Arbitrary Initial Values Research Articles

Controller design for inverted pendulum stabilizing on equilibrium manifold based on vector field

In general, mechanical systems are stabilized on their equilibrium point. Equilibrium point is often not unique and they are continuously connected, which is an equilibrium manifold. To stabilize the mechanical system on an equilibrium manifold will enable optimal control including the selection of the stabilizing position. In this paper, we propose a controller design method that stabilizes a mechanical system on an equilibrium manifold based on vector field. The equilibrium manifold is derived from dynamic equations, and by setting an appropriate evaluation function, (1) an optimal equilibrium point from arbitrary initial value is calculated, (2) a trajectory, input and vector field are derived based on linear control theory, (3) a controller is designed using functional approximation. Simulations show that different initial values are stabilized to different equilibrium points, and experimental results show the effectiveness of the proposed method.

Global existence and blowup for Choquard equations with an inverse-square potential

In this paper, the Choquard equation with an inverse-square potential and both focusing and defocusing nonlinearities in the energy-subcritical regime is investigated. For all the cases, the local well-posedness result in H1(RN) is established. Moreover, the global existence result for arbitrary initial values is proved in the defocusing case while a global existence/blowup dichotomy below the ground state is established in the focusing case.

Nonlinear observer-based exhaust manifold pressure estimation and fault detection for gasoline engines with exhaust gas recirculation

This article presents a nonlinear observer-based method to estimate the exhaust manifold pressure for the gasoline engines equipped with an exhaust gas recirculation system. A dynamic model is designed to estimate the exhaust manifold pressure, which includes both the intake manifold and exhaust manifold dynamics focusing on gas mass flows. Based on the developed model, a nonlinear exhaust manifold pressure observer is proposed to replace the exhaust manifold pressure sensor, and the global convergence is analyzed by a constructed Lyapunov function and the physical meaning of the time-varying parameters. The experimental validations show that the observer-based exhaust manifold pressure estimator is able to converge to the real value at arbitrary initial value and estimates the exhaust manifold pressure accurately during both the steady-state and transient conditions. Finally, the proposed exhaust manifold pressure observer is applied into the fault detection problem for the exhaust gas recirculation system. The experimental validations show that the observer is able to be used to estimate the exhaust gas recirculation ratio and as an extra signal to assist to detect the faults of the exhaust gas recirculation system accurately.

Extracting Community Structures in Complex Networks Based on Discrete Neural Network Algorithm

The community structure in a complex network is a subset of nodes whose internal nodes are closely connected and relatively sparsely connected to other parts of the network. The community structure is a key structural law of complex networks, so the association of complex networks is accurately analyzed. Structure is a very important topic in the study of complex networks.This paper studies the problem of complex network community structure extraction, and proposes the DHNN algorithm. This algorithm shows that from the arbitrary initial value, after several iterations, it finally converges to an attractor or a limit loop of length 2, giving the energy of DHNN. The relationship between function and modularity function proves that the stable point of the network corresponds to a very large modular function Q value, and the example verification work is carried out. For the DHNN algorithm proposed in this paper, the simulation experiment is carried out on the actual network. The results show that the eigenvalue eigenvector algorithm of DHNN community structure extraction algorithm Newman has a large Q value. At the same time, the DHNN algorithm does not need to calculate the eigenvalue eigenvectors, and only needs a simple addition multiplication operation to extract the community structure in the network. Therefore, the proposed algorithm, especially the DHNN algorithm, has powerful computing power. Community structures in larger, complex networks can be extracted.

Distributed situational observer in a displaced orbit: relative dynamics and control

We design a distributed situational observer using formation flying in a displaced orbit. The main focus of our investigation is the relative dynamics and control of displaced orbits obtained by low-thrust propulsion. The spatial dynamics in Newtonian form are used to derive the numerical relative motions, and their natural frequencies discovered by eigenvalue decomposition separate from each other at a critical height that differentiates the structural stability, bifurcation, and instability. Using the Jordan decomposition, six fundamental motions are achieved, including the stationary multiequilibria, the periodic oscillations that correspond to the natural frequencies, and the maximum leaving or approaching velocity caused by the different geometric and algebraic multiplicities. Off-axis equilibrium is obtained by a proposed open-loop control, and the motions nearby are proven to be equivalent to the numerical relative motions. The reduced dynamics in Hamiltonian form are used to derive the analytical solutions for linearized relative motions. Bounded relative trajectories with arbitrary initial values are achieved by two extraclosed-loop controls. Using the off-axis equilibrium and resonance of natural frequencies, the applications of a fixed relative baseline vector for interferometric SAR or Fresnel zone lens missions and repeating relative ground tracks for a phased array antenna mission are addressed in terms of the trajectory design.

On differential–algebraic equations in infinite dimensions

We consider a class of differential–algebraic equations (DAEs) with index zero in an infinite dimensional Hilbert space. We define a space of consistent initial values, which lead to classical continuously differential solutions for the associated DAE. Moreover, we show that for arbitrary initial values we obtain mild solutions for the associated problem. We discuss the asymptotic behaviour of solutions for both problems. In particular, we provide a characterisation for exponential stability and exponential dichotomies in terms of the spectrum of the associated operator pencil.

Snap-Stabilizing Tasks in Anonymous Networks

We consider snap-stabilizing algorithms in anonymous networks. Self-stabilizing algorithms are well known fault tolerant algorithms : a self-stabilizing algorithm will eventually recover from arbitrary transient faults. On the other hand, an algorithm is snap-stabilizing if it can withstand arbitrary initial values and immediately satisfy its safety requirement. It is a subset of self-stabilizing algorithms. Distributed tasks that are solvable with self-stabilizing algorithms in anonymous networks have already been characterized by Boldi and Vigna in [BV02b]. In this paper, we show how the more demanding snap-stabilizing algorithms can be handled with standard tools for (not stabilizing) algorithms in anonymous networks. We give a characterization of which tasks are solvable by snap-stabilizing algorithms in anonymous networks. We also present a snap-stabilizing version of Mazurkiewicz' enumeration algorithm. This work exposes, from a task-equivalence point of view, the complete correspondence in anonymous networks between self or snap-stabilizing tasks and distributed tasks with various termination detection requirements.

Optimal Phase-to-Phase Control of Chemical Oscillations

We investigate the effectiveness of phase manipulation of chemical oscillations with open loop control based on phase model description. Minimum-power controls are applied to alter the phase of the oscillation from an arbitrary initial value to a desired value within one oscillatory cycle. We demonstrate the applicability of the controls by changing the instantaneous oscillation period of an oscillatory electrochemical system from an arbitrary predetermined initial phase. The experiments showed that the instantaneous period can be effectively modified from any initial phase for a range of ±30% of the natural (uncontrolled) period. Although the method is tested with electrochemical oscillations, the phase model description is general and holds promise in applications in a wide range of disciplines, for example, circadian rhythm adjustment in biology and therapeutic procedures in neuromedicine.

Non-Unique Fixed Point Results in Extended B-Metric Space

In this paper, we investigate the existence of fixed points that are not necessarily unique in the setting of extended b-metric space. We state some examples to illustrate our results.

Fast transform spectral method for Poisson equation and radiative transfer equation in cylindrical coordinate system

ABSTRACTDirect matrix operation is extremely memory-consuming to solve the basic equations of the radiation-hydrodynamics (R-HD) problems, e.g., Poisson equation and radiative transfer equation (RTE), especially in the cases of large grid number and multidimensions. In this work, the fast transform spectral method (FTSM), which requires much less memory than the direct matrix operation, is developed to avoid large dense matrix operation. The proposed method converges monotonically for arbitrary initial value and is verified via the multidimensional Poisson equations and one-dimensional RTE in cylindrical coordinate system. Benchmarks are also introduced to demonstrate the good accuracy of this method. The performance of the FTSM has been validated by comparing with the matrix multiplication transform spectral method (MMTSM). The results show that, the presented method has good robustness and accuracy, when the directly matrix operation of MMTSM is out of memory the FTSM still works well with high accuracy when the grid number is large enough. This means that the FTSM can be a better selection for the R-HD problems when large number grid is needed and especially for multidimensions.

Parameters estimation of HIV infection model of CD4+T-cells by applying orthonormal Bernstein collocation method

The HIV infection model of CD4[Formula: see text][Formula: see text]T-cells corresponds to a class of nonlinear ordinary differential equation systems. In this study, we provide the approximate solution of this model by using orthonormal Bernstein polynomials (OBPs). By applying the proposed method, the nonlinear system of ordinary differential equations reduces to a nonlinear system of algebraic equations which can be solved by using a suitable numerical method such as Newton’s method. We prove some useful theorems concerning the convergence and error estimate associated to the present method. Finally, we apply the proposed method to get the numerical solution of this model with the arbitrary initial conditions and values. Furthermore, the numerical results obtained by the suggested method are compared with the results achieved by other previous methods. These results indicate that this method agrees with other previous methods.

Compensating for evanescent modes and estimating characteristic impedance in waveguide acoustic impedance measurements.

The ear-canal acoustic impedance and reflectance are useful for assessing conductive hearing disorders and calibrating stimulus levels in situ. However, such probe-based measurements are affected by errors due to the presence of evanescent modes and incorrect estimates or assumptions regarding characteristic impedance. This paper proposes a method to compensate for evanescent modes in measurements of acoustic impedance, reflectance, and sound pressure in waveguides, as well as estimating the characteristic impedance immediately in front of the probe. This is achieved by adjusting the characteristic impedance and subtracting an acoustic inertance from the measured impedance such that the non-causality in the reflectance is minimized in the frequency domain using the Hilbert transform. The method is thus capable of estimating plane-wave quantities of the sought-for parameters by supplying only an arbitrary initial value for the characteristic impedance. From a comparison with a simulated waveguide, it is shown that this method can accurately estimate these quantities in a waveguide that is uniform at the position of the probe. Finally, it is demonstrated how evanescent modes, characteristic impedance, and the proposed methodology can affect the measured acoustic impedance and reflectance of an occluded-ear simulator.

Piecewise homotopy analysis method and convergence analysis for formally well-posed initial value problems

In this paper, we propose piecewise homotopy analysis method (PHAM) to extend the convergence region of the homotopy analysis solution for well-posed initial value problems. A convergence theorem of the homotopy analysis solution in the expression of polynomials in the form of Cauchy-Kowalevskaya theorem is given for the nonlinear equation which is analytical near the initial point. We also discuss the influence of the convergence-control parameter h. Our convergence result supports Liao’s conjecture (1): the convergence region increases with the increasing of h(<0). PHAM solution with the symbol of arbitrary initial values has a general form on every convergent subinterval, since the formal series solution is determined by governing equation and initial values. So, we only should substitute the initial values to general form of PHAM solution to obtain the analytical expression on a target subintervals. We also present three typical examples to illustrate the effectiveness and validity of PHAM and convergence results.

Distributed Economic Dispatch for Smart Grids With Random Wind Power

In this paper, we present a distributed economic dispatch (ED) strategy based on projected gradient and finite-time average consensus algorithms for smart grid systems. Both conventional thermal generators and wind turbines are taken into account in the ED model. By decomposing the centralized optimization into optimizations at local agents, a scheme is proposed for each agent to iteratively estimate a solution of the optimization problem in a distributed manner with limited communication among neighbors. It is theoretically shown that the estimated solutions of all the agents reach consensus of the optimal solution asymptomatically. This scheme also brings some advantages, such as plug-and-play property. Different from most existing distributed methods, the private confidential information, such as gradient or incremental cost of each generator, is not required for the information exchange, which makes more sense in real applications. Besides, the proposed method not only handles quadratic, but also nonquadratic convex cost functions with arbitrary initial values. Several case studies implemented on six-bus power system, as well as the IEEE 30-bus power system, are discussed and tested to validate the proposed method.

Perturbational blowup solutions to the compressible Euler equations with damping.

BackgroundThe N-dimensional isentropic compressible Euler system with a damping term is one of the most fundamental equations in fluid dynamics. Since it does not have a general solution in a closed form for arbitrary well-posed initial value problems. Constructing exact solutions to the system is a useful way to obtain important information on the properties of its solutions.Method In this article, we construct two families of exact solutions for the one-dimensional isentropic compressible Euler equations with damping by the perturbational method. The two families of exact solutions found include the cases gamma >1 and gamma =1, where gamma is the adiabatic constant.ResultsWith analysis of the key ordinary differential equation, we show that the classes of solutions include both blowup type and global existence type when the parameters are suitably chosen. Moreover, in the blowup cases, we show that the singularities are of essential type in the sense that they cannot be smoothed by redefining values at the odd points.ConclusionThe two families of exact solutions obtained in this paper can be useful to study of related numerical methods and algorithms such as the finite difference method, the finite element method and the finite volume method that are applied by scientists to simulate the fluids for applications.

Finding of a numerical solution tothe Cauchy - Dirichlet problem for Boussinesq - Lo`ve equation using finitedifferences method

The article is devoted to the numerical investigation of Boussinesq - L`ove mathematical model. Algorithm for finding numerical solution to the Cauchy - Dirichlet problem for Boussinesq - Lo`ve equation modeling longitudinal oscillations in a thin elastic rod with regard to transverse inertia was obtained on the basis of phase space method and by using finite differences method. This problem can be reduced to the Cauchy problem for Sobolev type equation of the second order, which is not solvable for arbitrary initial values. The constructed algorithm includes additional check if initial data belongs to the phase space. The algorithm is implemented as a program in Matlab. The results of numerical experiments are obtained both in regular and degenerate cases. The graphs of obtained solutions are presented in each case.

Numerical Investigation of One Sobolev Type Mathematical Model

The article is devoted to a numerical investigation of the Boussinesq -- L$\grave{o}$ve mathematical model. Algorithm for finding of the numerical solution to the Cauchy -- Dirichlet problem for the Boussinesq -- L$\grave{o}$ve equation modeling longitudinal oscillations in a thin elastic rod with regard to transverse inertia was obtained on the basis of a phase space method and by using a finite differences method. This problem can be reduced to the Cauchy problem for the Sobolev type equation of the second order, which is not solvable for arbitrary initial values. The constructed algorithm includes the additional check if initial data belongs to the phase space. The algorithm is implemented as a program in Matlab. The results of numerical experiments are obtained both in regular and degenerate cases. The graphs of obtained solutions are presented in each case.

Blow-up in a semilinear parabolic problem with variable source under positive initial energy

In this paper, we consider a class of semilinear parabolic equations with variable source under homogeneous Dirichlet boundary conditions in a bounded domain with smooth boundary and For all we prove that the classical solutions to the above equation blow-up in finite time with arbitrary positive initial energy and suitable large initial values. This result extends a recent result by Wu et al. [Appl. Math. Lett. 2013;26:539–543] which asserts the blow-up of solutions for , provided that

Classical gravitational back-reaction

The quantum gravitational back-reaction on inflation is based on the self-gravitation of infrared gravitons which are ripped out of the vacuum during inflation. The only quantum part of this process is the creation of gravitons; after they have emerged from the vacuum their behaviour is essentially classical. To test the thesis that a sufficiently dense ensemble of classical gravitons can hold the Universe together in pure gravity with a positive cosmological constant, we compute the initial value and first time derivative of an invariant measure of the expansion rate for arbitrary classical initial value data. Our result is that the self-gravitation from the kinetic energy of an initial ensemble of gravitons can indeed slow expansion enough to hold the Universe together.

Development of a macro-scale model from a meso-scale model for cell culture population dynamics

In this paper, we present a novel macro-scale analytical model that allows the prediction of how the population size will change in a cell culture starting from an arbitrary initial value. General biological knowledge and some empirical observations are used to design an agent-based discrete-time model at the meso-scale, which then serves as a simulation environment and provides the necessary insights for the development of the continuous-time, differential equation-based, compact macro-scale model. This model can be parameter-tuned and employed for predicting how the population size changes. The paper gives a procedure for the estimation of parameter values of the macro-scale model via some simple tests to be conducted on the cell culture at hand. The performance of the macro-scale model is validated via simulation results that show how well the macro-scale model captures the population dynamics as obtained from the meso-scale model, while the biological plausibility of the meso-scale model is taken for granted.