Consensus tracking via quantized iterative learning control for singular nonlinear multi-agent systems with state time-delay and initial state error

Nonlinear Dynamics - This paper investigates the quantized iterative learning consensus tracking problem for singular nonlinear multi-agent systems (MASs) in the presence of state time-delay and...     

Optimal control of the deployment (and retrieval) of a tethered satellite under small initial disturbances

The deployment and retrieval processes of satellites from a space station are demanding tasks during the operations of tethered satellite systems. The satellite should be steered into its working state within a reasonable amount of time and without too much control efforts. For the pure in-plane oscillation we have found time-optimal solutions with bang–bang control strategy for the deployment and retrieval process. In our working group we have also investigated different stabilization methods of the vertical equilibrium configuration, for example parametric swing control and chaotic control. In this article we concentrate on the final stage of the operation, when the oscillations around the vertical configuration should be brought to halt. While this task is quite simple for a motion of the satellite in the orbital plane, it is considerably more difficult, if the satellite has been perturbed out of that plane. We first analyze the control for a purely out-of-plane oscillation, which is governed by a Hamiltonian Hopf bifurcation, and then investigate the combined control for the spatial dynamics. Using a center manifold ansatz for the in-plane oscillations, we can show, that it is possible to diminish the oscillations of the tethered satellite in both directions, but the decay is extremely slow.     

Edge waves under initial stress

The frequency equation giving the phase velocity of a wave at the edge of a thick plate under initial stress is obtained. Some particular cases are discussed to derive (a) the velocity of edge waves in a thin plate and (b) the velocity of Rayleigh waves in a plate of infinite thickness under initial stress. The results are compared with those for zero initial stress.     

Stress state of a cross-base prism under torsion

The stress state of a cross-base prism under torsion is analyzed. The lower- and upper bounds for stresses are found by solving an infinite system of linear algebraic equations and using Koyalovich’s limitants method. It is proved that the infinite system is regular and that its solution exists and is unique. The asymptotic behavior of the unknowns is established. The convergence of the series for stresses is accelerated Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 79–93, November 2008.     

Transversely isoiropic beam under initial stress

Starling from Novozhilov’s nonlinear equations of elasticity by appropriate simplification and integration over the beam cross-section, a linearized set of equations for a transversely isotropic beam under initial non-uniform state of stress is obtained. In the absence of initial stress, the obtained equations are reduced to well-known Timoshenko beam equations.These equations are applied to investigate the vibration and buckling characteristics of a transversely isotropic beam under uniform initial axial force and bending moment.     

Asymmetric bifurcations in a pressurised circular thin plate under initial tension

It has been known for some time that under certain circumstances the axisymmetric solution describing the deformation experienced by a stretched circular thin plate or membrane under sufficiently strong normal pressure does not represent an energy-minimum configuration. By using the method of adjacent equilibrium a set of coordinate-free bifurcation equations is derived here by adopting the Föppl–von Kármán plate theory. A particular class of asymmetric bifurcation solutions is then investigated by reduction to a system of ordinary differential equations with variable coefficients. The localised character of the eigenmodes is confirmed numerically and we also look briefly at the role played by the background tension on this phenomenon.     

Reflection of plane waves under initial stresses at a free surface

The paper deals with the phenomenon of reflection of plane elastic waves in a free surface when the medium is initially stressed. It has been shown analytically that the reflected P and SV waves depend on initial stresses present in the medium. The numerical values of reflection coefficients for different initial stresses and the angle of incidence have been calculated by the Computer I.C.L. 1901-A and the results are given in the form of graphs. Many interesting results are found in the paper which are not seen in an initially stress-free medium.     

The rational mechanics and thermodynamics of polymeric fluids based upon the concept of a variable relaxed state

The conceptual framework of polymer continuum mechanics based upon Eckart's idea of a variable relaxed state is developed. No constitutive models are explicitly used. The theory admits four constitutive functions only, the scalar specific internal energy, the vectorial heat flux, and two tensorial fluxes representing non-elastic stress and flow (slippage). The non-linearity of the constitutive relations includes self-induced anisotropy (Leonov) with Reiner-Rivlin's equation representing a special example for this. — The effectiveness of this non-linear theory is demonstrated by treating elongational flows of polymer melts.     

Discrete-time sliding mode control for robust tracking and model following of systems with state and input delays

This paper presents a novel robust tracking and model following control scheme for a class of linear systems with mismatched state and input delays. The algorithm is based on discrete-time sliding mode control (SMC) and time-delay control theory. The proposed scheme ensures the stability and robustness against time delays without state transformation, and achieves the ultimate boundedness of the tracking error. The selection of sliding surface and the existence of sliding mode are two important issues, which have been addressed. Chattering phenomenon and reaching phase are avoided. Simulation results demonstrate the validity of the proposed scheme.     

Fracture of sedimentary rocks under a complex triaxial stress state

Most sedimentary rocks have layered structure, and their strength properties are therefore anisotropic; as a consequence, the rock strength depends on the direction of the applied stresses. In this case, various fracture mechanisms are possible. The following two possible fracture mechanisms are considered: actions along the bedding planes, which are weakening surfaces, and along the planes where stresses exceeding the total rock strength are attained. A triaxial independent loading test bench was used to study the fracture conditions for layered rocks composed of productive oil-and-gas strata in complex true triaxial loading tests. The study shows a good qualitative agreement between experimental results and theoretical estimates.     

Sufficiency for optimal control with state and control constraints

Sufficient conditions are derived for optimal control of a dynamical system described by ordinary differential equations and subject to constraints on both state and control.