Synchronization of linear dynamical networks under stochastic impulsive coupling protocols

This paper investigates a stochastic impulsive coupling protocol for synchronization of linear dynamical networks based on discrete-time sampled-data. The convergence of the networks under the proposed protocol is discussed, and some sufficient conditions are showed to guarantee almost sure exponential synchronization. Moreover, this coupling protocol with a pinning control scheme is developed to lead the state of all nodes to almost sure exponentially converge to a virtual synchronization target. It is shown that the almost sure exponential synchronization can be achieved by only interacting based on the stochastic feedback information at discrete-time instants. Some numerical examples are finally provided to present the effectiveness of the proposed stochastic coupling protocols.     

Robust quantized consensus of discrete multi-agent systems under input saturation

In this paper, we consider the quantized consensus problem of multiple discrete-time integrator agents which suffer from input saturation. As agents transmit state information through communication networks with limited bandwidth, the states of agents have to be quantized into a finite number of bits before transmission. To handle this quantized consensus problem, we introduce an internal time-varying saturation function into the controllers of all agents and ensure that the range of the state of each agent can be known in advance by its neighboring agents. Based on such shared state range information, we construct a quantized consensus protocol which implements a finite-bit quantization strategy to all states of agents and can guarantee the achievement of the asymptotic consensus under any given input saturation threshold. Such desired consensus can be guaranteed at as low bit rate as 1 bit per time step for each agent. Moreover, we can place an upper bound on the convergence rate of the consensus error of agents. We further improve that quantized consensus protocol to a robust version whose parameters are determined with only an upper bound on the number of agents and does not require any more global information of the inter-agent network. Simulations are done to confirm the effectiveness of our quantized consensus protocols.     

Synchronization of switched logical control networks via event-triggered control

This paper investigates the event-triggered control design for state/output synchronization of switched k-valued logical control networks (SKVLCNs). Firstly, based on the algebraic form of SKVLCNs, some necessary and sufficient conditions are presented for the event-triggered state/output synchronization of SKVLCNs. Secondly, using the partitioning technique of matrix, a constructive procedure is proposed to design state feedback event-triggered controllers for the synchronization of SKVLCNs. Finally, an illustrative example is worked out to show the effectiveness of the obtained new results.     

Distributed consensus tracking control based on state and disturbance observations for mixed-order multi-agent mechanical systems

In this paper, we study the cooperative consensus control problem of mixed-order (also called hybrid-order) multi-agent mechanical systems (MMSs) under the condition of unmeasurable state, unknown disturbance and constrained control input. Here, the controlled mixed-order MMSs are consisted of the mechanical agents having heterogeneous nonlinear dynamics and even non-identical orders, which means that the agents can be of different types and their states to be synchronized can be not exactly the same. In order to achieve the ultimate synchronization of all mixed-order followers, we present a novel distributed adaptive tracking control protocol based on the state and disturbance observations. Wherein, a distributed state observer is used to estimate the followers’ and their neighbors’ unmeasurable states. And, a novel estimated-state-based disturbance observer (DOB) is proposed to reduce the effect of unknown lumped disturbance for the mixed-order MMSs. The proposed control protocol and observers are fully distributed and can be calculated for each follower locally. Lyapunov theory is used for proving the stability of the proposed control algorithm and the convergence of the cooperative tracking errors. A practical cooperative longitudinal landing control example of unmanned aerial vehicles (UAVs) is given to illustrate the effectiveness of the presented control protocol.     

Fixed-time outer synchronization of hybrid-coupled delayed complex networks via periodically semi-intermittent control

In this paper, the fixed-time synchronization between two delayed complex networks with hybrid couplings is investigated. The internal delay, transmission coupling delay and self-feedback coupling delay are all included in the network model. By introducing and proving a new and important differential equality, and utilizing periodically semi-intermittent control, some fixed-time synchronization criteria are derived in which the settling time function is bounded for any initial values. It is shown that the control rate, network size and node dimension heavily influence the estimating for the upper bound of the convergence time of synchronization state. Finally, numerical simulations are performed to show the feasibility and effectiveness of the control methodology by comparing with the corresponding finite-time synchronization problem.     

Adaptive synchronization of unknown heterogeneous agents: An adaptive virtual model reference approach

This work deals with state synchronization of heterogeneous linear agents with unknown dynamics. The problem is solved by formulating the synchronization problem as a special model reference adaptive control where each agent tries to converge to the model defined by its neighbors. For those agents that do not know the reference signal that drives the flock, a fictitious reference is estimated in place of the actual one: the estimation of such reference is distributed and requires measurements from neighbors. By using a matching condition assumption, which is imposed so that the agents can converge to the same behavior, the fictitious reference estimation leads to adaptive laws for the feedback and the coupling gains arising from distributed matching conditions. In addition, the coupling connection is not scalar as in most literature, but possibly vector-valued. The proposed approach is applicable to heterogeneous agents with arbitrarily large matched uncertainties. A Lyapunov-based approach is derived to show analytically asymptotic convergence of the synchronization error: robustification in the presence of bounded errors or unknown (constant) leader input is also discussed. Finally, a motivational example is presented in the context of Cooperative Adaptive Cruise Control and numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Distributed fault detection for nonlinear multi-agent systems under fixed-time observer

This paper mainly investigates the fault detection problem for nonlinear multi-agent systems with actuator faults. For fault detection, a fixed-time observer is proposed by employing auxiliary variable received from neighbor agents. Then, with the aid of the observer, a residual vector is introduced by the auxiliary variable to detect the faults occurring on any followers, and each observer can estimate the whole state of followers. Moreover, the convergence time is dependent on the parameters of the designed observer and independent of initial condition of system state. Finally, the theoretical result is verified by a simulation example.     

On convergence of the discrete-time nonlinear extended state observer

This paper concerns with the convergence of the discrete-time nonlinear extended state observer (ESO). Several kinds of discrete-time nonlinear ESO (NLESO) are proposed and then sufficient conditions based on linear matrix inequality (LMI) method are obtained to quantitatively reveal the relationship between the plant, the sampling interval, the parameter values of NLESO and its convergence. The theoretical results are verified by simulation using a motion control system. It shows that there may exist an optimal ω_o for a certain fixed sampling interval, and a smaller sampling interval generally generates better performance. What’s more, the proposed digital implementations of NLESO improve its performance over traditional Euler approximation discretization method.     

Adaptive synchronization of complex networks with general distributed update laws for coupling weights

This paper discusses adaptive synchronization control for complex networks interacted in an undirected weighted graph, and aims to provide a novel and general approach for the design of distributed update laws for adaptively adjusting coupling weights. The proposed updating laws are very general in the sense that they encompass most weight update laws reported in the literature as special cases, and also provide new insights in the analysis of network system evolution and graph weight convergence. We show a rigorous proof for the synchronization stability of the overall complex network to a synchronized state, and demonstrate the convergence of adaptive weights for each edge to some bounded constants. A detailed comparison with available results is provided to elaborate the new features and advantages of the proposed adaptive strategies as compared with conventional adaptive laws. The effectiveness of the proposed approach is also validated by several typical simulations.     

Event-triggered interval-based state estimator for continuous-time linear systems

In this paper we propose an interval-based state estimator for continuous-time linear systems with discrete-time measurements using an event-triggered mechanism and an explicit reachability method. An output injection method combined with a state variables permutation procedure are applied to design the robust estimator. In addition, the convergence of the proposed set-membership state estimator and the existence of a lower bound on the inter-event times are shown. Throughout a numerical example, the performance of this estimator are illustrated and compared to related works.     

Propagation of projective synchronization in a series connection of chaotic systems

Projective synchronization is a type of chaos synchronization where the response system states are scaled replicas of the drive system states. This paper deals with the propagation of projective synchronization in a series connection of N chaotic discrete-time drive systems and N response systems. By exploiting an observer-based approach, the paper demonstrates that dead-beat projective synchronization (i.e., exact synchronization in finite time for any scaling factor) is achieved between the nth drive and nth response systems. In particular, it is shown that projective synchronization starts from the innermost (Nth) drive-response system pair and propagates toward the outermost (first) drive-response system pair. Only a single scalar synchronizing signal connects the cascaded drive and response systems. Finally, an example illustrates the propagation of different types of chaos synchronization in a series connection consisting of a Gingerbreadman map, a third order hyperchaotic Henon map and a Lozi map.     

Fixed-time scaled consensus of multi-agent systems with input delay

The design of fixed-time scaled consensus protocol for multi-agent systems with input delay is developed in this article. First, by virtue of Artstein model reduction method, the time-delay system is converted into a delay-free one. Then, two novel controllers are designed such that the fixed-time scaled consensus of multi-agent systems can be realized for the undirected and directed topology, respectively. Sufficient conditions are derived to guarantee that all agents converge to the assigned ratios instead of the same value under any bounded input delay. Besides, an explicit estimate can be given for the uniform convergence time independent of the initial conditions. Moreover, it is proved that the convergence value of the system is not affected by the initial states of agents any more, but only related to initial states of the virtual agents set in advance. Finally, numerical simulations are given to demonstrate the feasibility of the proposed algorithms.     

Lag quasi-synchronization of incommensurate fractional-order memristor-based neural networks with nonidentical characteristics via quantized control: A vector fractional Halanay inequality approach

This work realizes lag quasi-synchronization of incommensurate fractional-order memristor-based neural networks (FMNNs) with nonidentical characteristics via quantized control. The motivations behind this research work are threefold: (1) quantized controllers, which generate discrete control signals, can be more easily realized in computers than non-quantized controllers, and can consume smaller communication capacity; (2) incommensurate orders in a single FMNN and nonidentical characteristics in drive-response FMNNs are inescapable due to the differences among the circuit elements used to implement FMNNs; (3) convergence analysis of delayed incommensurate fractional-order nonlinear systems, which is the basis for the derivation of synchronization criterion, has not been handled perfectly. As an effective tool for convergence analysis of delayed incommensurate fractional-order nonlinear systems, especially for estimation of ultimate state bound, a vector fractional Halanay inequality is established at first. Then, a quantized synchronization controller, in which the dead-zone is introduced into some logarithmic quantizers to avoid chattering phenomenon, is designed. By means of vector Lyapunov function together with the newly derived vector fractional Halanay inequality, the synchronization criterion is proved theoretically. Lastly, numerical simulations supplementarily illustrate the correctness of the synchronization criterion. In contrast with the hypotheses in the relevant literature, the hypotheses in this paper are weaker.     

Adaptive synchronization of coupled harmonic oscillators under switching topology

This paper investigates the adaptive synchronization for coupled harmonic oscillators with switching topology. Edge-based adaptive control protocols are proposed for both leaderless and leader-following synchronization for coupled harmonic oscillators with switching topology. Using Lyapunov stability theory, by parting the topology graph into connected components (containing at least two connected vertices) and isolated vertex components (containing a isolated vertex), full distributed adaptive synchronization conditions are obtained, which can guarantee that the synchronization conditions do not require any global information except a mild connection assumption. Finally numerical simulations are presented to illustrate the theoretical findings.     

Synchronization of coupled heterogeneous complex networks

By only designing the internal coupling, quasi synchronization of heterogeneous complex networks coupled by N nonidentical Duffing-type oscillators without any external controller is investigated in this paper. To achieve quasi synchronization, the average of states of all nodes is designed as the virtual target. Heterogeneous complex networks with two kinds of nonlinear node dynamics are analyzed firstly. Some sufficient conditions on quasi synchronization are obtained without designing any external controller. Quasi synchronization means that the states of all nonidentical nodes will keep a bounded error with the virtual target. Then the heterogeneous complex network with impulsive coupling which means the network only has coupling at some discrete impulsive instants, is further discussed. Some sufficient conditions on heterogeneous complex network with impulsive coupling are derived. Based on these results, heterogeneous complex network can still reach quasi synchronization even if its nodes are only coupled at discrete impulsive instants. Finally, two examples are provided to verify the theoretical results.     

Flocking motion in swarms with limited sensing radius and heterogeneous input constraints

This paper addresses the flocking motion problem for swarms of agents with two restrictions: limited communication/detection ranges and different input constraints. In this problem, the distance between pairs of agents determines if a communication/detection link exists among them, while each agent has a different control action bound. We use the notion of proximity graph to model communication/detection between agents and provide distributed controllers designed for leaderless and leader-followers flocking motion scenarios. Our proposed designs preserve the connectivity of the proximity graph while the control effort satisfies the bound of each particular agent. Unlike previous results, our protocols take advantage of the group’s input heterogeneity to use agents with a greater capacity to compensate for neighbors that are less capable of meeting the group’s requirements. Additionally, our designs are based only on local state errors and are robust to non-modeled edge failures. To illustrate the effectiveness of our proposal, we use numerical simulations of different flocking scenarios.     

Analysis of distributed consensus protocols with multi-equilibria under time-delays

In this paper, we propose a novel method for addressing the multi-equilibria consensus problem for a network of n agents with dynamics evolving in discrete-time. In this method, we introduce, for the first time in the literature, two concepts called primary and secondary layer subgraphs. Then, we present our main results on directed graphs such that multiple consensus equilibria states are achieved, thereby extending the existing single-state consensus convergence results in the literature. Furthermore, we propose an algorithm to determine the number of equilibria for any given directed graph automatically by a computer program. We also analyze the convergence properties of multi-equilibria consensus in directed networks with time-delays under the assumption that all delays are bounded. We show that introducing communication time-delays does not affect the number of equilibria of the given network. Finally, we verify our theoretical results via numerical examples.     

Adaptive synchronization of complex dynamic networks with switching parameters subject to state constraints in power system

This paper deals with the synchronization control of power complex networks with switching parameters. In the meantime, the node state constraints are considered during the synchronization process. Admittedly, synchronization problem encountered in power complex networks is becoming progressively important due to the increasing connection and disconnection operations resulting from sustainable energy and controllable load. Hereon, the network model considering switching parameters of each node is established to describe the topology variation of power systems that may be confronted in practical terms. Then, by utilizing the adaptive backstepping technique with a barrier Lyapunov function (BLF), a novel synchronization controller is constructed recursively which accomplishes the nodes full states tracking within the predefined transient behavior. Owing to the characteristic of BLF, the designed controller as well as its adaptive law could guarantee both the constrained state of each node restricted by a prescribed range and the synchronization performance. Meanwhile, the bounded output of the system could track the desired trajectory. Finally, scenario simulations are performed to demonstrate the effectiveness and superiority of the proposed method.     

State structures in digital filter configurations—I. conventional and nodal state structures

This paper presents a formal precedure for determining the state-space representations of any digital network consisting of adders, multipliers, and delays. Such representations are called state structures whenever the state variables are exclusively identified to the appropriately chosen internal node variables of the network. In general, the state structures corresponding to a given network are not unique. In Part I of the paper we present techniques of obtaining the various state structures where the associated state vectors have dimensions equal to the number of dynamic elements (in our case delays) in the network. In Part II we shall treat the subject of lowering the dimension of such state-space representations.