Stability Arguments Research Articles

Diffusion control for a tempered anomalous diffusion system using fractional-order PI controllers

This paper is concerned with diffusion control problem of a tempered anomalous diffusion system based on fractional-order PI controllers. The contribution of this paper is to introduce fractional-order PI controllers into the tempered anomalous diffusion system for mobile actuators motion and spraying control. For the proposed control force, convergence analysis of the system described by mobile actuator dynamical equations is presented based on Lyapunov stability arguments. Moreover, a new Centroidal Voronoi Tessellation (CVT) algorithm based on fractional-order PI controllers, henceforth called FOPI-based CVT algorithm, is provided together with a modified simulation platform called Fractional-Order Diffusion Mobile Actuator-Sensor 2-Dimension Fractional-Order Proportional Integral (FO-Diff-MAS2D-FOPI). Finally, extensive numerical simulations for the tempered anomalous diffusion process are presented to verify the effectiveness of our proposed fractional-order PI controllers.

Three-dimensional topological insulators and bosonization

Massless excitations at the surface of three-dimensional time-reversal invariant topological insulators possess both fermionic and bosonic descriptions, originating from band theory and hydrodynamic BF theory, respectively. We analyze the corresponding field theories of the Dirac fermion and compactified boson and compute their partition functions on the three-dimensional torus geometry. We then find some non-dynamic exact properties of bosonization in (2+1) dimensions, regarding fermion parity and spin sectors. Using these results, we extend the Fu-Kane-Mele stability argument to fractional topological insulators in three dimensions.

Sliding mode disturbance observer-based control of a twin rotor MIMO system

This work proposes a robust tracking controller for a helicopter laboratory setup known as the twin rotor MIMO system (TRMS) using an integral sliding mode controller. To eliminate the discontinuity in the control signal, the controller is augmented by a sliding mode disturbance observer. The actuator dynamics is handled using a backstepping approach which is applicable due to the continuous chattering-free nature of the command signals generated using the disturbance observer based controller. To avoid the complexity of analytically differentiating the command signals, a first order sliding mode differentiator is used. Stability analysis of the closed loop system and the ultimate boundedness of the tracking error is proved using Lyapunov stability arguments. The proposed controller is validated by several simulation studies and is compared to other schemes in the literature. Experimental results using a hardware-in-the-loop system validate the robustness and effectiveness of the proposed controller.

Rainbow triangles in three-colored graphs

Erdős and Sós proposed the problem of determining the maximum number F(n) of rainbow triangles in 3-edge-colored complete graphs on n vertices. They conjectured that F(n)=F(a)+F(b)+F(c)+F(d)+abc+abd+acd+bcd, where a+b+c+d=n and a,b,c,d are as equal as possible. We prove that the conjectured recurrence holds for sufficiently large n. We also prove the conjecture for n=4k for all k≥0. These results imply that lim⁡F(n)(n3)=0.4, and determine the unique limit object. In the proof we use flag algebras combined with stability arguments.

Improved control of distributed parameter systems using wireless sensor and actuator networks: An observer-based method**Project supported by the National Natural Science Foundation of China (Grant Nos. 61174021 and 61473136) and the 111 Project of China (Grant No. B12018).

In this paper, the control problem of distributed parameter systems is investigated by using wireless sensor and actuator networks with the observer-based method. Firstly, a centralized observer which makes use of the measurement information provided by the fixed sensors is designed to estimate the distributed parameter systems. The mobile agents, each of which is affixed with a controller and an actuator, can provide the observer-based control for the target systems. By using Lyapunov stability arguments, the stability for the estimation error system and distributed parameter control system is proved, meanwhile a guidance scheme for each mobile actuator is provided to improve the control performance. A numerical example is finally used to demonstrate the effectiveness and the advantages of the proposed approaches.

Marginally stable and turbulent boundary layers in low-curvature Taylor–Couette flow

Marginal stability arguments are used to describe the rotation number dependence of torque in Taylor–Couette (TC) flow for radius ratios $\unicode[STIX]{x1D702}\geqslant 0.9$ and shear Reynolds number $\mathit{Re}_{S}=2\times 10^{4}$. With an approximate representation of the mean profile by piecewise linear functions, characterised by the boundary-layer thicknesses at the inner and outer cylinder and the angular momentum in the centre, profiles and torques are extracted from the requirement that the boundary layers represent marginally stable TC subsystems and that the torque at the inner and outer cylinder coincide. This model then explains the broad shoulder in the torque as a function of rotation number near $R_{\unicode[STIX]{x1D6FA}}\approx 0.2$. For rotation numbers $R_{\unicode[STIX]{x1D6FA}}<0.07$ the TC stability conditions predict boundary layers in which the shear Reynolds numbers are very large. Assuming that the TC instability is bypassed by some shear instability, a second narrower maximum in torque appears, in very good agreement with numerical simulations. The results show that marginal stability theory, despite its shortcomings in other cases, can explain quantitatively the non-monotonic torque variation with rotation number for both the broad maximum as well as the narrow maximum.

Robust finite-time estimation of biased sinusoidal signals: A volterra operators approach

A novel finite-time convergent estimation technique is proposed for identifying the amplitude, frequency and phase of a biased sinusoidal signal. Resorting to Volterra integral operators with suitably designed kernels, the measured signal is processed yielding a set of auxiliary signals in which the influence of the unknown initial conditions is removed. A second-order sliding mode-based adaptation law–fed by the aforementioned auxiliary signals–is designed for finite-time estimation of the frequency, amplitude, and phase. The worst case behavior of the proposed algorithm in presence of the bounded additive disturbances is fully characterized by Input-to-State Stability arguments. The effectiveness of the estimation technique is evaluated and compared with other existing tools via extensive numerical simulations.

Gravity Loop Corrections to the Standard Model Higgs in Einstein Gravity

We study one-loop quantum gravity corrections to the standard model Higgs potential \(V(\phi) \grave{\rm a}\) la Coleman-Weinberg and examine the stability question of \(V(\phi) \) in the energy region of Planck mass scale, \(\mu\simeq M_{\rm Pl}\) \((M_{\rm Pl}=1.22\times10^{19}{\rm GeV})\). We calculate the gravity one-loop corrections to \(V(\phi)\) in Einstein gravity by using the momentum cut-off \(\Lambda\). We have found that even small gravity corrections compete with the standard model term of \(V(\phi)\) and affect the stability argument of the latter part alone. This is because the latter part is nearly zero in the energy region of \(M_{\rm Pl}\).

Planar Smooth Path Guidance Law for a Small Unmanned Aerial Vehicle with Parameter Tuned by Fuzzy Logic

A guidance law has been designed to guide the small unmanned aerial vehicle towards the predefined horizontal smooth path. The guidance law only needs the mathematical expression for the predefined path, the positions, and the velocities of the vehicle in the horizontal inertial frame. The stability of the guidance law has been demonstrated by the Lyapunov stability arguments. In order to improve the path following performance, one of the parameters of the guidance law is tuned by using the fuzzy logic which will still keep its stability. The simulation experiments in the Matlab/Simulink environment to realize the square-, circular-, and the athletics track-style paths following are given to verify the effectiveness of the proposed method. The simulation results show that the path following performance will be improved with smaller overshoot and oscillation amplitude and shorter arrival time with the parameter tuned.

Pluralist Partially Comprehensive Doctrines, Moral Motivation, and the Problem of Stability

Recent scholarship has drawn attention to John Rawls’s concern with stability—a concern that, as Rawls himself notes, motivated Part III of A Theory of Justice and some of the more important changes of his political turn. For Rawls, the possibility of achieving ‘stability for the right reasons’ depends on citizens possessing sufficient moral motivation. I argue, however, that the moral psychology Rawls develops to show how such motivation would be cultivated and sustained does not cohere with his specific descriptions of ‘pluralist (partially comprehensive)’ doctrines. Considering Rawls’s claims that ‘most’ citizens—both in contemporary liberal democracies and in the well-ordered society—possess such doctrines, this incompatibility threatens to undermine his stability arguments. Despite the enormous importance of pluralist doctrines and the potential difficulties they pose for Rawls’s project, remarkably little attention has been paid to them. By critically examining these difficulties, the article begins to address this oversight.

Moral Psychology, Stability and the Law of Peoples

In this paper I want to take seriously Rawls’s characterization of his The Law of Peoples as carrying forward the project of Political Liberalism. Political Liberalism articulates Rawls’s reworking of the stability argument from Part III of A Theory of Justice to better square it with the fact of reasonable pluralism. As presented in Theory the stability argument is an argument from moral psychology. Though the argument changes in Political Liberalism, the moral psychology does not. Accordingly, I draw on both the moral psychology Rawls articulates in Theory and its revised deployment in Political Liberalism to illuminate certain features of the account of international right and justice Rawls sets out in The Law of Peoples.

A novel disturbance observer-based backstepping controller with command filtered compensation for a MIMO system

This paper presents a novel disturbance observer-based trajectory tracking controller based on the integral backstepping approach. To avoid the complexity of analytically calculating derivatives of virtual control signals in the standard backstepping technique, a command filtered backstepping approach is utilized. The proposed control approach is formulated for a class of nonlinear MIMO systems and provides robustness against external disturbances. This approach is applied on an aerodynamic laboratory setup known as the twin rotor MIMO system (TRMS). Stability analysis of the proposed controller is presented using Lyapunov stability arguments and singular perturbation theory. Simulation studies show that the proposed controller successfully allows the system outputs to track arbitrary reference trajectories and reject arbitrary constant disturbances that may occur due to partial actuator failure. The reliability and effectiveness of the approach is validated experimentally by implementation of the proposed controller on a hardware-in-the-loop system.

Nonlinear spontaneous symmetry breaking in active polar films

The behaviour of an active polar suspension in a fluid film is analysed in the vanishing Reynolds number limit. We perform a detailed study of the transitions to spontaneously flowing steady states and their associated density variations. Beyond the onset of instability, we find a new transverse symmetry breaking of the flow generated in the film. This spontaneous symmetry breaking is observed despite symmetric boundary conditions (with respect to orientation) on either side of the film. We study this new phenomenon by means of numerical simulations and nonlinear theory, showing that it can be ascribed to the nonlinear coupling, characteristic of polar active systems, of the density gradients with the flow velocity and the orientation field. As such a theoretical analysis based on linear stability arguments typically used to identify phase boundaries is unable to describe it. An extension of the theory to allow for higher-density regimes is also proposed.

A segregated explicit algebraic structure-based model for wall-bounded turbulent flows

The Algebraic Structure-based Model (ASBM) is an engineering model of turbulence that incorporates information about the morphology of turbulent structures, and thus characterizes additional turbulence information beyond what is provided solely by the Reynolds stresses. In this work, a new formulation of the ASBM is developed that exhibits three defining characteristics. The first is a near-wall correction segregated from the homogeneous component of the model, which allows for a new paradigm for model development and comparison. The second characteristic is a set of fully-explicit equations that replace the original implicit formulation and make evident the highly nonlinear nature of the model. Finally, the last defining characteristic is based on the coupling of the ASBM with turbulent transport equations that provide the required turbulent scales. Using arguments of consistency, stability, and accuracy we arrive at a model that uses transport equations for k and ϵ. The resulting model is simpler to implement, more robust, and amenable to further development. The analysis of the new ASBM formulation is carried out by computing fully-developed channel, pipe and squared duct flows.

Prediction-based feedback control and synchronization algorithm of fractional-order chaotic systems

In this paper, a fractional-order prediction-based feedback control scheme (Fo-PbFC) is proposed to stabilize the unstable equilibrium points and to synchronize the fractional-order chaotic systems (FoCS). The design of Fo-PbFC, derived and based on Lyapunov stabilization arguments and matrix measure, is theoretically rigorous and represents a powerful and simple approach to provide a reasonable trade-off between computational overhead, storage space, numerical accuracy and stability analysis in control and synchronization of a class of FoCS. Numerical simulations are also provided to verify the validity and the feasibility of the proposed scheme by considering the fractional-order Newton–Leipnik chaotic and the fractional-order Mathieu–Van Der Pol hyperchaotic systems as illustrative examples.

Model-independent inference of neutron star radii from moment of inertia measurements

A precise moment of inertia measurement for PSR J0737-3039A in the double pulsar system is expected within the next five years. We present here a new method of mapping the anticipated measurement of the moment of inertia directly into the neutron star structure. We determine the maximum and minimum values possible for the moment of inertia of a neutron star of a given radius based on physical stability arguments, assuming knowledge of the equation of state only at densities below the nuclear saturation density. If the equation of state is trusted up to the nuclear saturation density, we find that a measurement of the moment of inertia will place absolute bounds on the radius of PSR J0737-3039A to within $\pm$1 km. The resulting combination of moment of inertia, mass, and radius measurements for a single source will allow for new, stringent constraints on the dense-matter equation of state.

Time-varying formation tracking of multiple manipulators via distributed finite-time control

Compared with traditional fixed formation for a group of dynamical systems, time-varying formation can produce the following benefits: (i) covering the greater part of complex environments and (ii) collision avoidance. This paper studies the time-varying formation tracking for multiple manipulator systems (MMSs) under fixed and switching directed graphs with a dynamic leader, whose acceleration cannot change too fast. An explicit mathematical formulation of time-varying formation is developed based on the related practical applications. A class of extended inverse dynamics control algorithms combined with distributed sliding-mode estimators are developed to address the aforementioned problem. By invoking finite-time stability arguments, several novel criteria (including sufficient criteria, necessary and sufficient criteria) for global finite-time stability of MMSs are established. Finally, numerical experiments are presented to verify the effectiveness of the theoretical results.

Design and optimization of generalized prediction-based control scheme to stabilize and synchronize fractional-order hyperchaotic systems

This work addresses the problem of designing a controller for the stabilization and synchronization processes of a large class of Fractional-order Chaotic (resp. hyperchaotic) Systems (FoCS). A Generalized Prediction-based Control (GPbC) law is presented in this paper. Based on Lyapunov stabilization arguments and a recent stability theorem of fractional-order systems, stability analysis of the closed-loop control system is investigated. The design and multiobjective optimization of GPbC scheme offers some superior properties such as faster finite-time convergence, higher control precision which very low energy consumption and stability conditions guarantee in control and synchronization of FoCS. Some numerical simulations are provided to confirm the validity of the proposed analytical results.

Neural Field Models with Threshold Noise.

The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate function so prevalent in large scale neuronal modelling. In this paper we explore the effects of such threshold noise without recourse to averaging and show that spatial correlations can have a strong effect on the behaviour of waves and patterns in continuum models. Moreover, for a prescribed spatial covariance function we explore the differences in behaviour that can emerge when the underlying stationary distribution is changed from Gaussian to non-Gaussian. For travelling front solutions, in a system with exponentially decaying spatial interactions, we make use of an interface approach to calculate the instantaneous wave speed analytically as a series expansion in the noise strength. From this we find that, for weak noise, the spatially averaged speed depends only on the choice of covariance function and not on the shape of the stationary distribution. For a system with a Mexican-hat spatial connectivity we further find that noise can induce localised bump solutions, and using an interface stability argument show that there can be multiple stable solution branches.

Lyapunov Stability and Accuracy of Direct Integration Algorithms Applied to Nonlinear Dynamic Problems

AbstractIn structural dynamics, direct integration algorithms are commonly used to solve the temporally discretized differential equations of motion. Numerous research efforts focused on the stability and accuracy of different integration algorithms for linear elastic structures. However, investigations of those properties applied to nonlinear structures are limited. Systematic Lyapunov stability and accuracy analyses of several direct integration algorithms for nonlinear structural dynamics are presented. These integration algorithms include the implicit methods of the Newmark family of integration algorithm and the TRBDF2 algorithm, and the explicit methods of operator-splitting (OS) algorithms. Two versions of the OS algorithms, using initial and tangent stiffness formulations, are investigated. The latter one is shown to possess similar stability properties to the implicit Newmark integration. Some arguments of stability regarding these direct integration algorithms from past studies are found to be g...