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Boundary Output Feedback Stabilization of Nonlinear Diffusion Equations
No full textInternational audienceThis paper studies the problem of output feedback stabilization of a nonlinear diffusion equation, generally referred to as the generalized porous media equation. This equation occurs in a number of physical phenomena involving fluid flow, heat transfer or nonlinear diffusion. The generalized porous media equation differs from classical reaction-diffusion equations due to the presence of a nonlinear version of the Laplacian operator. This nonlinearity induces numerous challenges in terms of stability assessment and control design. In this context, the present paper reports one of the very first contributions regarding the output feedback control of the porous media equation. The reported approach takes advantage of the monotonicity property of the nonlinearity and adopts a perturbation-based approach by leveraging spectral reduction methods
Collaborative Action on Timing InterferenCes: Summary and Perspectives at Mid-term
No full textInternational audienceCAOTIC is an ambitious initiative aimed at pooling and coordinating the efforts of major French research teams working on timing analysis of multicore real-time systems, with a focus on interference due to shared resources. The objective is to enable the efficient use of multicores in critical systems. Based on a better understanding of timing anomalies and interference, considering the specificities of applications (structural properties and execution model), and revisiting the links between timing analysis and synthesis processes (code generation, mapping, scheduling), we target significant progresses in timing analysis models and techniques for critical systems, as well as in methodologies for their application in industry. In this paper, at project mid-term, we show the progress of the project. We also present some original work, about the use of a Tricore plaform and its timing model, and discuss open questions and future work
Agile Laser Wavelength Tuning Using Dynamic Targeting
No full textInternational audienceTunable lasers are essential and versatile tools in photonics, with applications including telecommunications, spectroscopy, and sensing. Advancements have aimed to precisely control the lasing wavelength, expand tuning ranges, suppress mode hopping, and enable photonic integration. In this work, we explore the adaptation of dynamic targeting, a technique originally developed to stabilize lasers under optical feedback, as a method for achieving agile, fast, and continuous wavelength tuning. This technique works by adjusting the feedback rate and phase, enabling a stable and controlled frequency shift. We experimentally demonstrate reliable and reproducible tuning over 2.1 GHz using a free-space optical setup. Simulations further suggest that this approach could extend the tuning range to tens of GHz, with a potential scan speed exceeding 10 17 Hz/s. These results highlight dynamic targeting as a promising route toward agile frequency control in semiconductor lasers for photonic integrated circuits
On the identification of rigid body boundary conditions from full-field measurements
No full textInternational audienceThis study presents a method to identify Dirichlet boundary conditions (BCs) and constitutive parameters from heterogeneous experimental data, solving a multi-objective optimization problem. The BCs are parameterized as remote rigid body motions leading to a very low number of unknowns and allowing for faster convergence. This methods enables for accurate models of material and structural tests to be obtained. A comparison with classical methods of BC determination is introduced, demonstrating the advantages of the proposed approach. The identified models are evaluated by introducing a validation metric based on experimental data and their uncertainties. The approach is illustrated by using a multi-instrumented tensile test on a well-characterized material. Beyond this validation example, the introduced method paves the way for improved model updating of large-scale tests
A Hybrid Message-level Modeling Approach for Fast Yet Accurate Simulation of Multiprocessor Shared Bus Effects on Data Flow Applications Execution
No full textInternational audienceFast yet accurate performance and timing prediction of complex parallel data flow applications on multiprocessor systems remains a challenging discipline. The main reason is that the applications contain numerous degrees of parallelism (task, pipeline, data) but they necessitate sharing resources, such as communication buses and memories, within execution platforms. Executing such applications on resource-limited platforms leads to timing interferences that are difficult to accurately express in pure analytical approaches or to excessive simulation duration for cycle-accurate models. In this work, we propose a message-level communication model for fast yet accurate performance prediction for data flow applications executed on MPSoCs with shared memories and buses. This approach combines a high level executable model of the communication infrastructure with a formal description of the synchronization instants related to low-level communication mechanisms. This combination significantly reduces the number of simulation events while still accurately predicting the effects of contention at shared resources. We evaluated our work against measurements from a real prototype and cycle-accurate performance prediction models on two case-studies from the computer vision domain. We illustrated how the computational complexity of our approach can be adapted to deliver high simulation efficiency. In our experiment, we achieved an average accuracy of 99% in latency prediction compared to real implementation for the different use-cases and mappings we considered. In the experiments where the approach is used with limited computational complexity, simulation speed-ups of an order of magnitude of 104 compared to cycle-accurate models are achieved, while maintaining a fully acceptable accuracy (more than 98%). Good suitability for fast and accurate exploration of the design space is demonstrated by the proposed models
Components Operationally: Reversibility and System Engineering: Essays Dedicated to Jean-Bernard Stefani on the Occasion of His 65th Birthday
No full textInternational audienc
Correctly rounded evaluation of a function: why, how, and at what cost?
No full textThe two accompanying files are: - The SageMath code computing upper bounds for the hardness to round of exp, trigonometric and hyperbolic functions over the firstfew binades surrounding 1;- the LACoR library that implements the BH algorithm for computing upper bounds on the hardness to roundInternational audienceThe goal of this article is to give a survey on the various computational and mathematical issues and progress related to the problem of providing efficient correctly rounded elementary functions in floating-point arithmetic. We also aim at convincing the reader that a future standard for floating-point arithmetic should require the availability of a correctly rounded version of a well-chosen core set of elementary functions. We discuss the interest and feasibility of this requirement
On Detecting Elastoplastic Shakedown Using Minimal Digital Image Correlation Results and an Elastic Model: Demonstration for AA6061 Auxetic Sheets
No full textInternational audienceBackground. Shakedown occurs in elastoplastic bodies subject to cyclic loading when limited plastic deformation in the early stages of cycling gives rise to residual stresses that arrest the plastic response. As a result, purely elastic behavior is recovered upon further load cycling.Objective. This paper outlines a new procedure for identifying macroscopic shakedown responses using minimal kinematic measurements from digital image correlation and a purely elastic finite element model.Method. In contrast to traditional shakedown detection methods that track the evolution of total or equivalent plastic strains upon cycling, the proposed approach obviates assumptions about the inelastic nature of the constituent material of interest altogether. The proposed approach is inspired by Melan's static lower bound shakedown theorem and it offers advantages in terms of computational and experimental effort, providing robustness against material uncertainties, and flexibility for a variety of applications.Results. The approach is demonstrated on aluminum metamaterial sheets that are auxetic due to their arrangement of periodic perforations. In the demonstration, a set of uniaxial experiments at room temperature are analyzed where a range of cyclic stress amplitudes are imposed at non-zero mean stresses.Conclusions. The proposed shakedown determination protocol was verified by comparing with traditional methods that track the incremental evolution of equivalent plastic strain. The new procedure provides a rapid and robust approach that is suitable for high-throughput experimentation
Boundary output feedback stabilization of a cascade of N heat equations
No full textInternational audienceThis paper solves the problem of output feedback stabilization for a cascade of N heat equations that are coupled at the boundary, the input being a scalar boundary control applied to the first heat equation of the cascade, and the scalar output being either a distributed or a pointwise in-domain measurement done on the last equation of the cascade. Two different configurations are studied in details. The first one consists of a cascade of N heat equations with totally disconnected spectra. The second one consists of a cascade of N identical heat equations, inducing eigenvalues of multiplicity N . In both cases, the problem is solved thanks to a spectral analysis and a study of the modal controllability and observability properties. The key point is that the generalized eigenvectors form a Riesz basis of the state space. The stabilization property is established in L^2 and H^1 norms
Dispersion in porous media with porosity gradients
No full textHeterogeneous porous media are found in many engineering and natural processes, either by design to improve the efficiency of the system, or as a consequence of the process itself. Here, we focus on dispersive transport in porous media displaying spatially evolving heterogeneities, characterized by continuous spatial variations of their properties. Using upscaling, we derive the macroscopic transport equations for momentum and species dispersion and identify additional terms implying spatial derivatives of the porosity. While these terms do not influence the definition of the effective diffusion-dispersion tensor, we find that they remain in the closure problems for momentum transport and lead to the definition of two new effective permeability tensors. Length-scale considerations show that the closure problems for momentum transport can be simplified to facilitate their solving. To assess the validity of the derived model, we solve the macroscopic transport equations in a stationary dispersive mixing process: a Y-junction mixing chamber filled with porous media with spatially evolving heterogeneities. The consequences of distribution and strength of the porosity gradients on fluid velocity and concentration field are systematically compared to direct numerical simulations for various Péclet numbers, showing excellent agreement even in disordered porous media. Notably, we show that Péclet-dependent non-symmetric mixing layers can be produced using porous media with controlled porosity gradients. Our results highlight the potential for the development of novel industrial processes utilizing porous media with spatially evolving heterogeneities such as continuous flow chemistry