Push-Pull Finite-Time Convergence Distributed Optimization Algorithm

With the widespread application of distributed systems, many problems need to be solved urgently. How to design distributed optimization strategies has become a research hotspot. This article focuses on the solution rate of the distributed convex optimization algorithm. Each agent in the network has its own convex cost function. We consider a gradient-based distributed method and use a push-pull gradient algorithm to minimize the total cost function. Inspired by the current multi-agent consensus cooperation protocol for distributed convex optimization algorithm, a distributed convex optimization algorithm with finite time convergence is proposed and studied. In the end, based on a fixed undirected distributed network topology, a fast convergent distributed cooperative learning method based on a linear parameterized neural network is proposed, which is different from the existing distributed convex optimization algorithms that can achieve exponential convergence. The algorithm can achieve finite-time convergence. The convergence of the algorithm can be guaranteed by the Lyapunov method. The corresponding simulation examples also show the effectiveness of the algorithm intuitively. Compared with other algorithms, this algorithm is competitive.

Target Tracking Algorithm Using Finite-time Convergence Smooth Second-order Sliding Mode Controller for Mobile Robots

Target tracking control for wheeled mobile robot （WMR） need resolve the problems of kinematics model and tracking algorithm.High-order sliding mode control is a valid method used in the nonlinear tracking control system,which can eliminate the chattering of sliding mode control.Currently there lacks the research of robustness and uncertain factors for high-order sliding mode control.To address the fast convergence and robustness problems of tracking target,the tracking mathematical model of WMR and the target is derived.Based on the finite-time convergence theory and second order sliding mode method,a nonlinear tracking algorithm is designed which guarantees that WMR can catch the target in finite time.At the same time an observer is applied to substitute the uncertain acceleration of the target,then a smooth nonlinear tracking algorithm is proposed.Based on Lyapunov stability theory and finite-time convergence,a finite time convergent smooth second order sliding mode controller and a target tracking algorithm are designed by using second order sliding mode method.The simulation results verified that WMR can catch up the target quickly and reduce the control discontinuity of the velocity of WMR.

Robust controller design for compound control missile with fixed bounded convergence time

A robust controller for bank to turn(BTT) missiles with aerodynamic fins and reaction jet control system(RCS) is developed based on nonlinear control dynamic models comprising couplings and aerodynamic uncertainties. The fixed time convergence theory is incorporated with the sliding mode control technique to ensure that the system tracks the desired command within uniform bounded time under different initial conditions. Unlike previous terminal sliding mode approaches, the bound of settling time is independent of the initial state, which means performance metrics like convergence rate can be predicted beforehand. To reduce the burden of control design in terms of robustness, extended state observer(ESO) is introduced for uncertainty estimation with the output substituted into the controller as feedforward compensation. Cascade control structure is employed with the proposed control law and therein the compound control signal is obtained.Afterwards, control inputs for two kinds of actuators are allocated on the basis of their inherent characteristics. Finally, a number of simulations are carried out and demonstrate the effectiveness of the designed controller.

Differential geometric guidance command with finite time convergence using extended state observer

For improving the performance of differential geometric guidance command(DGGC), a new formation of this guidance law is proposed, which can guarantee the finite time convergence(FTC) of the line of sight(LOS) rate to zero or its neighborhood against maneuvering targets in three-dimensional(3D) space. The extended state observer(ESO) is employed to estimate the target acceleration, which makes the new DGGC more applicable to practical interception scenarios. Finally, the effectiveness of this newly proposed guidance command is demonstrated by the numerical simulation results.

Long-time Convergence of Numerical Approximations for Semilinear Parabolic Equations (Ⅱ)

In this article we extend ours framework of long time convergence for numeracal approximations of semilinear parabolic equations prorided in “Wu Haijun and Li Ronghua, Northeast. Math. J., 16(1)(2000), 1—28”, to the Gauss Ledendre full discretization. When apply the result to the Crank Nicholson finiteelement full discretization of the Navier Stokes equations, we can remore the grid ratio restriction of “Heywood, J. G. and Rannacher, R., SIAM J. Numer. Anal., 27(1990), 353—384”, and weaken the stability condition on the continuous solution.

Convergence and Superconvergence of Fully Discrete Finite Element for Time Fractional Optimal Control Problems

In this paper, we consider a fully discrete finite element approximation for time fractional optimal control problems. The state and adjoint state are approximated by triangular linear fi nite elements in space and L1 scheme in time. The control is obtained by the variational discretization technique. The main purpose of this work is to derive the convergence and superconvergence. A numerical example is presented to validate our theoretical results.

Drift Analysis in Studying the Convergence and Hitting Times of Evolutionary Algorithms: An Overview

This paper introduces drift analysis approach in studying the convergence and hitting times of evolutionary algorithms. First the methodology of drift analysis is introduced, which links evolutionary algorithms with Markov chains or supermartingales. Then the drift conditions which guarantee the convergence of evolutionary algorithms are described. And next the drift conditions which are used to estimate the hitting times of evolutionary algorithms are presented. Finally an example is given to show how to analyse hitting times of EAs by drift analysis approach.

A Mathematical Model of Real-Time Simulation and the Convergence Analysis on Real-Time Runge-Kutta Algorithms

In this paper, a mathematical model of real-time simulation is given, and the problem of convergence on real-time Runge-Kutta algorithms is analysed. At last a theorem on the relation between the order of compensation and the convergent order of real-time algorithm is proved.

Dynamics and Long Time Convergence of the Extended Fisher-Kolmogorov Equation under Numerical Discretization

We present a numerical study of the long time behavior of approxima- tion solution to the Extended Fisher-Kolmogorov equation with periodic boundary conditions. The unique solvability of numerical solution is shown. It is proved that there exists a global attractor of the discrete dynamical system. Furthermore, we obtain the long-time stability and convergence of the difference scheme and the upper semicontinuity d（Ah,τ, .A） → O. Our results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems.

LONG-TIME CONVERGENCE OF GENERALIZED DIFFERENCE METHOD FOR NAVIER-STOKES EQUATIONS

In this paper, we first provide a generalized difference method for the 2-dimensional Navier-Stokes equations by combing the ideas of staggered scheme m and generalized upwind scheme in space, and by backward Euler time-stepping. Then we apply the abstract framework of to prove its long-time convergence. Finally, a numerical example for solving driven cavity flows is given.

Convergence of food chain model with time delays

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Explicit Approximation Solutions and Proof of Convergence of the Space-Time Fractional Advection Dispersion Equations

The space-time fractional advection dispersion equations are linear partial pseudo-differential equations with spatial fractional derivatives in time and in space and are used to model transport at the earth surface. The time fractional order is denoted by β∈ and ?is devoted to the space fractional order. The time fractional advection dispersion equations describe particle motion with memory in time. Space-fractional advection dispersion equations arise when velocity variations are heavy-tailed and describe particle motion that accounts for variation in the flow field over entire system. In this paper, I focus on finding the precise explicit discrete approximate solutions to these models for some values of ?with ?, ?while the Cauchy case as ?and the classical case as ?with ?are studied separately. I compare the numerical results of these models for different values of ?and ?and for some other related changes. The approximate solutions of these models are also discussed as a random walk with or without a memory depending on the value of . Then I prove that the discrete solution in the Fourierlaplace space of theses models converges in distribution to the Fourier-Laplace transform of the corresponding fractional differential equations for all the fractional values of ?and .

A Composite State Convergence Scheme for Bilateral Teleoperation Systems

State convergence is a novel control algorithm for bilateral teleoperation of robotic systems. First, it models the teleoperation system on state space and considers all the possible interactions between the master and slave systems. Second, it presents an elegant design procedure which requires a set of equations to be solved in order to compute the control gains of the bilateral loop. These design conditions are obtained by turning the master-slave error into an autonomous system and imposing the desired dynamic behavior of the teleoperation system. Resultantly, the convergence of master and slave states is achieved in a well-defined manner. The present study aims at achieving a similar convergence behavior offered by state convergence controller while reducing the number of variables sent across the communication channel. The proposal suggests transmitting composite master and slave variables instead of full master and slave states while keeping the operator's force channel intact. We show that,with these composite and force variables;it is indeed possible to achieve the convergence of states in a desired way by strictly following the method of state convergence. The proposal leads to a reduced complexity state convergence algorithm which is termed as composite state convergence controller. In order to validate the proposed scheme in the absence and presence of communication time delays, MATLAB simulations and semi-real time experiments are performed on a single degree-of-freedom teleoperation system.

Timing of the Early Paleozoic Yangtze and Cathysian Convergence： Constraint from U-Pb Geochronology of Hydrothermal Zircons from Mafic Mylonite within the Shoucheng-Piaoli Ductile Shear Zone, Northern Guangxi

Objective The northern Guangxi region is in the southwestern part of the Southern China continent,which is located at the junction of the southwest section of the Early Paleozoic Yangtze block and Cathaysian block.A series of NNE-trending ductile shear zones are developed in this region,and these ductile shear zones are mostly previously suggested boundary faults of the Early Paleozoic Yangtze block and Cathaysian block,such as the Shoucheng–Piaoli ductile shear zone in Northern Guangxi （Meng Yuanku et al., 2016; Zhang Xuefeng et al., 2015）.

Finite time convergent control using terminal sliding mode

A method for terminal sliding mode control design is discussed. As we know, one of the strong points of terminal sliding mode control is its finite-time convergence to a given equilibrium of the system under consideration, which may be useful in specific applications. The proposed method, different from many existing terminal sliding model control desin methods, is studied, and then feedback laws are designed for a class of nonlinear systems, along with illustrative examples.

Adaptive backstepping finite-time sliding mode control of spacecraft attitude tracking

This paper investigates the finite-time attitude tracking problem for rigid spacecraft. Two backstepping finite-time slid- ing mode control laws are proposed to solve this problem in the presence of inertia uncertainties and external disturbances. The first control scheme is developed by combining sliding mode con- trol with a backstepping technique to achieve fast and accurate tracking responses. To obtain higher tracking precision and relax the requirement of the upper bounds on the uncertainties, a se- cond control law is also designed by combining the second or- der sliding mode control and an adaptive backstepping technique. This control law provides complete compensation of uncertainty and disturbances. Although it assumes that the uncertainty and disturbances are bounded, the proposed control law does not require information about the bounds on the uncertainties and disturbances. Finite-time convergence of attitude tracking errors and the stability of the closed-loop system are ensured by the Lya- punov approach. Numerical simulations on attitude tracking control of spacecraft are provided to demonstrate the performance of the proposed controllers.

On the Convergence of the Dual-Pivot Quicksort Process

Sorting an array of objects such as integers, bytes, floats, etc is considered as one of the most important problems in Computer Science. Quicksort is an effective and wide studied sorting algorithm to sort an array of n distinct elements using a single pivot. Recently, a modified version of the classical Quicksort was chosen as standard sorting algorithm for Oracles Java 7 routine library due to Vladimir Yaroslavskiy. The purpose of this paper is to present the different behavior of the classical Quicksort and the Dual-pivot Quicksort in complexity. In Particular, we discuss the convergence of the Dual-pivot Quicksort process by using the contraction method. Moreover we show the distribution of the number of comparison done by the duality process converges to a unique fixed point.

Convergence Analysis of Cuckoo Search by Creating Markov Chain

Cuckoo search(CS) has been used successfully for solving global optimization problems.From a theoretical point of view,the convergence of the CS is an important issue.In this paper,convergence analysis of CS was studied.The transition probability characteristics of the population to construct a Markov chain were analyzed.The homogeneity of the Markov chain was derived based on stochastic process theory.Then it was proved to be an absorbing state Markov chain.Consequently,the global convergence of CS was deduced based on conditions of convergence sequence and total probability formula,and the expected convergence time was given.Finally,a series of experiments were conducted.Experimental results were analyzed and it is observed that CS seems to perform better than PSO.

Convergence Analysis of a Self-Stabilizing Algorithm for Minor Component Analysis

The M?ller algorithm is a self-stabilizing minor component analysis algorithm.This research document involves the study of the convergence and dynamic characteristics of the M?ller algorithm using the deterministic discrete time(DDT)methodology.Unlike other analysis methodologies,the DDT methodology is capable of serving the distinct time characteristic and having no constraint conditions.Through analyzing the dynamic characteristics of the weight vector,several convergence conditions are drawn,which are beneficial for its application.The performing computer simulations and real applications demonstrate the correctness of the analysis’s conclusions.