Consensus Control With a Constant Gain for Discrete-time Binary-valued Multi-agent Systems Based on a Projected Empirical Measure Method

This paper studies the consensus control of multiagent systems with binary-valued observations.An algorithm alternating estimation and control is proposed.Each agent estimates the states of its neighbors based on a projected empirical measure method for a holding time.Based on the estimates,each agent designs the consensus control with a constant gain at some skipping time.The states of the system are updated by the designed control,and the estimation and control design will be repeated.For the estimation,the projected empirical measure method is proposed for the binary-valued observations.The algorithm can ensure the uniform boundedness of the estimates and the mean square error of the estimation is proved to be at the order of the reciprocal of the holding time(the same order as that in the case of accurate outputs).For the consensus control,a constant gain is designed instead of the stochastic approximation based gain in the existing literature for binary-valued observations.And,there is no need to make modification for control since the uniform boundedness of the estimates ensures the uniform boundedness of the agents’states.Finally,the systems updated by the designed control are proved to achieve consensus and the consensus speed is faster than that in the existing literature.Simulations are given to demonstrate the theoretical results.

Projective synchronization of a hyperchaotic system via periodically intermittent control

We further study the projective synchronization of a new hyperchaotic system. Different from the most existing methods, intermittent control is applied to chaotic synchronization in the present paper. We formulate the intermittent control system that governs the dynamics of the projective synchronization error, then derive the sufficient conditions for the exponential stability of intermittent control system by using the Lyapunov stability theory, and finally establish the periodically intermittent controller according to the stability criterion by which the projective synchronization is expected to be achieved. The analytical results are also demonstrated by several numerical simulations.

Generalized projective synchronization of a class of chaotic （hyperchaotic） systems with uncertain parameters

In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic （hyperchaotic） systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic L system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.

Robust modified projective synchronization of fractional-order chaotic systems with parameters perturbation and external disturbance

Based on fractional-order Lyapunov stability theory, this paper provides a novel method to achieve robust modified projective synchronization of two uncertain fractional-order chaotic systems with external disturbance. Simulation of the fractional-order Lorenz chaotic system and fractional-order Chen＇s chaotic system with both parameters uncertainty and external disturbance show the applicability and the efficiency of the proposed scheme.

Observer based projective reduced-order synchronization of different chaotic systems

The projective reduced-order synchronization of two different chaotic systems with different orders is investigated based on the observer design in this paper.According to the observer theory,the reduced-order observer is designed.The projective synchronization can be realized by choosing the transition matrix of the observer as a diagonal matrix.Further,the synchronization between hyperchaotic Chen system(fourth order)and Rssler system(third order)is taken as the example to demonstrate the effectiveness of the proposed observer.Numerical simulations confirm the effectiveness of the method.

Modified scaling function projective synchronization of chaotic systems

This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point; a periodic orbit, or even a chaotic attractor in the phase space. Based on LaSalle＇s invariance set principle, the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method.

Adaptive generalized projective synchronization of two different chaotic systems with unknown parameters

This paper presents a general method of the generalized projective synchronization and the parameter identification between two different chaotic systems with unknown parameters. This approach is based on Lyapunov stability theory, and employs a combination of feedback control and adaptive control. With this method one can achieve the generalized projective synchronization and realize the parameter identifications between almost all chaotic （hyperchaotic） systems with unknown parameters. Numerical simulations results are presented to demonstrate the effectiveness of the method.

Generalized Projective Synchronization Between Rssler System and New Unified Chaotic System

Based on symbolic computation system Maple and Lyapunov stability theory,an active control method isused to projectively synchronize two different chaotic systems—Lorenz-Chen-Lü system(LCL)and Rssler system,which belong to different dynamic systems.In this paper,we achieve generalized projective synchronization between thetwo different chaotic systems by directing the scaling factor onto the desired value arbitrarily.To illustrate our result,numerical simulations are used to perform the process of the synchronization and successfully put the orbits of drivesystem(LCL)and orbits of the response system(Rssler system)in the same plot for understanding intuitively.

Projective synchronization in coupled fractional order chaotic Rossler system and its control

This paper proposes a method to achieve projective synchronization of the fractional order chaotic Rossler system. First, construct the fractional order Rossler system＇s corresponding approximate integer order system, then a control method based on a partially linear decomposition and negative feedback of state errors is utilized on the new integer order system. Mathematic analyses prove the feasibility and the numerical simulations show the effectiveness of the proposed method.

Generalized projective synchronization of chaotic systems via adaptive learning control

In this paper, a learning control approach is applied to the generalized projective synchronisation （GPS） of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov--Krasovskii functional stability theory, a differential-difference mixed parametric learning law and an adaptive learning control law are constructed to make the states of two different chaotic systems asymptotically synchronised. The scheme is successfully applied to the generalized projective synchronisation between the Lorenz system and Chen system. Moreover, numerical simulations results are used to verify the effectiveness of the proposed scheme.

Project Systems Engineering for Developing Space Robots

Space robots possess unique distinguishing features unlike general robots on earth, due to the particular environments in space. The developing of various practical space robots promoting the improvement of space science and technology is a complex man-machine-environment engineering problem. This paper analyses from the systems engineering viewpoint the space robot system in the scope of the architecture of robotics discipline, space environment characteristics, man-machine-environment system of space robots, the general methodology of project systems engineering and the process of space robot systems engineering.

Large and Moderate Deviations for Projective Systems and Projective Limits

One of the active fields in applied probability, the last two decades, is that of large deviations theory i.e. the one dealing with the (asymptotic) computation of probabilities of rare events which are exponentially small as a function of some parameter e.g. the amplitude of the noise perturbing a dynamical system. Basic ideas of the theory can be tracked back to Laplace, the first rigorous results are due to Cramer although a clear definition was introduced by Varadhan in 1966. Large deviations estimates have been proved to be the crucial tool in studying problems in Statistics, Physics (Thermodynamics and Statistical Mechanics), Finance (Monte-Carlo methods, option pricing, long term portfolio investment) and in Applied probability (queuing theory). The aim of this work is to describe one of the (recent) methods of proving large deviations results, namely that of projective systems. We compare the method with the one of projective limits and show the advantages of the first. These advantages are due to the fact that: 1) the arguments are direct and the proofs of the basic results of the theory are much easier and simpler;2) we are able to extend most of these results using suitable projective systems. We apply the method in the case of a) sequences of i.i.d. r.v.’s and b) sequences of exchangeable r.v.’s. All the results are being proved in a simple “unified” way.

A system dynamics model for billion trees tsunami afforestation project of Khyber Pakhtunkhwa in Pakistan:Model application to afforestation activities

As part of the global effort to plant billion trees,an afforestation project is launched in Pakistan in Khyber Pakhtunkhwa(KP)province to conserve existing forests and to increase area under forest cover.The present study is designed to build a Systems'model by incorporating major activities of the Billion Tree Tsunami Afforestation Project(BTTAP)with special focus on afforestation activities to estimate the growth in forest area of KP.Availability of complete dataset was a challenge.To fix the model,the raw data taken from the project office has been utilized.Planning Commission Form 1-Phase I&II helped us with additional information.We relied on the data available for one and half period of the project as rest of the data is subject to the completion of the project.Our results show that the project target to enhance area under forest differs from the target to afforest area under the project.The system dynamics'model projection shows that the forest area of KP would be 23.59 million hectares at the end of the BTTA project,thus having an increase of 3.29%instead of 2%that has been initially proposed.However,the results show that the progress to meet the target in some afforestation classes is slow as compared to other categories.Farm forestry,plantation on communal lands and owners'plantation need special focus of the authority.Deforestation would affect 0.02 million hectares area of the project.The model under study may be used as a reference model that can be replicated to other areas where billion tree campaigns are going on.

A new three-dimensional chaotic system and its modified generalized projective synchronization

Based on the Chen chaotic system, this paper constructs a new three-dimensional chaotic system with higher order nonlinear term and studies the basic dynamic behaviours of the system. The modified generalized projective synchronization has been observed in the coupled new three-dimensional chaotic system with unknown parameters. Furthermore, based on Lyapunov stability theory, it obtains the control laws and adaptive laws of parameters to make modified generalized projective synchronization of the coupled new three-dimensional chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.

Exact Projective Excitations of Nonautonomous Nonlinear Schrödinger System in (1 + 1)-Dimensions

With the aid of a direct projective approach, a general transformation solution for the nonautonomous nonlinear Schr?dinger (NLS) system is derived. Based on certain known exact solutions of the projective equation, some periodic and localized excitations with novel properties are correspondingly revealed by entrancing appropriate system parameters. The integrable constraint conditions for the nonautonomous NLS system derived naturally here are consistent with the compatibility condition via the Painlevé analysis in other literature.

Modified projective synchronization of a fractional-order hyperchaotic system with a single driving variable

In this paper, the modified projective synchronization （MPS） of a fractional-order hyperchaotic system is inves- tigated. We design the response system corresponding to the drive system on the basis of projective synchronization theory, and determine the sufficient condition for the synchronization of the drive system and the response system based on fractional-order stability theory. The MPS of a fractional-order hyperchaotic system is achieved by transmitting a single variable. This scheme reduces the information transmission in order to achieve the synchronization, and extends the applicable scope of MPS. Numerical simulations further demonstrate the feasibility and the effectiveness of the proposed scheme.

Projective Synchronization of One Fractional-order Chaotic System

In this paper,projective synchronization of one fractional-order chaotic system is studied.Firstly,the chaotic attractor is given.Then,suitable projective synchronization controllers are investigated based on the Lyapunov stability theory.Finally,the numerical simulations verify the validity and correction of the method.

Observer Based Projective Synchronization Method for a Class of Chaotic System-Part I: Linear Synchronization Subsystem

In this three-part paper, an observer based projective synchronization method for a class of chaotic system is proposed. At the transmitter, a general observer is used to create the scalar signal for synchronizing. In this part, the structure of the projective synchronization method is presented. And the condition of projection synchronization is theoretically analyzed when the synchronization subsystem is linear.

Adaptive projective synchronization of unified chaotic systems and its application to secure communication

In this paper, a simple adaptive linear feedback control method is proposed for controlling the scaling factor between two coupled unified chaotic systems to a desired value, based on the invarianee principle of differential equations. Under this control strategy, one can arbitrarily select the scaling factor. Numerical simulations are given to support the effectiveness of the proposed method and show the robustness against noise. Furthermore, a secure communication scheme based on the adaptive projective synchronization of unified chaotic systems is presented and numerical simulation shows its feasibility.

A Count Sketch Maximal Weighted Residual Kaczmarz Method with Oblique Projection for Highly Overdetermined Linear Systems

Motivated by the count sketch maximal weighted residual Kaczmarz (CS-MWRK) method presented by Zhang and Li (Appl. Math. Comput., 410, 126486), we combine the count sketch tech with the maximal weighted residual Kaczmarz Method with Oblique Projection (MWRKO) constructed by Wang, Li, Bao and Liu (arXiv: 2106.13606) to develop a new method for solving highly overdetermined linear systems. The convergence rate of the new method is analyzed. Numerical results demonstrate that our method performs better in computing time compared with the CS-MWRK and MWRKO methods.