How to synchronize an out of sync system?

Synchronization with other machines is one of those tasks that an intelligent machine should be able to perform. To do so, a general method of synchronization must be defined and that is the ambition of this article. For this purpose, we recall what the main concepts of systemic modelling consist of. Then we define what a Synchronization Problem is and distinguish three types of synchronization problems : predetermined (PSP), stochastic (SSP) and asymptotic (ASP). So, to find the best solution, we define three optimized synchronization problems : Optimized Predetermined Synchronization Problems , Optimized Stochastic Synchronization Problems (OSSP) and Optimized Asymptotic Synchronization Problems (OASP). A general method for solving an optimized synchronization problem and thus synchronize an out of sync system, is then given; it includes four steps : step 1, identify the synchronization functions; step 2, identify the synchronization case : predetermined, stochastic or asymptotic; step 3, select an optimization criterion and solve the optimized synchronization problem corresponding to the chosen synchronization case; step 4, find a control which permits to track the system trajectory, optimal solution of the selected optimized synchronization problem. In the next section, we present a heuristic algorithm that checks the constraints of an ASP for any initial state of the system to be synchronized. The principle of this algorithm is to pursue or track a perfectly synchronized solution. Finally, we present and solve two synchronization problems in the field of Mobile Robot Systems: a synchronized satelliteization problem and the Horse Carousel Problem. We apply to these two problems the general method given above by choosing the asymptotic synchronization case and our tracking algorithm. Simulation results show the efficiency of the method and the relevance of using a tracking algorithm.

How to synchronize an out of sync system?

Synchronization with other machines is one of those tasks that an intelligent machine should be able to perform. To do so, a general method of synchronization must be defined and that is the ambition of this article. For this purpose, we recall what the main concepts of systemic modelling consist of. Then we define what a Synchronization Problem is and distinguish three types of synchronization problems : predetermined (PSP), stochastic (SSP) and asymptotic (ASP). So, to find the best solution, we define three optimized synchronization problems : Optimized Predetermined Synchronization Problems , Optimized Stochastic Synchronization Problems (OSSP) and Optimized Asymptotic Synchronization Problems (OASP). A general method for solving an optimized synchronization problem and thus synchronize an out of sync system, is then given; it includes four steps : step 1, identify the synchronization functions; step 2, identify the synchronization case : predetermined, stochastic or asymptotic; step 3, select an optimization criterion and solve the optimized synchronization problem corresponding to the chosen synchronization case; step 4, find a control which permits to track the system trajectory, optimal solution of the selected optimized synchronization problem. In the next section, we present a heuristic algorithm that checks the constraints of an ASP for any initial state of the system to be synchronized. The principle of this algorithm is to pursue or track a perfectly synchronized solution. Finally, we present and solve two synchronization problems in the field of Mobile Robot Systems: a synchronized satelliteization problem and the Horse Carousel Problem. We apply to these two problems the general method given above by choosing the asymptotic synchronization case and our tracking algorithm. Simulation results show the efficiency of the method and the relevance of using a tracking algorithm.

Consensus in networks of uncertain robot manipulators without using neighbors’ velocity information

In this paper, new distributed adaptive methods are proposed for solving both leaderless and leader–follower consensus problems in networks of uncertain robot manipulators, by estimating only the gravitational torque forces. Comparing with the existing adaptive methods, which require the estimation of the whole dynamics, presented methods reduce the excitation levels required for efficient parameter search, the convergence time, and the complexity of the regressor. Additionally, proposed schemes eliminate the need for velocity information exchange between the agents. Global asymptotic synchronization is shown by introducing new Lyapunov functions. Simulation results are provided for a network of 10 4-DOF robot manipulators.

Asymptotic synchronization of a coupled system of wave equations on a rectangular domain with reflecting sides

We show the sufficiency of Kalman’s rank condition for the uniqueness of solution to a coupled system of wave equations in a rectangular domain. The approach does not need any gap condition on the spectrum of the differential operator and the usual multiplier geometrical condition. Then, the study on the asymptotic synchronization by groups can be improved for the corresponding system.

Synchronization of a Hyperchaotic Finance System

In this article, we propose a series of control strategies to synchronize two chaotic financial systems. Due to the characteristics of chaotic systems, the system is very sensitive to its initial values. Thus, the behaviour of two systems with different initial values will be completely different. In order to realize the synchronization of two financial chaotic systems, we designed a series of controls including controllers to realize global asymptotic synchronization and controllers to realize global exponential synchronization to make the two systems fully synchronized. We provide mathematical proofs to show that the designed controls are effective. Numerical methods are used to verify the effectiveness of the controls.

Global Asymptotic Synchronization of Fractional Order Multi-linked Memristive Neural Networks with Time-varying Delays via Discontinuous Control

In this paper, we address the global asymptotic synchronization (GAS) problem of the Master-Slave fractional order multi-linked memristive neural networks (FOMMNNs). Firstly, we propose the FOMMNNs which incorporate the fractional calculus into multi-linked memristive neural networks (MMNNs) for the first time. Then, by utilizing the fractional differential inclusions and set-valued mapping theories, the addressed FOMMNNs with discontinuous state switching at the right-hand side and time-varying delays are converted into the continuous FOMMNNs. Under the frameworks of fractional Caputo derivative and fractional Fillipov solution, by the way of building up appropriate Lyapunov functionals and utilizing some synchronous analysis technology, several sufficient criteria ensuring that the Master-Slave FOMMNNs can realize global asymptotic synchronization (GAS) under two different state-feedback controllers are obtained.

Asymptotic synchronization of fractional order non-identical complex dynamical networks with Parameter Uncertainties

This article specically deals with the asymptotic synchronization of non-identical complex dynamic fractional order networks with uncertainty. Initially, by using the Riemann-Liouville derivative, we developed a model for the general non-identical complex network, and based on the properties of fractional order calculus and the direct Lyapunov method in fractional order, we proposed that drive and response system if nonidentical complex networks ensuring asymp-totic synchronization by using neoteric control. Second, taking into account the uncertainties of non-identical complex networks in state matrices and evaluating theirrequirements forasymptotic synchronization. In addition, to explain the eectiveness of the proposed approach, two numerical simulations are given.