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This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint framework, we analyze the performance of these generalized algorithms in terms of worst-case robustness and convergence rate. The utility of our framework is demonstrated by showing how one of the extended algorithms, originally designed for consensus, is now able to solve a multitask inference problem. more...

This paper proposes model reduction approaches for consensus network systems based on a given clustering of the underlying graph. Namely, given a consensus network system of time-scaled agents evolving over a weighted undirected graph and a graph clustering, a parameterized reduced consensus network system is constructed with its edge weights and nodal time-scales as the parameters to be optimized. H-infinity- and H-2-based optimization approaches are proposed to select the reduced network parameters such that the corresponding approximation errors, i.e., the H-infinity- and H-2-norms of the error system, are minimized. The effectiveness of the proposed model reduction methods is illustrated via a numerical example., Comment: This paper is accepted for publication in the 2022 American Control Conference (ACC) more...

Nanoscale engineered materials combined with wearable wireless technologies can deliver a new level of health monitoring. A reduced graphene oxide-nylon composite material is developed and tested, demonstrating its usefulness as a material for sensors in wearable, long-term electrocardiogram (ECG) monitoring via a comparison to one of the widely used ECG sensors. The structural analysis by scanning electron (SEM) and atomic force microscopy (AFM) shows a limited number of defects on a macroscopic scale. Fourier Transform Infrared (FTIR) and Raman spectroscopy confirm the presence of rGOx, and the ratio of D- and G-features as a function of thickness correlates with the resistivity analysis. The negligible effect of the defects and the tunability of electrical and optical properties, together with live ECG data, demonstrate its signal transduction capability., Comment: 7 main text and 4 supporting figures, under review more...

This paper examines the $\mathcal{H}_\infty$ performance problem of the edge agreement protocol for networks of agents operating on independent time scales, connected by weighted edges, and corrupted by exogenous disturbances. $\mathcal{H}_\infty$-norm expressions and bounds are computed that are then used to derive new insights on network performance in terms of the effect of time scales and edge weights on disturbance rejection. We use our bounds to formulate a convex optimization problem for time scale and edge weight selection. Numerical examples are given to illustrate the applicability of the derived $\mathcal{H}_\infty$-norm bound expressions, and the optimization paradigm is illustrated via a formation control example involving non-homogeneous agents., Comment: 14 pages, 9 figures. Accepted to the European Journal of Control more...

This paper deals with the balanced truncation model reduction of discrete-time, linear time-varying, heterogeneous subsystems interconnected over finite arbitrary directed graphs. The information transfer between the subsystems is subject to a communication latency of one time-step. The presented method guarantees the preservation of the interconnection structure and further allows for its simplification. In addition to truncating temporal states associated with the subsystems, the method allows for the order reduction of spatial states associated with the interconnections between the subsystems and even the removal of whole interconnections. Upper bounds on the l2-induced norm of the resulting error system are derived. The proposed method is illustrated through an example., Comment: 16 pages, 4 figures, journal more...

The aim of this work is to prove that the connected parts of Farey complex structure in plane are triangles or quadrangles. To do this work we go back to plane convex polygones with oriented edge for wich we prove that if two consecutive vectors of the edge never are in the same quadrant, then the polygone is a triangle or a quadrangle. Then we prove that the connected parts of Farey complex have this property., Comment: in French, Expos\'e au s\'eeminaire de logique cat\'egorique, universit\'e Paris-Diderot Paris 20/03/2013 more...

Pipelines tubes are part of vital mechanical systems largely used in petrochemical industries. They serve to transport natural gases or liquids. They are cylindrical tubes and are submitted to the risks of corrosion due to high PH concentrations of the transported liquids in addition to fatigue cracks due to the alternation of pressure-depression of gas along the time, initiating therefore in the tubes body micro-cracks that can propagate abruptly to lead to failure. The development of the prognostic process for such systems increases largely their performance and their availability, as well decreases the global cost of their missions. Therefore, this paper deals with a new prognostic approach to improve the performance of these pipelines. Only the first mode of crack, that is, the opening mode, is considered. more...

Increasing the HMA base thickness and modifying the HMA mixture properties to improve the resistance to fatigue cracking are among the most popular methods for achieving long-lasting pavements. Such methods are based on the idea of reducing the tensile strain at the bottom of the HMA layer below the Fatigue Endurance Limit (FEL), a level of strain below which no cumulative damage occurs to the HMA mixture. This study investigates the effectiveness of several design strategies involved in long-life, perpetual pavement design. A 3D Finite Element model of the pavement involving a linear viscoelastic constitutive model for HMA materials and non-uniform tire contact stresses is developed using ABAQUS 6.11. The effects of asphalt base course thickness and mixture type, rich binder layer, and aggregate subbase layer are examined. Four asphalt base course mixture types, namely dense graded, polymer modified, high modulus, and standard binder, are studied as a function of the asphalt base course thickness. The results underline a better performance of the high-modulus asphalt base, as compared to the other base course mixtures. The aggregate subbase layer on top of subgrade soil showed a relatively minor effect on the longitudinal and lateral strain response at the bottom of asphalt base course. The addition of a rich binder layer at the bottom of the asphalt base course showed a significant reduction in tensile strains. Tables are provided as a guideline to assess the different alternatives in design of long-life perpetual pavements., Comment: This paper has been withdrawn by author more...

This paper examines the strain response of typical HMA overlays above jointed PCC slabs prone to bottom-up reflective cracking. The occurrence of reflective cracking under the combined effect of traffic and environmental loading significantly reduces the design life of the HMA overlays and can lead to its premature failure. In this context, viscoelastic material properties combined with cyclic vehicle loadings and pavement temperature distribution were implemented in a series of FE models in order to study the evolution of horizontal tensile and shear strains at the bottom of the HMA overlay. The effect of several design parameters, such as subbase and subgrade moduli, vehicle speed, overlay thickness, and temperature condition, on the horizontal and shear strain response was investigated. Results obtained show that the rate of horizontal and shear strain increase at the bottom of the HMA overlay drop with higher vehicle speed, higher subgrade modulus, and higher subbase modulus. Moreover, the rate of horizontal strain accumulation increases with higher overlay thickness. Although initial strain values were higher at positive pavement temperature distributions, the corresponding rate of strain increase were higher at negative pavement temperatures. Finally, an extrapolation of the strain history curve for various pavement design parameters was used to estimate the number of cycles for bottom-up crack initiation., Comment: This paper has been withdrawn by author more...