Keywords: Infinite-dimensional Systems and PDEs Models, Impulsive Systems, Robust Control
Abstract: This paper tackles the stability analysis of a system driven by linear ordinary differential equation coupled to a one-dimensional heat equation. The particularity of this study concerns the nature of the coupling, which is performed using an event-triggered scheme, through a boundary condition of the partial differential equation. After proving the existence and regularity of solutions of the system, the idea is to introduce an enriched energy functional as a candidate Lyapunov functional to prove the exponential stability. Actually, we will obtain a sufficient stability condition expressed as a linear matrix inequality to satisfy. This condition is suitable for solving an emulation problem corresponding to the appropriate tuning of the event-triggered control. Our result is finally illustrated with a numerical example.

Keywords: Process Control and Chemical Processes, Robust Analysis and Control, Simulation
Abstract: Hydrogen, recognized as a clean and efficient energy source, is a promising alternative fuel due to its environmental benefits. This paper explores the hydrocarbon pyrolysis, with a focus on ethane pyrolysis for hydrogen generation. A novel structure control system is proposed, comprising numerical and supervisory levels, to optimize hydrogen extraction. The methodology incorporates process modelling, polynomial control design, and supervisory mechanisms, validated through simulations and experimental testing. The study emphasizes the potential for implementing this solution in existing petrochemical platforms, reinforcing hydrogen’s role in sustainable energy production.

Keywords: Challenges for Industry and Education, Control Education Strategies
Abstract: This paper presents a novel approach for engaging undergraduate students in the field of Control Engineering, by providing compelling real-world examples. This project-based learning is illustrated through the specific case-study of an industrial project undertaken by undergraduate students in CentraleSupélec, Paris-Saclay University.

Keywords: Control Courses and Labs, Outreach in Control Education and Engineering, Challenges for Industry and Education
Abstract: Bioprocesses offer promising answers within the framework of sustainable development. This paper presents a course on advanced estimation and control strategies for microorganism cultivation in bioreactors. The course, part of CentraleSupélec's engineering education program, aims to equip students with skills to optimize bioreactor performance. Despite decades of research, industrial implementation of advanced control strategies remains limited, with only basic controls used. This course addresses this gap, providing students with comprehensive knowledge of optimal bioreactor operation for sustainable applications. Offered as an elective, it focuses on advanced control strategies tailored for this kind of system. It covers a wide range of theoretical concepts for nonlinear systems, such as Kalman filtering, asymptotic observers, model predictive control, input-output linearizing control, adaptive control, and experimental and analytical optimization. The main goal is to provide students with the skills that could help them to address environmental challenges.

Keywords: Multivariable Systems, Drilling Systems, Vibration and Control, Simulation
Abstract: Vibration management has become a critical issue in the construction of new ground-based telescopes. Due to the increase of the primary mirrors and the improvement of their facilities, not being limited by the light gathering capacity of the telescope's own optics, the effects of telescope vibrations on image stability are henceforth perceptible. In the case of large telescopes, commonly equipped with an adaptive optics (AO) system to obtain near-diffraction-limited images, the effects of vibrations in both amplitude and frequency distribution must be assessed to avoid limiting the correction capacity of AO. This requires a strategy to characterize the potential impact of vibrations on image stability. This paper presents a novel strategy for vibration management during the design phase of ground-based telescopes. A use case for the European Solar Telescope (EST) is outlined in this document. First, the proposed criterion to allocate vibrations in different locations of the telescope is described. As EST is currently in the preliminary design phase, the use of models emerges as a significant support for project development. Main models involved in the proposed strategy to analyze the effects of vibration in image stability are presented. Preliminary simulation-based results obtained, and their applicability along the design of the telescope, are also discussed.

Keywords: Functional Systems, Time-varying Systems
Abstract: In this talk, we discuss the fundamental theorem of calculus and its algebraic implications in differential rings, focusing on functions with singularities and a generalized notion of evaluation. We give an overview of integro-differential rings and operators, deriving normal forms and identities using rewrite rules. This approach generalizes results like shuffle relations for nested integrals and the Taylor formula, incorporating additional terms for singularities. We also examine linear ODEs within this framework, extending to systems of arbitrary size with matrix coefficients. This talk is based on joint work with Clemens Raab.

Keywords: Model Predictive Control, Control
Abstract: Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant coefficients. The control task is formulated as an inference problem by conditioning the Gaussian process prior on the setpoints and incorporating pointwise soft-constraints as further virtual setpoints. We apply this method to systems of nonlinear differential equations, obtaining local approximations through linearization around equilibrium points. In the case of asymptotically stable equilibrium points convergence is given through the Bayesian inference schema of the Gaussian Process. Results for this are demonstrated in a numerical example.

Keywords: Infinite-dimensional Systems and PDEs Models, Other Applications of Linear and Fractional Systems
Abstract: This paper introduces a computationally efficient algorithm in systems theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors defined based on advanced commutative algebra and algebraic analysis. The implementation of these priors is algorithmic and achieved using the Macaulay2 computer algebra software. An example application includes identifying the wave speed from noisy data for classical wave equations, which are widely used in physics. The method achieves high accuracy while enhancing computational efficiency.

Keywords: Time-invariant Systems
Abstract: The computation of the ( L^infty )-norm is an important issue in H_{infty} control, particularly for analyzing system stability and robustness. This paper focuses on symbolic computation methods for determining the ( L^infty )-norm of finite-dimensional linear systems, highlighting their advantages in achieving exact solutions where numerical methods often encounter limitations. Key techniques such as Sturm-Habicht sequences, Rational Univariate Representations (RUR), and Cylindrical Algebraic Decomposition (CAD) are surveyed, with an emphasis on their theoretical foundations, practical implementations, and specific applicability to ( L^infty )-norm computation. A comparative analysis is conducted between symbolic and conventional numerical approaches, underscoring scenarios in which symbolic computation provides superior accuracy, particularly in parametric cases. Benchmark evaluations reveal the strengths and limitations of both approaches, offering insights into the trade-offs involved. Finally, the discussion addresses the challenges of symbolic computation and explores future opportunities for its integration into control theory, particularly for robust and stable system analysis.

Keywords: Parameter Estimation, Observers and State Estimation, Identification
Abstract: To estimate parameters in ODE systems from noisy data, we propose adding a Gaussian Process Regression (GPR) step to an approach based on differential algebra. This replaces the interpolation step in the original algorithm and allows for more reliable estimation even in the presence of noise. We tested the method on a suite of benchmark problems from multiple disciplines. With GPR, we are able to retain the robust features inherent in the algebraic approach, while extending applicability to realistic data with noise.

Keywords: Symbolic Computation and Control, Fault Diagnosis and Fault Tolerant Control, Periodic Systems
Abstract: Combining methods from linear algebra, algebraic geometry, computer algebra, module theory, and homological algebra, in this paper, we characterize the general solutions of ideal demodulation problems arising in gearbox vibration analysis. More precisely, within the frequency domain, the separation of the toothed gearbox vibration from the measured signal raises the problem of finding a centrohermitian column vector u and r centrohermitian row vectors v_1, ..., v_r which minimize the Frobenius norm || D_1 u v_1 + D_2 u v_2 + ... + D_r u v_r - M||_Frobenius, where M is a centrohermitian matrix defined by the measurement and the D_i's are fixed centrohermitian matrices which depend on the demodulation problem under-study. To study this polynomial optimal problem, in a series of papers, the rank factorization problem corresponding to solving the ideal case, i.e., to finding u and v_1, ..., v_r satisfying D_1 u v_1 + D_2 u v_2 + ... + D_r u v_r = M, was investigated. Partial characterizations of the solutions were obtained. This paper aims at characterizing the general solutions to the rank factorization problem. The results obtained are implemented in the dedicated Maple package RankFactorizationProblem.

Keywords: Predictor-based Control, Delay Compensation
Abstract: We develop an input delay-compensating feedback law for linear switched systems with time-dependent switching. Because the future values of the switching signal, which are needed for constructing an exact predictor-feedback law, may be unavailable at current time, the key design challenge is how to construct a proper predictor state. We resolve this challenge constructing an average predictor-based feedback law, which may be viewed as an exact predictor-feedback law for a particular average system without switching. We establish that, under the predictor-based control law introduced, the closed-loop system is exponentially stable, provided that the plant's parameters are sufficiently close to the corresponding parameters of the average system. In particular, the allowable difference is inversely proportional to the size of delay and proportional to the dwell time of the switching signal. Since no restriction is imposed on the size of delay or dwell time themselves, such a limitation on the parameters of each mode is inherent to the problem considered (in which no a priori information on the switching signal is available), and thus, it cannot be removed. The stability proof relies on two main ingredients—a Lyapunov functional constructed via backstepping and derivation of solutions' estimates for the difference between the average and the exact predictor states. We present consistent, numerical simulation results, which illustrate the necessity of employing the average predictor-based law for achieving stabilization and desired performance of the closed-loop system.

Keywords: Stabilization, Control Design, Robust Analysis
Abstract: Two control designs of exponentially stabilizing feedbacks for two families of time- varying continuous-time systems with a pointwise delay in the input are proposed. A smallness condition is imposed on the delay. In contrast to the classical reduction model approach, the results do not necessitate knowledge of the state transition matrix.

Keywords: PID Control, Time-varying Delays, Control Design
Abstract: PID control represents a widely used methodology in many industrial applications including among others processes with delays in the input-output channels. For such processes, it is well-accepted that large delays are at the origin of bad performance, and it is important to have a better understanding of the effects induced by the delays on the dynamical behavior of the closed-loop system. Furthermore, these delays may be uncertain and time-varying. In this work, we present robust and least-fragile PI controller design against uncertain time-varying delays. In particular, we will explicit construct such controllers for a class of delay systems modeling a coupled tanks system.

Keywords: Hybrid Systems and Delays, Sampled-Data and Delays, Predictor-based Control
Abstract: This research aims to develop a solution for controlling disturbed linear systems with delayed control inputs and discrete output measurements by using a hybrid state dynamic predictor. The predictor is based on an impulsive observer framework and integrates a novel discrete system to approximate the delays. Conditions for the convergence of prediction errors within the hybrid system were established. Using these predictor variables, a sliding mode controller (SMC) is designed. The closed-loop system is thoroughly analyzed using the Lyapunov stability method. Simulations on systems with delays confirm the effectiveness of the proposed method.

Keywords: Control Design, Robust Analysis, Time-domain Methods
Abstract: This paper deals with the problem of stabilizing linear systems with delayed input using a data-driven control design. The main idea is to provide a stabilization condition expressed in terms of linear matrix inequalities resulting from the application of the Lyapunov-Krasovskii theorem and using only prior data experiments. The uncertainties of the system encapsulated in the data are encoded in a quadratic constraint. The method allows the identification of the system matrices as well as the delay, using the least-square approximation error. An example of a sampled-data batch reactor illustrates and validates the proposed methodology.

Keywords: Time-domain Methods
Abstract: This paper investigates the smooth, memoryless, time-varying control design for a class of chained nonholonomic systems, comprising a linear subsystem and a bilinear chained subsystem with input delays. For the linear subsystem, a smooth, memoryless, nonhomogeneous control law is proposed by leveraging certain properties of parametric Lyapunov equations, ensuring exponential convergence. The bilinear chained subsystem is then transformed into a linear time-varying system via a linear time-varying state transformation. By exploiting the structural properties of nonholonomic systems and employing the Razumikhin stability theorem, a smooth, linear, memoryless, time-varying controller is developed. The effectiveness of the proposed methods is demonstrated using a model of an underactuated axisymmetric spacecraft.

Keywords: Frequency-domain Methods, Stabilization, Robust Analysis
Abstract: This paper aims to highlight connections between projective geometry and stabilization problems. Within the fractional representation approach, we introduce the definition of the projective line Proj(A) over a ring A of proper and stable transfer functions and the definition of the projective line Proj(K) over the quotient field K of A. We show that the groups of homographies of these projective lines correspond to the Möbius transformations defined over A or K. We generalize the definitions of a well-posed system and internal stabilizability to consider plants defined over Proj(K). The vanishing of the denominator of a plant or controller is no longer considered a pathological case, and the Youla-Kucera parameterization of all stabilizing controllers is shown to be always well-defined. Finally, we show that the points of Proj(A) can be interpreted as transfer functions with coprime factorizations. Concepts of projective geometry, such as distant relation and distant graph on Proj(A), are introduced, and their system-theoretic interpretations are given.

Keywords: Frequency-domain Methods, Stabilization, Robust Analysis
Abstract: Within the fractional representation approach, a fractional ideal can naturally be attached to a linear system defined by a transfer function. System properties are then reflected in the algebraic properties of this fractional ideal. Therefore, standard algebraic methods can be used to study system properties in detail. This paper studies the equivalence of systems corresponding to isomorphic associated fractional ideals. These natural equivalences bijectively transform a system into systems sharing the structural properties. This paper proves that these equivalences are defined by two kinds of M"obius transformations. Finally, this result is used to show how a stabilizing controller or a (weakly) coprime factorization is transformed by the application of these M"obius transformations.

Keywords: Modeling and Identification, Control Design, Approximation Methods
Abstract: Model predictive control (MPC) is a popular control engineering practice, but requires a sound knowledge of the model. Model-free predictive control (MFPC), a burning issue today, also related to reinforcement learning (RL) in AI, is reformulated here via a linear differential equation with constant coefficients, thanks to a new perspective on optimal control combined with recent advances in the field of model-free control (MFC). It is replacing Dynamic Programming, the Hamilton-Jacobi-Bellman equation, and Pontryagin's Maximum Principle. The computing burden is low. The implementation is straightforward. Two nonlinear examples, a chemical reactor and a two tank system, are illustrating our approach. A comparison with the HEOL setting, where some expertise of the process model is needed, shows only a slight superiority of the later. A recent identification of the two tank system via a complex ANN architecture might indicate that a full modeling and the corresponding machine learning mechanism are not always necessary neither in control, nor, more generally, in AI.

Keywords: Control Design, Approximation Methods, Sampled-Data and Delays
Abstract: This paper aims to develop the connections between the discretization schemes of continuous linear differential time-delay systems and the inverse image functor (which has been well-studied in algebraic geometry, topology, and algebraic analysis). Using methods from module theory and homological algebra, we first introduce a mathematical framework to study how discretization schemes preserve or lose structural properties of linear differential time-delay systems. We then show how this problem of torsion-free controllability advocates for a future algorithmic study of the composition of two standard functors (duality and torsion product) and the so-called Grothendieck's spectral sequence associated with this functor composition.

Keywords: Infinite-dimensional Systems and Delays, Stabilization
Abstract: In this paper, we study the interplay between controllability (in particular, spectral controllability) and discretization for the wave equation with boundary control. First, we recall how it can be transformed into an equivalent linear delay system and show how varying polynomial operators allows recovering diverse boundary conditions. Then, by analyzing the delay system associated with the wave equation, we examine controllability properties, focusing on whether controllability is preserved under discretization. We show that, depending on the polynomials defining the boundary conditions, the same discretization scheme can lead to different outcomes: a spectrally controllable continuous-time partial differential equation (viewed as an appropriate delay system) may result in either a controllable discretized system or a non-controllable one, regardless of the discretization period.

Keywords: Observation and Observer Design, Modeling and Identification
Abstract: The present work revisits the Kalman/Luenberger observer design and proposes a parametrization of its observer gain through differential algebraic methods. In most practical cases observer gain is advantageously calculated through the so-called optimization methods consisting of solving a non-differential Riccati equation where the potential difficulties remain in the choice of weighting or uncertainty covariance matrices. In possible other situations it may be of interest to have at hand a straightforward parametrization of the observer gain. The unanswered theoretical question then is how to solve the under-determined equations specifying the observer gain in the multi-output case. Here it is proposed a solution which is purely based upon the differential algebraic geometry approach of observations problems which has been introduced for general nonlinear systems.

Keywords: Art and Engineering, Control Education
Abstract: Studies have shown the advantages of combining Art and Science allowing a greater range of engagement by students across multiple senses and thus improving their long term retention and understanding of complex scientific notions, as well as the potential to reach out to broader audiences. This paper offers some insights from the oosCaR - 2D Animated Cartoons for Control Education Rise project. The goal of this project is to develop 2D animated cartoons on Control to both motivate engineering students to pursue further studies in Control and also to help them better appreciate some of the foundational concepts. In consequence, the authors hope this will increase the impact of Control on the younger generation.

Keywords: Art and Engineering, Control Education
Abstract: Improving the learning of Control theory among the younger generation requires to rethink the teaching methods completely. Presenting complex scientific concepts in an attractive way to young students, while remaining rigorous, is a challenge for the Control education community. Integrating Art and humor in developing Control resources has the advantage of helping students to better understand the main concepts in system modeling and Control in a funny and engaging manner. This paper focuses on the creation of Control cartoons for undergraduate students in CentraleSupélec, Paris-Saclay University, and provides feedback on the cartoons development phase.

Keywords: Art and Engineering
Abstract: Art, one of the oldest forms of human expression, has continuously evolved, embracing new forms and techniques throughout history. The precision and versatility of robots make them ideal tools for artists. The STRAD (STReet Art Drone) project aims to craft a 10-meter-high mural on a vertical surface with sub-centimetric precision. To achieve this goal, we designed an Aerial Manipulator with Elastic Suspension coupled with an elliptic pulley-counterweight mechanism, allowing the manipulator to transition smoothly between equilibrium positions using only its thrusters. A bouncing pointillism method has also been explored using a modified quadcopter.

Keywords: Art and Engineering
Abstract: The Thermodance project combines dance and scientific pedagogy to (i) develop modeling approaches based on the participants body movement and interaction, (ii) practice scientific intuition by putting the participants into movement (principles of embodied cognition), (iii) produce immersive outreach activities to engage the public through dance, and (iv) co-create choreographies inspired from the developed body-based models and their underlying scientific concepts. Since 2022, several courses and workshops have been held with students and participants from a wide range of backgrounds. Each occurrence concluded with an open performance during which the audience was invited to actively participate, manipulate, feel and embody scientific concepts through dance. Participants showed great engagement in scientific practice, and self-reported improvements in conceptual comprehension and scientific curiosity. Through this practice, scientists, students, and the general public are invited to focus on feeling, sensations and intuition, offering an alternative and accessible approach to advanced scientific concepts.

Keywords: Art and Engineering
Abstract: Mechanics, a compulsory module in engineering curricula, is often seen as challenging due to complex equations and traditional examples. This paper proposes a blend of art, engineering and gamification to make the subject more tangible. Two approaches are highlighted: 3D printed hands-on demonstrators for teaching and gamification through escape room formats for outreach. These tools and outcomes are shared via open source platforms and social media for wide accessibility. Positive evaluation data confirm the effectiveness of the measures. Additionally, womxn empowerment through networking and creative theater play are presented.

Keywords: Art and Engineering, Human Machine Systems, Networked Systems
Abstract: Immersive experiences and art installations are becoming ever more popular. While they are usually developed using specialized technology (such as head-mounted displays) or dedicated, fully controlled environments (often black rooms with video projections on the walls and floor), the implementation of immersive installations in open, public spaces (such as city squares or shopping malls) remains a particularly challenging and interesting task: How to deal with unfavorable conditions on site (noise, stray light etc.) and how to effectively engage passers-by? In this paper, we present the generative evolutive interactive installation Ariadne’s Fibres, located in one of the busiest shopping malls in Paris, France. With advanced tracking of passers-by, it provides a unique experimental platform for field research on what may catch attention and trigger immersion. In this context, Ariadne’s Fibres is part of an ongoing study investigating, through trajectory analysis and questionnaires, the key parameters for immersion in open, public spaces.

Keywords: Art and Engineering, Human Machine Systems, Networked Systems
Abstract: At La Nuit Blanche 2024, visitors discovered The Eye of the Sun, a giant eye that stared at them and followed them. It was curious about them, inviting them to come closer to touch it and unveil what was hiding inside. The Eye appeared to the visitors as an autonomous agent and naturally invited engagement and interaction. Here, we briefly present the technology and control systems involved in The Eye and open up connections towards user experience studies around immersive, interactive artworks.

Keywords: Art and Engineering, Human Machine Systems, Networked Systems
Abstract: Advances in immersive technology continue to enrich the breadth, depth, and intensity of the audience experience. The L∞p is a 360-degree immersive and interactive stage for the creation and dissemination of new augmented forms of live performance and digital installation that engage artists, scientists, and audiences, say experiencers, in an unconstrained multi-sensory collective experience. In one of the settings, experiencers stepped into Spacetime Prospectives, a series of tales about time and space as differently described by physics. With The L∞p, we intend to set the experiencers' imaginations in motion and augment the experience of time and space in many ways.