Bounded Consensus Tracking of Heterogeneous Multiagent Systems Under Digraphs With Diverse Communication and Input Delays.

We study the bounded consensus tracking problem for the heterogeneous multiagent system composed of single- and double-integrator agents in the presence of diverse communication and input delays. The objective is to ensure bounded tracking when only a portion of agents has access to the desired trajectory while agents interact with each other through a directed communication network. To achieve this goal, we propose a protocol consisting of a consensus-based trajectory estimator followed by a controller tracking the estimated trajectory for each agent. Though the agents involved in the mission are heterogeneous, the estimators of all the agents are designed as coupled single integrators to provide estimates of the acceleration, velocity, and position along the desired trajectory. The coupled single-integrator estimator followed by the tracking controller strategy leads to a decoupling whereby the allowable estimator gains for an agent depend only on its communication delays and its controller gains depend only on its input delay. The tracking errors remain bounded even if the desired acceleration is unknown to all the agents. Simulation results are carried out to validate the proposed consensus tracking algorithm.

Coupled plate-string vibrations in the presence of a finite bridge: Effect on natural frequencies and harmonicity.

Harmonicity of natural frequencies is investigated for a string vibrating against a finite bridge mounted on a flexible plate. This coupled system is akin to the vibration of strings in musical instruments like the sitar, where the top plate is approximated as a clamped circular plate. The bridge is assumed to be parabolic and rigidly attached to the plate at one point. For simplicity, the plate is replaced by linear and torsional springs with frequency dependent dynamic stiffness to account for the continuous nature of the plate. Governing equations of motions are obtained using Hamilton's principle, which are linearized about the static configuration. It is observed that the coupled natural frequencies below the first structural frequencies are inharmonic in a manner opposed to the inharmonicity due to the bending rigidity of the string. A detailed parametric study on the effect of plate thickness, position, mass, and geometry of the bridge on the natural frequencies is performed. It is found that a proper choice of these parameters can significantly increase the harmonic content in the frequencies for real strings. This study guides the proper choice of system parameters to obtain better harmonic relation between the coupled structure-string modes with real strings.

Dual scan CT image recovery from truncated projections.

There are computerized tomography (CT) scanners available commercially for imaging small objects and they are often categorized as mini-CT X-ray machines. One major limitation of these machines is their inability to scan large objects with good image quality because of the truncation of projection data. An algorithm is proposed in this work which enables such machines to scan large objects while maintaining the quality of the recovered image.

Route to chaos for combustion instability in ducted laminar premixed flames.

Complex thermoacoustic oscillations are observed experimentally in a simple laboratory combustor that burns lean premixed fuel-air mixture, as a result of nonlinear interaction between the acoustic field and the combustion processes. The application of nonlinear time series analysis, particularly techniques based on phase space reconstruction from acquired pressure data, reveals rich dynamical behavior and the existence of several complex states. A route to chaos for thermoacoustic instability is established experimentally for the first time. We show that, as the location of the heat source is gradually varied, self-excited periodic thermoacoustic oscillations undergo transition to chaos via the Ruelle-Takens scenario.

Bistability and chaos in the Taylor-Green dynamo.

Using direct numerical simulations, we study dynamo action under Taylor-Green forcing for a magnetic Prandtl number of 0.5. We observe bistability with weak- and strong-magnetic-field branches. Both the dynamo branches undergo subcritical dynamo transition. We also observe a host of dynamo states including constant, periodic, quasiperiodic, and chaotic magnetic fields. One of the chaotic states originates through a quasiperiodic route with phase locking, while the other chaotic attractor appears to follow the Newhouse-Ruelle-Takens route to chaos. We also observe intermittent transitions between quasiperiodic and chaotic states for a given Taylor-Green forcing.

Dynamics of zero-Prandtl number convection near onset.

We present a detailed bifurcation scenario of zero-Prandtl number Rayleigh-Bénard convection using direct numerical simulations (DNS) and a 27-mode low-dimensional model containing the most energetic modes of DNS. The bifurcation analysis reveals a rich variety of convective flow patterns and chaotic solutions, some of which are common to that of the 13-mode model of Pal et al. [EPL 87, 54003 (2009)]. We also observed a set of periodic and chaotic wavy rolls in DNS and in the model similar to those observed in experiments and numerical simulations. The time period of the wavy rolls is closely related to the eigenvalues of the stability matrix of the Hopf bifurcation points at the onset of convection. This time period is in good agreement with the experimental results for low-Prandtl number fluids. The chaotic attractor of the wavy roll solutions is born through a quasiperiodic and phase-locking route to chaos.