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We give a notion of Scott rank for separable metric structures based on the definability of the (metric closures of) automorphism orbits in continuous infinitary logic. This is a continuous analogue of work of Montalb\'an for countable structures. In the process, we prove some results concerning definability, type omitting, and back-and-forth for metric structures.

Reinforcement learning (RL) controllers are flexible and performant but rarely guarantee safety. Safety filters impart hard safety guarantees to RL controllers while maintaining flexibility. However, safety filters can cause undesired behaviours due to the separation between the controller and the safety filter, often degrading performance and robustness. In this paper, we analyze several modifications to incorporating the safety filter in training RL controllers rather than solely applying it during evaluation. The modifications allow the RL controller to learn to account for the safety filter, improving performance. This paper presents a comprehensive analysis of training RL with safety filters, featuring simulated and real-world experiments with a Crazyflie 2.0 drone. We examine how various training modifications and hyperparameters impact performance, sample efficiency, safety, and chattering. Our findings serve as a guide for practitioners and researchers focused on safety filters and safe RL., Comment: 8 pages, 9 figures. Code is publicly available at https://github.com/Federico-PizarroBejarano/safe-control-gym/tree/training_rl_paper

A practical method for identifying the propeller model and inertia matrix of a marine Autonomous Surface Vehicle (ASV) is proposed in this work. Special attention is paid to limiting the instrumentation requirements. Based on a generic grey-box dynamic modelling addressing the considered catamaran-shaped ASV architecture, the static/dynamic behaviour of both propellers and the vessel dynamic are jointly estimated using the sole measurements of position, heading, and propellers pulse width modulation (PWM) signals. No accelerometer is required. Two distinct grey-box configurations involving either a static polynomial or a dynamic modelling of each propeller are proposed and compared. The resulting ASV identification methodology is shown to provide insight into the whole vessel inertial characteristics, which are key enablers in the development of autonomous navigation and control systems. Model validation was performed using data collected from the reported experiments. Model prediction errors related to both linear velocities and yaw rate are evaluated and compared based on given metrics. The results underscore the robustness and accuracy of the identified models in capturing the essential dynamics of the ASV, with a determination coefficient that consistently exceeds 0.94 for all estimated velocities.

In this article, the Hausdorff dimension is estimated using the box-counting dimension and the information dimension. It is shown that the former is an upper bound for the Hausdorff dimension, while the latter is a lower bound for the box-counting dimension, and that the information dimension is an upper bound for the Hausdorff dimension. Additionally, the dimension of the Henon attractor is estimated using the box-counting dimension., Comment: 14 pages, in Spanish language

In this work, we will study a numerical method that allows finding an approximation of the exact solution for a in-situ combustion model using the nonlinear mixed complementary method, which is a variation of the Newtons method for solving nonlinear systems based on an implicit finite difference scheme and a nonlinear algorithm mixed complementarity, FDA-MNCP. The method has the advantage of provide a global convergence in relation to the finite difference method and method of Newton that only has local convergence. The theory is applied to model in-situ combustion, which can be rewritten in the form of mixed complementarity also we do a comparison with the FDA-NCP method, Comment: 17 Pages

Contribution: This Full paper in the Research Category track describes a practical, scalable platform that seamlessly integrates Generative AI (GenAI) with online educational forums, offering a novel approach to augment the instructional capabilities of staff. The platform empowers instructional staff to efficiently manage, refine, and approve responses by facilitating interaction between student posts and a Large Language Model (LLM). This contribution enhances the efficiency and effectiveness of instructional support and significantly improves the quality and speed of responses provided to students, thereby enriching the overall learning experience. Background: Grounded in Vygotsky's socio-cultural theory and the concept of the More Knowledgeable Other (MKO), the study examines how GenAI can act as an auxiliary MKO to enrich educational dialogue between students and instructors. Research Question: How effective is GenAI in reducing the workload of instructional staff when used to pre-answer student questions posted on educational discussion forums? Methodology: Using a mixed-methods approach in large introductory programming courses, human Teaching Assistants (AI-TAs) employed an AI-assisted platform to pre-answer student queries. We analyzed efficiency indicators like the frequency of modifications to AI-generated responses and gathered qualitative feedback from AI-TAs. Findings: The findings indicate no significant difference in student reception to responses generated by AI-TAs compared to those provided by human instructors. This suggests that GenAI can effectively meet educational needs when adequately managed. Moreover, AI-TAs experienced a reduction in the cognitive load required for responding to queries, pointing to GenAI's potential to enhance instructional efficiency without compromising the quality of education., Comment: 8 pages, 1 figure. Accepted for publication in Frontiers in Education 2024

This paper explores the potential of large language models (LLMs) to make the Aeronautical Regulations of Colombia (RAC) more accessible. Given the complexity and extensive technicality of the RAC, this study introduces a novel approach to simplifying these regulations for broader understanding. By developing the first-ever RAC database, which contains 24,478 expertly labeled question-and-answer pairs, and fine-tuning LLMs specifically for RAC applications, the paper outlines the methodology for dataset assembly, expert-led annotation, and model training. Utilizing the Gemma1.1 2b model along with advanced techniques like Unsloth for efficient VRAM usage and flash attention mechanisms, the research aims to expedite training processes. This initiative establishes a foundation to enhance the comprehensibility and accessibility of RAC, potentially benefiting novices and reducing dependence on expert consultations for navigating the aviation industry's regulatory landscape. You can visit the dataset (https://huggingface.co/somosnlp/gemma-1.1-2b-it_ColombiaRAC_FullyCurated_format_chatML_V1) and the model (https://huggingface.co/datasets/somosnlp/ColombiaRAC_FullyCurated) here.

This brief deals with the satisfaction of the daily cooling demand by a hybrid system that consists of a vapour-compression refrigeration cycle and a thermal energy storage (TES) unit, based on phase change materials. The addition of the TES tank to the original refrigeration plant allows to schedule the cooling production regardless of the instantaneous demand, given that the TES tank can store cold energy and release it whenever deemed appropriate. The scheduling problem is posed as an optimization problem based on mixed-integer non-linear programming (MINLP), since it includes both discrete and continuous variables. The latter corresponds to the references on the main cooling powers involved in the problem (cooling production at the evaporator and TES charging/discharging), whereas the discrete variables define the operating mode scheduling. Therefore, in addition to the hybrid features of the physical plant, a hybrid optimal control strategy is also proposed. A receding horizon approach is applied, similar to model predictive control (MPC) strategies, while economic criteria are imposed in the objective function, as well as feasibility issues. The TES state estimation is also addressed, since its instantaneous charge ratio is not measurable. The proposed strategy is applied in simulation to a challenging cooling demand profile and the main advantages of the MINLP-based strategy over a non-linear MPC-based scheduling strategy previously developed are highlighted, regarding operating cost, ease of tuning, and ability to adapt to cooling demand variations., Comment: 22 pages, 11 figures. Postprint of the final published work

This work addresses the modelling, power control, and optimization of a thermal energy storage (TES) system combined with a vapour-compression refrigeration facility based on phase change materials (PCM). Given a novel design of a PCM-based TES tank and its interconnection with an existing refrigeration system, the joint dynamic modelling is first studied, exploring the different time scales that coexist at the interconnected system. Diverse operating modes are defined, according to the intended use of the TES tank as a cold-energy buffer to decouple cooling demand and production, whereas the static characteristic and power limits are calculated and show the high coupling between the main cooling powers involved (TES charging/discharging power, and direct power production at the evaporator). In this light, a decoupling control strategy is proposed, where the low-level controllers are simply PI regulators and the refrigerant/secondary mass flows are considered as virtual manipulated variables, applying a feedforward-based cascade strategy. The control performance is evaluated through a thorough simulation that includes all operating modes, where the reference tracking is shown to be fast and reliable enough to address high-level scheduling strategies, where the references on the main cooling powers are intended to be imposed considering economic and efficiency criteria., Comment: 37 pages, 20 figures. Postprint of the final published work

This paper proposes a computationally efficient simulation strategy for cold thermal energy storage (TES) systems based on phase change material (PCM). Taking as a starting point the recent design of a TES system based on PCM, designed to complement a vapour-compression refrigeration plant, the new highly efficient modelling strategy is described and its performance is compared against the pre-existing one. The need for a new computationally efficient approach comes from the fact that, in the near future, such a TES model is intended to be used in combination with the model of the own mother refrigeration plant, in order to address efficient, long-term energy management strategies, where computation time will become a major issue. Comparative simulations show that the proposed computationally efficient strategy reduces the simulation time to a small fraction of the original figure (from around 1/30th till around 1/120th, depending on the particular choice of the main sampling interval), at the expense of affordable inaccuracy in terms of the PCM charge ratio., Comment: 36 pages, 14 figures. Postprint of the final published work

This work proposes a nonlinear model predictive control-based guidance strategy for unmanned surface vehicles, focused on path following. The application of this strategy, in addition to overcome drawbacks of previous line-of-sight-based guidance laws, intends to enable the application of predictive strategies also to the low-level control, responsible for tracking the references provided by the guidance strategy. The stability and robustness of the proposed strategy are theoretically discussed. Furthermore, given the non-negligible computational cost of such nonlinear predictive guidance strategy, a practical nonlinear model predictive control strategy is also applied in order to reduce the computational cost to a great extent. The effectiveness and advantages of both proposed strategies over other nonlinear guidance laws are illustrated through a complete set of simulations., Comment: 21 pages, 15 figures. Postprint of the final published work

This work is focused on optimal control of mechanical compression refrigeration systems. A reduced-order state-space model based on the moving boundary approach is proposed for the canonical cycle, which eases the controller design. The optimal cycle (that satisfying the cooling demand while maximizing efficiency) is defined by three variables, but only two inputs are available, therefore the controllability of the proposed model is studied. It is shown through optimization simulations how optimal cycles for a range of the cooling demand turn out not to be achieved by keeping the degree of superheating to a minimum. The Practical NMPC and a well-known feedback-plus-feedforward strategy from the literature are compared in simulation, both showing trouble in reaching the optimal cycle, which agrees with the controllability study., Comment: 39 pages, 14 figures. Postprint of the final published work

This paper studies the design and dynamic modelling of a novel thermal energy storage (TES) system combined with a refrigeration system based on phase change materials (PCM). Cold-energy production supported by TES systems is a very appealing field of research, since it allows flexible cold-energy management, combining demand fulfilment with cost reduction strategies. The paper proposes and compares two different simulation models for a cold-energy storage system based on PCM. First, a continuous model is developed, the application of which is limited to decoupled charging/discharging operations. Given such conditions, it is a relatively precise model, useful for the tuning of the TES parameters. The second proposed model is a discrete one, which, despite implementing a discrete approximation of the system behaviour, allows to study more general conditions, such as series of partial charging/discharging operations. Simulation results of both models are compared regarding decoupled charging/discharging operations, and the ability of the discrete model to represent more realistic partial operations is analysed., Comment: 48 pages, 14 figures. Postprint of the final published work

In this work we study the exponential stability of the energy associated with a Naghdi shell model with localized internal dissipation. Using several tools from Riemannian Geometry we show the well possedness of the model, via semigroup theory, and obtain observability inequalities which allows to prove the exponential decay of the total energy. As a consequence then we use Russell Principle for obtain exact controllability.

In this paper we study the complexity in the information traffic that occurs in the peruvian financial market, using the Shannon entropy. Different series of prices of shares traded on the Lima stock exchange are used to reconstruct the unknown dynamics. We present numerical simulations on the reconstructed dynamics and we calculate the Shannon entropy to measure its complexity

In this paper, we use Time Scale Calculus (TSC) to formulate and solve pharmacokinetic models exploring multiple dose dynamics. TSC is a mathematical framework that allows the modeling of dynamical systems comprising continuous and discrete processes. This characteristic makes TSC particularly suited for multi-dose pharmacokinetic problems, which inherently feature a blend of continuous processes (such as absorption, metabolization, and elimination) and discrete events (drug intake). We use this toolkit to derive analytical expressions for blood concentration trajectories under various multi-dose regimens across several flagship pharmacokinetic models. We demonstrate that this mathematical framework furnishes an alternative and simplified way to model and retrieve analytical solutions for multi-dose dynamics. For instance, it enables the study of blood concentration responses to arbitrary dose regimens and facilitates the characterization of the long-term behavior of the solutions, such as their steady state., Comment: 42 pages, 5 figures

In this work we study a strongly coupled system between the equation of plates with fractional rotational inertial force $\kappa(-\Delta)^\beta u_{tt}$ where the parameter $0 <\beta\leq 1$ and the equation of an electrical network containing a fractional dissipation term $\delta(-\Delta)^\theta v_t$ where the parameter $0\leq \theta\leq 1$, the strong coupling terms are given by the Laplacian of the displacement speed $\gamma \Delta u_t$ and the Laplacian electric potential field $\gamma\Delta v_t$. When $\beta = 1$, we have the Kirchoff-Love plate and when $\beta = 0$, we have the Euler-Bernoulli plate recently studied in Su\'arez-Mendes (2022-Preprinter)\cite{Suarez}. The contributions of this research are: We prove the semigroup $S(t)$ associated with the system is not analytic in $(\theta,\beta)\in [0,1]\times(0,1]-\{( 1,1/2)\}$. We also determine two Gevrey classes: $s_1 >\frac{1}{2\max\{ \frac{1-\beta}{3-\beta}, \frac{\theta}{2+\theta-\beta}\}}$ for $2\leq \theta+2\beta$ and $s_2> \frac{2(2+\theta-\beta)}{\theta}$ when the parameters $\theta$ and $\beta$ lies in the interval $(0, 1)$ and we finish by proving that at the point $(\theta,\beta)=(1,1/2)$ the semigroup $S(t)$ is analytic and with a note about the asymptotic behavior of $S(t)$. We apply semigroup theory, the frequency domain method together with multipliers and the proper decomposition of the system components and Lions' interpolation inequality., Comment: 40 pages

Learning-based controllers have demonstrated superior performance compared to classical controllers in various tasks. However, providing safety guarantees is not trivial. Safety, the satisfaction of state and input constraints, can be guaranteed by augmenting the learned control policy with a safety filter. Model predictive safety filters (MPSFs) are a common safety filtering approach based on model predictive control (MPC). MPSFs seek to guarantee safety while minimizing the difference between the proposed and applied inputs in the immediate next time step. This limited foresight can lead to jerky motions and undesired oscillations close to constraint boundaries, known as chattering. In this paper, we reduce chattering by considering input corrections over a longer horizon. Under the assumption of bounded model uncertainties, we prove recursive feasibility using techniques from robust MPC. We verified the proposed approach in both extensive simulation and quadrotor experiments. In experiments with a Crazyflie 2.0 drone, we show that, in addition to preserving the desired safety guarantees, the proposed MPSF reduces chattering by more than a factor of 4 compared to previous MPSF formulations., Comment: 8 pages, 9 figures. Accepted to IEEE CDC 2023. Code is publicly available at https://github.com/Federico-PizarroBejarano/safe-control-gym/tree/smooth_mpsc_paper

This paper introduces "GAIDE: Generative AI for Instructional Development and Education," a novel framework for using Generative AI (GenAI) to enhance educational content creation. GAIDE stands out by offering a practical approach for educators to produce diverse, engaging, and academically rigorous materials. It integrates GenAI into curriculum design, easing the workload of instructors and elevating material quality. With GAIDE, we present a distinct, adaptable model that harnesses technological progress in education, marking a step towards more efficient instructional development. Motivated by the demand for innovative educational content and the rise of GenAI use among students, this research tackles the challenge of adapting and integrating technology into teaching. GAIDE aims to streamline content development, encourage the creation of dynamic materials, and demonstrate GenAI's utility in instructional design. The framework is grounded in constructivist learning theory and TPCK, emphasizing the importance of integrating technology in a manner that complements pedagogical goals and content knowledge. Our approach aids educators in crafting effective GenAI prompts and guides them through interactions with GenAI tools, both of which are critical for generating high-quality, contextually appropriate content. Initial evaluations indicate GAIDE reduces time and effort in content creation, without compromising on the breadth or depth of the content. Moreover, the use of GenAI has shown promise in deterring conventional cheating methods, suggesting a positive impact on academic integrity and student engagement., Comment: 6 pages plus references. v4: Accepted for publication in Frontiers in Education 2024, includes referenced supplementary material. v3: updated title, some expanded discussion, added process flowchart. v2: fix 1 arXiv reference number

Over the last year, the ascent of Generative AI (GenAI) has raised concerns about its impact on core skill development, such as problem-solving and algorithmic thinking, in Computer Science students. Preliminary anonymous surveys show that at least 48.5% of our students use GenAI for homework. With the proliferation of these tools, the academic community must contemplate the appropriate role of these tools in education. Neglecting this might culminate in a phenomenon we term the "Junior-Year Wall," where students struggle in advanced courses due to prior over-dependence on GenAI. Instead of discouraging GenAI use, which may unintentionally foster covert usage, our research seeks to answer: "How can educators guide students' interactions with GenAI to preserve core skill development during their foundational academic years?" We introduce "AI-Lab," a pedagogical framework for guiding students in effectively leveraging GenAI within core collegiate programming courses. This framework accentuates GenAI's benefits and potential as a pedagogical instrument. By identifying and rectifying GenAI's errors, students enrich their learning process. Moreover, AI-Lab presents opportunities to use GenAI for tailored support such as topic introductions, detailed examples, corner case identification, rephrased explanations, and debugging assistance. Importantly, the framework highlights the risks of GenAI over-dependence, aiming to intrinsically motivate students towards balanced usage. This approach is premised on the idea that mere warnings of GenAI's potential failures may be misconstrued as instructional shortcomings rather than genuine tool limitations. Additionally, AI-Lab offers strategies for formulating prompts to elicit high-quality GenAI responses. For educators, AI-Lab provides mechanisms to explore students' perceptions of GenAI's role in their learning experience., Comment: 6 pages plus references and appendices

Open-sourcing research publications is a key enabler for the reproducibility of studies and the collective scientific progress of a research community. As all fields of science develop more advanced algorithms, we become more dependent on complex computational toolboxes -- sharing research ideas solely through equations and proofs is no longer sufficient to communicate scientific developments. Over the past years, several efforts have highlighted the importance and challenges of transparent and reproducible research; code sharing is one of the key necessities in such efforts. In this article, we study the impact of code release on scientific research and present statistics from three research communities: machine learning, robotics, and control. We found that, over a six-year period (2016-2021), the percentages of papers with code at major machine learning, robotics, and control conferences have at least doubled. Moreover, high-impact papers were generally supported by open-source codes. As an example, the top 1% of most cited papers at the Conference on Neural Information Processing Systems (NeurIPS) consistently included open-source codes. In addition, our analysis shows that popular code repositories generally come with high paper citations, which further highlights the coupling between code sharing and the impact of scientific research. While the trends are encouraging, we would like to continue to promote and increase our efforts toward transparent, reproducible research that accelerates innovation -- releasing code with our papers is a clear first step.