{"id":2211,"date":"2023-11-29T23:35:48","date_gmt":"2023-11-29T23:35:48","guid":{"rendered":"https:\/\/elo-x.eu\/?p=2211"},"modified":"2025-03-19T10:09:59","modified_gmt":"2025-03-19T10:09:59","slug":"embedded-learning-and-optimization-for-interaction-aware-mpc","status":"publish","type":"post","link":"https:\/\/elo-x.eu\/?p=2211","title":{"rendered":"Embedded Learning and Optimization for Interaction-aware MPC"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"2211\" class=\"elementor elementor-2211\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-90bc3ec elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"90bc3ec\" 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-f2b556f\" data-id=\"f2b556f\" 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-86c9a5c elementor-widget elementor-widget-heading\" data-id=\"86c9a5c\" 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-xl\">Embedded Learning and Optimization for Interaction-aware\nModel Predictive Control<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1085760 my-divider elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"1085760\" 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-beeb054 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"beeb054\" 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-38efd90\" data-id=\"38efd90\" 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-a52d48f elementor-widget elementor-widget-text-editor\" data-id=\"a52d48f\" 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<span style=\"color: #352a87;\"><span style=\"font-size: 24px;\">Renzi Wang, STADIUS, ESAT, KU Leuven<\/span><\/span>\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-31bbb35 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"31bbb35\" 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-d843487\" data-id=\"d843487\" 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-391b193 elementor-widget elementor-widget-text-editor\" data-id=\"391b193\" 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 goal of this project is to develop embedded optimization and online learning algorithms for interaction-aware Model Predictive Control (MPC) for autonomous navigation in uncertain environments. In this project, an interaction-aware MPC formulation integrated with online learning has been developed. The integration of online learning in the MPC formulation allows for the customization of the prediction model, tailoring it to the specific dynamics of the system in interaction. This framework serves as the fundation for the further development of embedded learning and optimization methods.<\/p><p>\u00a0<\/p><p>A key contribution is our learning algorithm that identifies parameters in switching system models with state-dependent transition probabilities. Such a model has been demonstrated to effectively capture nonlinear dynamics. However, the state-dependent distribution creates a nonconvex stochastic control problem.<\/p><p>\u00a0<\/p><p class=\"whitespace-pre-wrap break-words\">To address this challenge, we propose a risk-sensitive MPC framework specifically designed for such stochastic systems. This risk-sensitive approach offers two significant advantages:<\/p><ul class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-decimal space-y-1.5 pl-7\"><li class=\"whitespace-normal break-words\">It enables more natural human-robot interactions<\/li><li class=\"whitespace-normal break-words\">It introduces additional problem structure that allows us to design customized algorithms for solving the nonconvex optimal control problems efficiently<\/li><\/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<\/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-6c37975 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6c37975\" 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-2c92c57\" data-id=\"2c92c57\" 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-b7a88c2 my-divider elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"b7a88c2\" 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-6f16671 elementor-widget elementor-widget-heading\" data-id=\"6f16671\" 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\">Interaction-aware Model Predictive Control for Autonomous Driving<\/h2>\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-2ae2e54 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2ae2e54\" 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-224abb4\" data-id=\"224abb4\" 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-6338624 elementor-widget elementor-widget-text-editor\" data-id=\"6338624\" 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 class=\"gs_citr\" tabindex=\"0\"><a href=\"https:\/\/elo-x.eu\/?p=671\">Wang, Renzi<\/a>, <a href=\"https:\/\/www.kuleuven.be\/wieiswie\/nl\/person\/00110604\">Mathijs Schuurmans<\/a>, and <a href=\"https:\/\/elo-x.eu\/?p=864\">Panagiotis Patrinos<\/a>. &#8220;<a href=\"https:\/\/ieeexplore.ieee.org\/abstract\/document\/10178332\">Interaction-aware model predictive control for autonomous driving<\/a>.&#8221; <i>2023 European Control Conference (ECC)<\/i>. IEEE, 2023.<\/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-8722eb8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8722eb8\" 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-72a2899\" data-id=\"72a2899\" 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-957f7c1 elementor-widget elementor-widget-text-editor\" data-id=\"957f7c1\" 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>We propose an interaction-aware stochastic model predictive control (MPC) strategy for lane merging tasks in automated driving. The MPC strategy is integrated with an online learning framework, which models a given driver\u2019s cooperation level as an unknown parameter in a state-dependent probability distribution. The online learning framework adaptively estimates the surrounding vehicle\u2019s cooperation level with the vehicle\u2019s past state trajectory and combines this with a kinematic vehicle model to predict the distribution of a multimodal future state trajectory. Learning is conducted using logistic regression, enabling fast online computations. The multi-future prediction is used in the MPC algorithm to compute the optimal control input while satisfying safety constraints. We demonstrate our algorithm in an interactive lane changing scenario with drivers in different randomly selected cooperation levels.<\/p><p>\u00a0<\/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-50 elementor-top-column elementor-element elementor-element-73c1594\" data-id=\"73c1594\" 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-705973c elementor-widget__width-initial elementor-widget elementor-widget-image\" data-id=\"705973c\" 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\/2023\/11\/motivation_lane_changing_page-0001-1024x683.jpg\" class=\"attachment-large size-large wp-image-2253\" alt=\"\" srcset=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/motivation_lane_changing_page-0001-1024x683.jpg 1024w, https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/motivation_lane_changing_page-0001-300x200.jpg 300w, https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/motivation_lane_changing_page-0001-768x512.jpg 768w, https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/motivation_lane_changing_page-0001-1536x1024.jpg 1536w, https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/motivation_lane_changing_page-0001-2048x1366.jpg 2048w\" sizes=\"100vw\" \/>\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\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-39a0a9c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"39a0a9c\" 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-a84db57\" data-id=\"a84db57\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\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-29ca8e8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"29ca8e8\" 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-c4027ba\" data-id=\"c4027ba\" 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-4b01355 my-divider elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"4b01355\" 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-c687fe8 elementor-widget elementor-widget-heading\" data-id=\"c687fe8\" 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\">EM++: A parameter learning framework for stochastic switching systems<\/h2>\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-8d21458 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8d21458\" 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-60eb0aa\" data-id=\"60eb0aa\" 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-ff6f801 elementor-widget elementor-widget-text-editor\" data-id=\"ff6f801\" 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><a href=\"https:\/\/elo-x.eu\/?p=671\">Renzi Wang<\/a>, <a href=\"https:\/\/www.kuleuven.be\/wieiswie\/en\/person\/00140817\">Alexander Bodard<\/a>, <a href=\"https:\/\/www.kuleuven.be\/wieiswie\/nl\/person\/00110604\">Mathijs Schuurmans<\/a>, and <a href=\"https:\/\/elo-x.eu\/?p=864\">Panagiotis Patrinos<\/a>. &#8220;<a href=\"https:\/\/arxiv.org\/abs\/2407.16359v1\" target=\"_blank\" rel=\"noopener\">EM++: A parameter learning framework for stochastic switching systems<\/a>&#8220;. 2024, submitted for publication.<\/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-4bc6d6a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4bc6d6a\" 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-65c1385\" data-id=\"65c1385\" 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-d850bde elementor-widget elementor-widget-text-editor\" data-id=\"d850bde\" 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>Obtaining a realistic and computationally efficient model will significantly enhance the performance of a model predictive controller. This is especially true for complex scenarios where the system being controlled must interact with other systems. This work proposes a general switching dynamical system model, and a custom majorization-minimization-based algorithm EM++ for identifying its parameters. For certain families of distributions, such as Gaussian distributions, this algorithm reduces to the well-known expectation-maximization method. We prove global convergence of the algorithm under suitable assumptions, thus addressing an important open issue in the switching system identification literature. The effectiveness of both the proposed model and algorithm is validated through extensive numerical experiments<\/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-50 elementor-top-column elementor-element elementor-element-e22846b\" data-id=\"e22846b\" 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-51308d2 elementor-widget__width-initial elementor-widget elementor-widget-image\" data-id=\"51308d2\" 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 decoding=\"async\" width=\"525\" height=\"224\" src=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/synthetic_example_comparison_boxplot_with_strips-1024x436.png\" class=\"attachment-large size-large wp-image-2846\" alt=\"\" srcset=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/synthetic_example_comparison_boxplot_with_strips-1024x436.png 1024w, https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/synthetic_example_comparison_boxplot_with_strips-300x128.png 300w, https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/synthetic_example_comparison_boxplot_with_strips-768x327.png 768w, https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/synthetic_example_comparison_boxplot_with_strips-1536x653.png 1536w, https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/synthetic_example_comparison_boxplot_with_strips.png 1754w\" sizes=\"100vw\" \/>\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\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-369cbef elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"369cbef\" 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-4ea643d\" data-id=\"4ea643d\" 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-32ef029 elementor-widget elementor-widget-heading\" data-id=\"32ef029\" 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\">Imitation Learning from Observations: An Autoregressive Mixture of Experts Approach<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8d670c3 elementor-widget elementor-widget-text-editor\" data-id=\"8d670c3\" 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><a href=\"https:\/\/elo-x.eu\/?p=671\">Renzi Wang<\/a>, <a href=\"https:\/\/elo-x.eu\/?p=1336\">Flavia Sofia Acerbo<\/a>, <a href=\"https:\/\/elo-x.eu\/?p=569\">Tong Duy Son<\/a>, and <a href=\"https:\/\/elo-x.eu\/?p=864\">Panagiotis Patrinos<\/a>. &#8220;<a href=\"https:\/\/arxiv.org\/pdf\/2411.08232\" target=\"_blank\" rel=\"noopener\">Imitation Learning from Observations: An Autoregressive Mixture of Experts Approach\u200b<\/a>&#8220;. <i>2025 European Control Conference (ECC)<\/i>. IEEE, 2025.<\/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-04bea16 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"04bea16\" 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-c63651e\" data-id=\"c63651e\" 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-5787032 elementor-widget elementor-widget-text-editor\" data-id=\"5787032\" 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>This paper presents a novel approach to imitation learning from observations, where an autoregressive mixture of experts model is deployed to fit the underlying policy. The parameters of the model are learned via a two-stage framework. By leveraging the existing dynamics knowledge, the first stage of the framework estimates the control input sequences and hence reduces the problem complexity. At the second stage, the policy is learned by solving a regularized maximum-likelihood estimation problem using the estimated control input sequences. We further extend the learning procedure by incorporating a Lyapunov stability constraint to ensure asymptotic stability of the identified model, for accurate multi-step predictions. The effectiveness of the proposed framework is validated using two autonomous driving datasets collected from human demonstrations, demonstrating its practical applicability in modelling complex nonlinear dynamics.<\/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-bf642c5\" data-id=\"bf642c5\" 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-af54275 elementor-widget elementor-widget-image\" data-id=\"af54275\" 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 decoding=\"async\" width=\"525\" height=\"366\" src=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/compare_stability_one_step_traj0.jpg\" class=\"attachment-large size-large wp-image-3029\" alt=\"\" srcset=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/compare_stability_one_step_traj0.jpg 906w, https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/compare_stability_one_step_traj0-300x209.jpg 300w, https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/compare_stability_one_step_traj0-768x535.jpg 768w\" sizes=\"100vw\" \/>\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\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-bbe0921 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bbe0921\" 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-2076f04\" data-id=\"2076f04\" 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-9bc8ee2 my-divider elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"9bc8ee2\" 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-8c42272 elementor-widget elementor-widget-heading\" data-id=\"8c42272\" 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\">Risk-Sensitive Model Predictive Control for Interaction-Aware Planning -- A Sequential Convexification Algorithm<\/h2>\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-64586f2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"64586f2\" 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-663f857\" data-id=\"663f857\" 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-8ed06c0 elementor-widget elementor-widget-text-editor\" data-id=\"8ed06c0\" 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><a href=\"https:\/\/elo-x.eu\/?p=671\">Renzi Wang<\/a>, <a href=\"https:\/\/www.kuleuven.be\/wieiswie\/nl\/person\/00110604\">Mathijs Schuurmans<\/a>, and <a href=\"https:\/\/elo-x.eu\/?p=864\">Panagiotis Patrinos<\/a>. &#8220;<a href=\"https:\/\/arxiv.org\/pdf\/2503.14328\">Risk-Sensitive Model Predictive Control for Interaction-Aware Planning<\/a><br \/>\u2014 A Sequential Convexification Algorithm \u2014&#8221;. 2025, submitted for publication.<\/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-a5e6e05 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a5e6e05\" 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-ed7bc9e\" data-id=\"ed7bc9e\" 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-7e11031 elementor-widget__width-initial elementor-widget elementor-widget-text-editor\" data-id=\"7e11031\" 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>This paper considers risk-sensitive model predictive control for stochastic systems with a decision-dependent distribution. This class of systems is commonly found in human-robot interaction scenarios. We derive computationally tractable convex upper bounds to both the objective function, and to frequently used penalty terms for collision avoidance, allowing us to efficiently solve the generally nonconvex optimal control problem as a sequence of convex problems. Simulations of a robot navigating a corridor demonstrate the effectiveness and the computational advantage of the proposed approach.<\/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-50 elementor-top-column elementor-element elementor-element-d9b33bd\" data-id=\"d9b33bd\" 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-6519e2b elementor-widget__width-initial elementor-widget elementor-widget-image\" data-id=\"6519e2b\" 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 loading=\"lazy\" decoding=\"async\" width=\"525\" height=\"246\" src=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/scenariotree3d_page-0001.jpg\" class=\"attachment-large size-large wp-image-2254\" alt=\"\" srcset=\"https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/scenariotree3d_page-0001.jpg 786w, https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/scenariotree3d_page-0001-300x141.jpg 300w, https:\/\/elo-x.eu\/wp-content\/uploads\/2023\/11\/scenariotree3d_page-0001-768x361.jpg 768w\" sizes=\"100vw\" \/>\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\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>Embedded Learning and Optimization for Interaction-aware Model Predictive Control Renzi Wang, STADIUS, ESAT, KU Leuven The goal of this project is to develop embedded optimization and online learning algorithms for interaction-aware Model Predictive Control (MPC) for autonomous navigation in uncertain environments. In this project, an interaction-aware MPC formulation integrated with online learning has been developed. &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/elo-x.eu\/?p=2211\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Embedded Learning and Optimization for Interaction-aware MPC&#8221;<\/span><\/a><\/p>\n","protected":false},"author":12,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[],"class_list":["post-2211","post","type-post","status-publish","format-standard","hentry","category-projects"],"_links":{"self":[{"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/posts\/2211","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\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/elo-x.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2211"}],"version-history":[{"count":72,"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/posts\/2211\/revisions"}],"predecessor-version":[{"id":3032,"href":"https:\/\/elo-x.eu\/index.php?rest_route=\/wp\/v2\/posts\/2211\/revisions\/3032"}],"wp:attachment":[{"href":"https:\/\/elo-x.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2211"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/elo-x.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2211"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/elo-x.eu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2211"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}