding several aspects, such as modeling, uncertainty quantification, and stability analysis. More in general, there is a lack of fundamental methods to design the layers in a rigorous and coordinated way in order to theoretically guarantee performance and safety under reasonable assumptions.<\/span><\/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<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-7dcf9f1\" data-id=\"7dcf9f1\" 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-25ae566 elementor-widget__width-auto elementor-pagination-position-outside elementor-widget elementor-widget-image-carousel\" data-id=\"25ae566\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;navigation&quot;:&quot;dots&quot;,&quot;slides_to_show&quot;:&quot;1&quot;,&quot;effect&quot;:&quot;fade&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;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 4\"><figure class=\"swiper-slide-inner\"><img decoding=\"async\" class=\"swiper-slide-image\" src=\"https:\/\/www.sas-lab.deib.polimi.it\/wp-content\/uploads\/2021\/12\/test2-1024x-768x432.jpg\" alt=\"test2-1024x\" \/><\/figure><\/div><div class=\"swiper-slide\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"2 of 4\"><figure class=\"swiper-slide-inner\"><img decoding=\"async\" class=\"swiper-slide-image\" src=\"https:\/\/www.sas-lab.deib.polimi.it\/wp-content\/uploads\/2021\/12\/Space_Shuttle_Discovery_rests_on_Launch_Pad_39B-768x531.jpg\" alt=\"Space_Shuttle_Discovery_rests_on_Launch_Pad_39B\" \/><\/figure><\/div><div class=\"swiper-slide\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"3 of 4\"><figure class=\"swiper-slide-inner\"><img decoding=\"async\" class=\"swiper-slide-image\" src=\"https:\/\/www.sas-lab.deib.polimi.it\/wp-content\/uploads\/2021\/12\/Airbus_A380-768x511.jpg\" alt=\"Airbus_A380\" \/><\/figure><\/div><div class=\"swiper-slide\" role=\"group\" aria-roledescription=\"slide\" aria-label=\"4 of 4\"><figure class=\"swiper-slide-inner\"><img decoding=\"async\" class=\"swiper-slide-image\" src=\"https:\/\/www.sas-lab.deib.polimi.it\/wp-content\/uploads\/2021\/12\/2015_BMW_i8_20039281571_2-768x432.jpg\" alt=\"2015 BMW i8\" \/><\/figure><\/div>\t\t\t<\/div>\n\t\t\t\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 class=\"elementor-element elementor-element-0c39264 elementor-widget elementor-widget-text-editor\" data-id=\"0c39264\" 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>Examples of hierarchical control systems<\/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-50cb8bb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"50cb8bb\" 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-2c5321b\" data-id=\"2c5321b\" 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-451dca7 elementor-widget elementor-widget-text-editor\" data-id=\"451dca7\" 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>Our research on hierarchical control systems aims to derive such methods using optimization-based techniques. Research questions include:<\/p>\n<ul>\n<li>how to embed the behavior of low-level feedback loops into simple-enough models to be managed at higher levels;<\/li>\n<li>how to evaluate the quality of such models, and how to monitor the performance of individual control functions and of their interactions;<\/li>\n<li>how to quantify and propagate the uncertainty at each hierarchical level and across levels;<\/li>\n<li>how to optimally coordinate various control systems at low levels when transitioning among different operating conditions;<\/li>\n<li>how to choose a hierarchical control topology such that complexity and computational load are minimized without sacrificing performance.<\/li>\n<\/ul>\n<div>The methods developed by SAS-Lab in these areas are motivated by and tested on real-world applications, such as airborne wind energy systems and autonomous aerial drones with vertical take off and landing capabilities.<\/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<\/div>",
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        "rendered": "<p>Optimization-based modeling and control of safety-critical multi-layered autonomous systems<\/p>\n<p> <a class=\"more-link\" href=\"https:\/\/www.sas-lab.deib.polimi.it\/it\/?p=744\">Read more<\/a><\/p>",
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