Robust Synchronization Research Articles

Robust Synchronization of Duffing System Using Integral Action in Backstepping Design

Backstepping is a realistic nonlinear control design algorithm based on Lyapunov design approach; therefore, it automatically ensures the convergence of the regulated variable to zero. In this paper, it has been proposed for robust synchronization of Duffing chaotic systems. Integral action is being used to enhance the control action of the controller in steady state against the disturbances. The salient feature of the design is that the derived control doesn’t contain any derivative terms; consequently it simplifies the controller realization. The effectiveness of the proposed controller has been demonstrated in simulation studies. The performance of the controller has been evaluated not only based on its synchronizing ability but also the disturbance rejection ability of the controller has been verified.

Robust Synchronization for Discrete-Time Coupled Markovian Jumping Neural Networks With Mixed Time-Delays

This paper concerns the robust synchronization problems for discrete-time coupled neural networks with discrete time delay and distributed time delays. Inner parameters in individual neural network are subject to be uncertain and both coupled matrixes and weight matrixes are supposed to switch from one mode to another because of the markovian jumping chain. Mixed time delays contain discrete and distributed time delays and the mixed time delays not only exist in the individual neural cell, but also exist in the coupled cells. By using the novel Lyapunov-Krasovskii functional method and Kronecker product as tools, mean square stability conditions are provided in terms of linear matrix inequalities. In numerical simulations, two examples (with and without unknown parameters) are given and simulation results show the robustness and effectiveness of our methods.

Synchronization of semi-Markov coupled neural networks with impulse effects and leakage delay

This paper examines the robust synchronization problem for a class of coupled neural networks in mean-square sense subject to semi-Markov jump, outer coupling, leakage and time-varying delay through a resilient memory state feedback controller, wherein the effect of impulse strategy is considered in the system design. Particular, impulsive perturbation and leakage delay are incorporated in the system model cannot be neglected since they make huge impact on the stability behaviour. By endowing Lyapunov’s direct method, a newest set of necessary conditions is enhanced in the form of linear matrix inequalities (LMIs) which guarantee that the addressed system can realize synchronization criterion. Based on these obtained LMIs, the explicit characterization of the designed controller is retrieved interms of linear matrix inequalities by using the convex optimization algorithm. Eventually, the analytical design are voiced by a numerical example which substantiate the superiority and efficiency of the proposed control design strategy.

Two-dimensional mutually synchronized spin Hall nano-oscillator arrays for neuromorphic computing.

In spin Hall nano-oscillators (SHNOs), pure spin currents drive local regions of magnetic films and nanostructures into auto-oscillating precession. If such regions are placed in close proximity to each other they can interact and may mutually synchronize. Here, we demonstrate robust mutual synchronization of two-dimensional SHNO arrays ranging from 2 × 2 to 8 × 8 nano-constrictions, observed both electrically and using micro-Brillouin light scattering microscopy. On short time scales, where the auto-oscillation linewidth [Formula: see text] is governed by white noise, the signal quality factor, [Formula: see text], increases linearly with the number of mutually synchronized nano-constrictions (N), reaching 170,000 in the largest arrays. We also show that SHNO arrays exposed to two independently tuned microwave frequencies exhibit the same synchronization maps as can be used for neuromorphic vowel recognition. Our demonstrations may hence enable the use of SHNO arrays in two-dimensional oscillator networks for high-quality microwave signal generation and ultra-fast neuromorphic computing.

Optimal traffic control at smart intersections: Automated network fundamental diagram

Recent advances in artificial intelligence and wireless communication technologies have created great potential to reduce congestion in urban networks. In this research, we develop a stochastic analytical model for optimal control of communicant autonomous vehicles (CAVs) at smart intersections. We present the automated network fundamental diagram (ANFD) as a macro-level modeling tool for urban networks with smart intersections. In the proposed cooperative control strategy, we make use of the headway between the CAV platoons in each direction for consecutive passage of the platoons in the crossing direction through non-signalized intersections with no delay. For this to happen, the arrival and departure of platoons in crossing directions need to be synchronized. To improve system robustness (synchronization success probability), we allow a marginal gap between arrival and departure of the consecutive platoons in crossing directions to make up for operational error in the synchronization process. We then develop a stochastic traffic model for the smart intersections. Our results show that the effects of increasing the platoon size and the marginal gap length on the network capacity are not always positive. In fact, the capacity can be maximized by optimizing these cooperative control variables. We analytically solve the traffic optimization problem for the platoon size and marginal gap length and derive a closed-form solution for a normal distribution of the operational error. The performance of the network with smart intersections is presented by a stochastic ANFD, derived analytically and verified numerically using the results of a simulation model. The simulation results show that optimizing the control variables increases the capacity by 138% when the error standard deviation is 0.1 s.

Finite-time and fixed-time synchronization control of fuzzy Cohen-Grossberg neural networks

This paper aims to investigate the finite-time and fixed-time robust synchronization of fuzzy Cohen-Grossberg neural networks with discontinuous activations. To deal with the discontinuous property, the framework of Filippov solution is invoked to solve the inexistence of the classical solutions. For the purpose of achieving fixed-time synchronization, we turn to investigating the fixed-time stability problem of the error system between the drive-response systems. By the functional differential inclusions theory, inequality technique and the non-smooth Lyapunov-Krasovskii functional and designing a simple discontinuous state-feedback control law for the response neural system, some sufficient algebraic criteria are derived to achieve synchronization within a fixed time, and the settling time is given. Moreover, based on the fixed-time robust synchronization and under the same basic assumptions, we further complete the finite-time synchronization of the addressed drive-response systems by designing a simple switching adaptive controller, and the upper bound of the settling time is also estimated. It should be regarded as the first time to study the finite-time synchronization of fuzzy Cohen-Grossberg neural networks with discontinuous activations based on the adaptive control. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed synchronization strategies.

Non-fragile robust finite-time synchronization for fractional-order discontinuous complex networks with multi-weights and uncertain couplings under asynchronous switching

This paper focus on the global robust non-fragile finite-time synchronization issue for fractional-order complex networks with multi-weights and uncertain couplings under asynchronous switching topology, where nonlinear dynamic nodes are discontinuous and non-decreasing. Firstly, the non-fragile controller with switching gains is designed. Secondly, under the fractional Filippov differential inclusion framework and the network topologies with no-delayed and delayed couplings, by adopting multiple Lur’e Postnikov-type Lyapunov functional, nonsmooth analysis method and the average dwell time technique, the global robust non-fragile finite-time synchronization conditions are achieved in terms of linear matrix inequalities (LMIs), respectively. Finally, the validity of the theoretical results developed in this paper is verified by two numerical simulations.

Robust adaptive synchronization of complex network with bounded disturbances

In this paper, we investigate distributed robust adaptive synchronization for complex networked systems with bounded disturbances. We propose both average synchronization protocol and leader-following synchronization protocol based on adaptive control and variable structure control strategies. The synchronization conditions do not require any global information except a connection assumption under the adaptive control method. Furthermore, the external disturbances are attenuated effectively. Finally, we present numerical simulations to illustrate the theoretical findings.

Output global oscillatory synchronisation of heterogeneous systems

The global output synchronisation problem for heterogeneous nonlinear systems having relative degree 2 or higher is studied. The proposed approach consists in two steps. First, a partial projection of individual subsystems into the Brockett oscillators is performed using a sliding-mode control. Second, the network of these oscillators is synchronised using the global synchronisation results of a particular second-order nonlinear oscillator model from Ahmed, Ushirobira, and Efimov [(2019). Robust global synchronization of brockett oscillators. IEEE Transactions on Control of Network Systems, 6(1), 289–298]. Our approach is based on output feedback and uses a higher order sliding mode observer to estimate the states and perturbations of the synchronised nonlinear systems. Along with numerical simulations, the performance of the proposed synchronisation scheme is experimentally verified on a network of Van der Pol oscillators.

A Robust Transceiver for Narrow-Band Communications in Presence of Carrier Frequency Offset

We address narrow-band communications in presence of large and time-varying carrier frequency offset (CFO) at the receiver. This is a general assumption which includes the condition due to the Doppler effect where the transmitter and/or receiver are moving with a relative time-varying speed. A robust transceiver system is proposed to dynamically estimate and compensate the CFO. The proposed system is particulary attractive for low data-rate communications (e.g., voice service) where the CFO is significantly larger than the data bandwidth. A two-step carrier recovery scheme is developed with large acquisition range and fast frequency tracking. The proposed method provides accurate CFO estimation with affordable complexity. We also devise a robust frame synchronization scheme to provide accurate timing in presence of CFO. Furthermore, non-coherent detection with soft-decision decoding is employed to provide a low-complexity receiver with acceptable sensitivity. The proposed transceiver design is implemented on FPGA and real-time experiments are conducted on a Xilinx ZC706 evaluation base board along with AD-FMCOMMS3 daughterboard. After validating the experiments compared to the simulation results, the design was optimized for implementation on XC7Z020 and further integrated with the analog front-end on a board with smaller footprint.

Robust synchronisation control of discontinuous CGNNs with time-varying delays

Fixed-time synchronisation requires that the settling time is independent of the initial synchronisation errors and the upper bound of the settling time can be given in advance. From this point of view, the fixed time synchronisation is more favourable and applicable. This paper aims to investigate the fixed-time synchronisation and fixed-time anti-synchronisation of Cohen-Grossberg master-slave neural networks with discontinuous neuron activations and time delays. For the purpose of fixed-time synchronisation, under the framework of Filippov solution, by using the Lyapunov-Krasovskii functional approach and designing a novel discontinuous feedback control procedure for the slave neural networks, some sufficient criteria are firstly derived to design the control parameters for achieving synchronisation within a fixed time for the proposed discontinuous Cohen-Grossberg neural networks. Then, based on the fixed-time synchronisation, another new discontinuous feedback controller is also designed to accomplish the fixed-time anti-synchronisation for the considered neural system. Finally, two numerical examples associated with main theorems and corollaries are presented to illustrate the proposed methodologies.

Stability analysis and robust synchronization of fractional‐order competitive neural networks with different time scales and impulsive perturbations

SummaryThis article mainly examine a class of robust synchronization, global stability criterion, and boundedness analysis for delayed fractional‐order competitive type‐neural networks with impulsive effects and different time scales. Firstly, by endowing the robust analysis skills and a new class of Lyapunov‐Krasovskii functional approach, the error dynamical system is furnished to be a robust adaptive synchronization in the voice of linear matrix inequality (LMI) technique. Secondly, by ignoring the uncertain parameter terms, the existence of equilibrium points are established by means of topological degree properties, and the solution representation of the considered network model are provided. Thirdly, a novel global asymptotic stability condition is proposed in the voice of LMIs, which is less conservative. Finally, our analytical results are justified with two numerical examples with simulations.

Passively synchronized dual-color mode-locked fiber lasers based on nonlinear amplifying loop mirrors.

We have proposed and implemented a scheme for passive all-optical synchronization between erbium and ytterbium mode-locked fiber lasers. The passive locking of repetition rates for the dual-color pulses was realized by cross-phase modulation within phase-biased nonlinear amplifying loop mirrors. In contrast to previous demonstrations, the synchronization system was configured in an all-polarization-maintaining structure, thus gaining substantially improved stability and robustness. Consequently, the maximum tolerance of a cavity-length mismatch of 16.2mm was achieved unprecedentedly, which was at least one order of magnitude longer than previously reported results for comparable temporal durations of involved pulses. The corresponding relative timing jitter was measured to be 31fs within a 1MHz bandwidth. Such a tight and robust synchronization fiber laser system offers great potential for various applications such as pump-probe microscopy, Raman scattering spectroscopy, and nonlinear frequency generation.

Synchronization of a periodic modulation of mirrors in an optomechanical system

Proposing an optomechanical cavity modulated periodically, we have studied the modulation synchronization of the mechanical modes of mirrors. A periodic modulation has been applied to one of the mirrors, where the second mirror has the capability of oscillation with no modulation on that. As a result of having the periodic modulation, we have found a phase-locking synchronization between the mechanical modes of the mirrors and the enhancement of quantum synchronization. Considering the fact that periodic modulation can make squeezed states, we have shown that there is a robust synchronization of periodic modulation against enhancement of detuning between the mirrors. Also, our results show that having a periodic modulation leads to a stationary entanglement generation between the mirrors.

Statistical characterisation and analysis of differential correlation‐based frame detector

Next generation satellite systems are required to perform robust frame synchronisation in the presence of large frequency offsets at low carrier-to-noise ratios. Differential correlation-based frame acquisition is an appealing choice for these systems as it provides adequate performance with reasonable complexity. However, the theoretical characterisation of the multi-span differential correlation metric is still an open problem due to the fact that the correlation outputs with multiple delays are correlated. In this study, the authors derived novel closed-form approximations for the distribution of the multi-span differential correlation metric as well as the probabilities of miss-detection and false alarm. The close agreement between the simulated and theoretical receiver operating curves validates the analysis. This analysis can be used to characterise the performance of multi-span differential correlation-based frame synchroniser in terms of the number of delays without running computationally extensive Monte Carlo simulations.

Observer-based robust synchronization of fractional-order multi-weighted complex dynamical networks

In this paper, the problem of robust synchronization of fractional-order multi-weighted complex dynamical networks in the presence of time-varying coupling delay and disturbances is studied via fractional-order equivalent-input-disturbance (FOEID) estimator-based non-fragile feedback control scheme. Precisely, FOEID-based disturbance estimator is incorporated in the feedback control input to compensate the disturbance effect in the resulting closed-loop system, which removes the disturbance effect without any prior knowledge of it. By utilizing FOEID method and synchronization error dynamics, the synchronization problem of fractional-order complex dynamical network is transformed into the stability problem of the augmented form of the closed-loop error system. Based on the Lyapunov stability theory, fractional calculus theory and some advanced integral inequalities, a novel set of sufficient conditions is established to ensure the robust asymptotic stability of the augmented error system subject to time-varying delay and disturbances. Finally, two numerical examples including a comparison study are given to illustrate the obtained theoretical results and the control design.

Robust Adaptive Attitude Synchronization of Uncertain Rigid Bodies on Special Orthogonal Group with Communication Delays and Gyro Biases

The paper proposes an attitude synchronization algorithm of rigid bodies on Special Orthogonal Group SO(3), with parameter uncertainties, external disturbances, gyro biases and communication delays. A set of two-order linear filters are introduced to cope with discontinuous communication delays, and only attitude information is required to be exchanged between rigid bodies. Then a set of gyro bias estimators are constructed with exponential convergence rates in the constant bias case and can also deal with time-varying gyro biases. Besides, a novel attractive manifold control method is also proposed so that the parameter estimation error terms can converge to zeros independent of persistent excitation condition. The proposed attractive manifold control method can be also robust toward external disturbances. The obtained control inputs are continuous and ensure the control performance of the closed-loop system, in the presence of discontinuous communication delays, external disturbances, parameter uncertainties and gyro biases. The effectiveness of the proposed algorithm is verified in the numerical simulations.

Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview

Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization algorithms due to their susceptibility to spurious local minima, simple iterative methods such as gradient descent have been remarkably successful in practice. The theoretical footings, however, had been largely lacking until recently. In this tutorial-style overview, we highlight the important role of statistical models in enabling efficient nonconvex optimization with performance guarantees. We review two contrasting approaches: (1) two-stage algorithms, which consist of a tailored initialization step followed by successive refinement; and (2) global landscape analysis and initialization-free algorithms. Several canonical matrix factorization problems are discussed, including but not limited to matrix sensing, phase retrieval, matrix completion, blind deconvolution, robust principal component analysis, phase synchronization, and joint alignment. Special care is taken to illustrate the key technical insights underlying their analyses. This article serves as a testament that the integrated consideration of optimization and statistics leads to fruitful research findings.

Event-triggered passivity and synchronization of delayed multiple-weighted coupled reaction–diffusion neural networks with non-identical nodes

This paper solves the event-triggered passivity and synchronization problems for delayed multiple-weighted coupled reaction–diffusion neural networks (DMWCRDNNs) composed of non-identical nodes with and without parameter uncertainties. On one side, by designing appropriate event-triggered controllers, several passivity and synchronization criteria for DMWCRDNNs with certain parameters under the designed event-triggered conditions are derived based on the Lyapunov functional method and some inequality techniques. On the other side, we consider that the external perturbations may lead the parameters in network model to containing uncertainties, robust event-triggered passivity and synchronization for DMWCRDNNs with parameter uncertainties are investigated. Finally, two examples with numerical simulation results are provided to illustrate the effectiveness of the obtained theoretical results.

Robust master-slave synchronization of chaos in a one-sided 1-DoF impact mechanical oscillator subject to parametric uncertainties and disturbances

This paper addresses the problem of robust master-slave synchronization of chaos in a 1-DoF impact mechanical oscillator with a single rigid constraint. The master is considered to be with nominal parameters, whereas the slave impacting system is considered to be subject to polytopic parametric uncertainties and disturbances. We adopt a state-feedback controller for the robust stabilization of the master-slave synchronization error and the Linear Matrix Inequality (LMI) approach for the design of stability conditions. We use the S-procedure Lemma in order to only consider the regions within which the two impacting systems evolve. Thus, the stability conditions are formulated in terms of Bilinear Matrix Inequalities (BMIs). Via some technical Lemmas and congruence transformations, we transform these BMIs into LMIs, which are numerically traceable. An improved LMI-based optimization problem is proposed to solve the problem of high gains of the controller. Finally, the robustness of the proposed state-feedback feedback controller towards parametric uncertainties and disturbances is presented through simulation results showing then the master-slave synchronization of chaos in the one-sided 1-DoF impact mechanical oscillator.