Formation flocking control and curl/divergence interpretation in second-order multi-agent networks

Manoeuvrable (or time-varying) formation control of second-order integral multi-agent networks with single virtual leaders is contrived by incorporating time-varying weighting matrices into flocking algorithms. Existence and properties are examined, including control bounded-ness, average trajectory and formation manoeuvrability with respect to the weighting matrices and virtual leader reference input. More specifically, it is shown that under the time-varying flocking algorithms, the multi-agents ultimately run into lattice formations and their kinematical features in terms of orientation, scaling, subspace specification and homogeneous/heterogeneous consensus can be manoeuvred. Moreover, by gain-scheduling assignment for the leader-average dynamics via the variation-of-constant formula and iterative learning optimisation, trajectory-tracking manoeuvrable formation control can be achieved. Technical advantages include: flexible formations rather than rigid ones can be dealt with; formation and trajectory tracking can be designed separately and implemented simultaneously; diverse formations are achievable by selecting the weighting matrices; trajectory-tracking control is independent of trajectory modelling. Numerical examples are illustrated to show the main results.

Impulsive consensus algorithms for second-order multi-agent networks with sampled information

The utilization of a conical target irradiated by a high power laser is proposed to study fast magnetic reconnection in relativistic plasma interactions. Such target, placed in front of the near critical density gas jet, splits the laser pulse, forming two parallel laser pulses in the 2D case and a donut shaped pulse in the 3D case. The magnetic annihilation and reconnection occur in the density downramp region of the subsequent gas jet. The magnetic field energy is converted into the particle kinetic energy. As a result, a backward accelerated electron beam is obtained as a signature of reconnection. The above mechanisms are demonstrated using particle-in-cell simulations in both 2D and 3D cases. Facilitating the synchronization of two laser beams, the proposed approach can be used in designing the corresponding experiments on studying fundamental problems of relativistic plasma physics.

This technical note presents a second-order multi-agent network for distributed optimization with a sum of convex objective functions subject to bound constraints. In the multi-agent network, the agents connect each others locally as an undirected graph and know only their own objectives and constraints. The multi-agent network is proved to be able to reach consensus to the optimal solution under mild assumptions. Moreover, the consensus of the multi-agent network is converted to the convergence of a dynamical system, which is proved using the Lyapunov method. Compared with existing multi-agent networks for optimization, the second-order multi-agent network herein is capable of solving more general constrained distributed optimization problems. Simulation results on two numerical examples are presented to substantiate the performance and characteristics of the multi-agent network.

Physics-informed neural networks (PINNs) are an emerging technology that can be used both in place of and in conjunction with conventional simulation methods. In this paper, we used PINNs to perform a forward simulation without leveraging known data. Our simulation was of a 2D natural convection-driven cavity using the vorticity-stream function formulation of the Navier-Stokes equations. We used both 2D simulations across the x and z domains at constant Rayleigh (Ra) numbers and 3D simulations across the x, z and Ra domains. The 3D simulation was tested for a PINN’s ability to learn solutions in a higher-dimensional space than standard simulations. The results were validated against published solutions at Ra values of 103\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{3}$$\\end{document}, 104\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{4}$$\\end{document}, 105\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{5}$$\\end{document}, and 106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{6}$$\\end{document}. Both the 2D simulations and 3D simulations successfully matched the expected results. For the 2D cases, more training iterations were needed for the model to converge at higher Ra values (105\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^5$$\\end{document} and 106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^6$$\\end{document}) than at lower Ra (103\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document} and 104\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^4$$\\end{document}) indicating increased nonlinear fluid-thermal coupling. The 3D case was also able to converge but, but it required more training than any of the 2D cases due to the curse of dimensionality. These results showed the validity of standard simulations via PINNs and the feasibility of higher-order parameter space solutions that are not possible using conventional methods. They also showcased the additional computational demand associated with increasing the dimensionality of the learned parameter space.

Comparison of ultrasonic attenuation within two- and three-dimensional polycrystalline media

The incompressible, steady, turbulent flow around an external aerial pod was analyzed in order to optimize the pod's geometry for minimum drag, which is important to reduce its effect on the aircraft's performance. The computations were conducted in a 2-dimentional axisymmetric and 3-dimentional computational domains using ANSYS-Fluent k-ω SST turbulence model for high Reynolds number, Re > 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> • The flow properties were selected at sea level conditions. The results revealed that both 2D and 3D simulations showed similar qualitative behavior for the drag variation along different dimensions of the pod. The optimal length of the pod in 2D was 11% shorter than the 3D simulations. Moreover, the 2D simulations over-predicted the drag compared to the same cases in 3D.

A parametric, three-dimensional, computational study examining steady state performance of a planar plug micronozzle is conducted. Nozzle depth and throat Reynolds number are varied for a single plug contour designed using an approximation for the Method of Characteristics. The Reynolds number is varied from 80 − 820, for nozzle depths of 90μm-360μm. Thrust and specific impulse are used as metrics to assess nozzle performance. Results from 3D simulation are compared to 2D simulation for the same planar geometry and 3D results for a 30◦ linear-walled nozzle of the same throat size. For all Reynolds numbers examined, 3D nozzles were found to under-perform the 2D case. The margin between the 3D and 2D cases decreases with increasing nozzle depth. The 3D plug nozzle outperforms the 3D 30◦ linear-walled nozzle in both 2D and 3D simulation for the range of Reynolds numbers examined.

Asynchronous impulsive control for consensus of second-order multi-agent networks

In recent years the role of FSI (fluid-structure interaction) simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary Lagrangian-Eulerian) or an Eulerian formulation. The majority of the reported 3D heart valve FSI simulations are performed with the Eulerian formulation, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an Eulerian-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations’ outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE formulation, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results.

Simulation calibration of modern engines to test bench measurements, mainly matching the indicated pressure curves in the combustion chamber, is a time consuming task that requires high user experience to manage a multitude of adjustment parameters. In the scope of this work an automated process for calibrating simulations at motored engine operating points is presented. This is achieved using characteristic pressure deviation curves, based on 1D simulations of a simplified base model. They incorporate the dimensionless deviation of the cylinder pressure originating from one parameter. A set of these curves is scaled and superposed to recreate the original pressure deviation between simulation and measurement. The scaling factor is used to quantify each parameter’s suggested adjustment value. This work presents the workflow of creating the characteristic pressure deviation curves, matching the deviation between measurement and simulation and determining the adjustment values. Further, the methodology is tested for interference of different parameters. A series of applications, ranging from 1D and 3D CFD simulation test cases to real world applications in different engines, concludes this work.

The ability to use supercritical fluids as a heat transfer medium has benefits near the critical point as the specific heat and thermal conductivity approach infinity. However, because of these large thermodynamic property variations estimates for the heat transfer coefficients and wall temperatures can be difficult. With large changes in thermodynamic properties, threedimensional simulations have been used for heat transfer predictions, which can be time-consuming and computationally expensive. To reduce computational expenses, a comparison is made between 2D-axisymmetric and 3D horizontal round tubes using STAR CCM+ 2206. 2D and 3D cases are investigated at various inlet temperatures, mass fluxes, heat-flux to mass-flux ratios, pipe diameters, and pressures to investigate the impact on axisymmetric simulation approximations. A comparison between 3D and 2D-axisymmetric simulations for the circumferentially averaged heat transfer coefficients, Richardson number, and expected pressure drop is made. Across all cases, the maximum percent difference in heat transfer coefficient was 9.4% for an inlet temperature of 295 K, mass flux of 400 kg · m−2 · s−1, operating pressure of 7.5 MPa, applied heat flux of 32 kW · m−2, through a 6 mm pipe. At an inlet temperature of 295 K, a mass flux of 200 kg · m−2 · s−1, an operating pressure of 8 MPa and an applied heat flux of 12 kW · m−2 through a 2 mm pipe, the maximum percent difference in Richardson number was 40.87%. With an inlet temperature of 307 K, mass flux of 600 kg · m−2 · s−1, an operating pressure of 8 MPa, and applied heat flux of 36 kW · m−2, through a 12 mm pipe, the maximum percent difference in pressure drop was 16.87%. The utilization of 2D-axisymmetric domains for supercritical fluids can reduce computational expenses while producing similar results to their 3D counterparts within 40% depending on parameter.

On fast queue consensus of discrete-time second-order multi-agent networks over directed topologies

A multiconsensus problem of multiagent networks is solved in this paper, where multiconsensus refers to that the states of multiple agents in each subnetwork asymptotically converge to an individual consistent value when there exist information exchanges among subnetworks. A distributed impulsive protocol is proposed to achieve multiconsensus of second-order multiagent networks in terms of three categories: 1) stationary multiconsensus; 2) the first dynamic multiconsensus; and 3) the second dynamic multiconsensus. This impulsive protocol utilizes only sampled position data and is implemented at sampling instants. For those three categories of multiconsensus, the control parameters in the impulsive protocol are designed, respectively. Moreover, necessary and sufficient conditions are derived, under which each multiconsensus can be reached asymptotically. Several simulations are finally provided to demonstrate the effectiveness of the obtained theoretical results.

A finite-volume method for simulating contact lines on unstructured meshes in a conservative level-set framework