Observer-Based Discrete-Time Nonnegative Edge Synchronization of Networked Systems

Variable Gain Impulsive Synchronization for Discrete-Time Delayed Neural Networks and Its Application in Digital Secure Communication

This article revisits the problems of impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks (DDNNs) in the presence of disturbance in the input channel. A new Lyapunov approach based on double Lyapunov functionals is introduced for analyzing exponential input-to-state stability (EISS) of discrete impulsive delayed systems. In the framework of double Lyapunov functionals, a pair of timer-dependent Lyapunov functionals are constructed for impulsive DDNNs. The pair of Lyapunov functionals can introduce more degrees of freedom that not only can be exploited to reduce the conservatism of the previous methods, but also make it possible to design variable gain impulsive controllers. New design criteria for impulsive stabilization and impulsive synchronization are derived in terms of linear matrix inequalities. Numerical results show that compared with the constant gain design technique, the proposed variable gain design technique can accept larger impulse intervals and equip the impulsive controllers with a stronger disturbance attenuation ability. Applications to digital signal encryption and image encryption are provided which validate the effectiveness of the theoretical results.

Decentralized H2 Control for Discrete-Time Networked Systems With Positivity Constraint

In this brief, we study the decentralized H2 state-feedback control problem for networked discrete-time systems with positivity constraint. This problem (for a single positive system), raised recently in the area of positive systems theory, is known to be challenging due to its inherent nonconvexity. In contrast to most works, which only provide sufficient synthesis conditions for a single positive system, we study this problem within a primal-dual scheme, in which necessary and sufficient synthesis conditions are proposed for networked positive systems. Based on the equivalent conditions, we develop a primal-dual iterative algorithm for solution, which helps prevent from converging to a local minimum. In the simulation, two illustrative examples are employed for verification of our proposed results.

Nonnegative Consensus Tracking of Networked Systems With Convergence Rate Optimization

This article investigates the nonnegative consensus tracking problem for networked systems with a distributed static output-feedback (SOF) control protocol. The distributed SOF controller design for networked systems presents a more challenging issue compared with the distributed state-feedback controller design. The agents are described by multi-input multi-output (MIMO) positive dynamic systems which may contain uncertain parameters, and the interconnection among the followers is modeled using an undirected connected communication graph. By employing positive systems theory, a series of necessary and sufficient conditions governing the consensus of the nominal, as well as uncertain, networked positive systems, is developed. Semidefinite programming consensus design approaches are proposed for the convergence rate optimization of MIMO agents. In addition, by exploiting the positivity characteristic of the systems, a linear-programming-based design approach is also proposed for the convergence rate optimization of single-input multi-output (SIMO) agents. The proposed approaches and the corresponding theoretical results are validated by case studies.

Further Improvements on Non-Negative Edge Consensus of Networked Systems

In this article, the non-negative edge consensus problem is addressed for positive networked systems with undirected graphs using state-feedback protocols. In contrast to existing results, the major contributions of this work included: 1) significantly improved criteria of consequentiality and non-negativity, therefore leading to a linear programming approach and 2) necessary and sufficient criteria giving rise to a semidefinite programming approach. Specifically, an improved upper bound is given for the maximum eigenvalue of the Laplacian matrix and the (out-) in-degree of the degree matrix, and an improved consensuability and non-negativevity condition is obtained. The sufficient condition presented only requires the number of edges of a nodal network without the connection topology. Also, with the introduction of slack matrix variables, two equivalent conditions of consensuability and non-negativevity are obtained. In the conditions, the system matrices, controller gain, as well as Lyapunov matrices are separated, which is helpful for parameterization. Based on the results, a semidefinite programming algorithm for the controller is readily developed. Finally, a comprehensive analytical and numerical comparison of three illustrative examples is conducted to show that the proposed results are less conservative than the existing work.

Consensus of Positive Networked Systems on Directed Graphs

This article addresses the distributed consensus problem for identical continuous-time positive linear systems with state-feedback control. Existing works of such a problem mainly focus on the case where the networked communication topologies are of either undirected and incomplete graphs or strongly connected directed graphs. On the other hand, in this work, the communication topologies of the networked system are described by directed graphs each containing a spanning tree, which is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains. Specifically, the problem involves complex eigenvalues, the Hurwitzness of complex matrices, and positivity constraints, which make analysis difficult in the Laplacian matrix. First, a necessary and sufficient condition for the consensus analysis of directed networked systems with positivity constraints is given, by using positive systems theory and graph theory. Unlike the general Riccati design methods that involve solving an algebraic Riccati equation (ARE), a condition represented by an algebraic Riccati inequality (ARI) is obtained for the existence of a solution. Subsequently, an equivalent condition, which corresponds to the consensus design condition, is derived, and a semidefinite programming algorithm is developed. It is shown that, when a protocol is solved by the algorithm for the networked system on a specific communication graph, there exists a set of graphs such that the positive consensus problem can be solved as well.

H∞ Control for Observer-Based Non-Negative Edge Consensus of Discrete-Time Networked Systems

This article is concerned with observer-based non-negative edge-consensus (OBNNEC) problems of networked discrete-time systems with or without actuator saturation. An algorithm which only uses actual outputs of neighboring edges is proposed by means of an H_∞ control method and modified algebraic Riccati equation (MARE)-based technique. The observer matrix and feedback matrix are constructed by solving the MARE and linear matrix inequality (LMI), respectively. Then, sufficient conditions for guaranteeing bounded inputs and non-negative edge states are derived. In addition, the low-gain characteristic of the MARE-based method is instrumental in guaranteeing non-negative edge states and deriving the feasible observer matrix and feedback matrix. Finally, two examples are shown to demonstrate the obtained theoretical results.

Consensus of Second-Order Hybrid Multiagent Systems by Event-Triggered Strategy

In this article, an event-triggered method is proposed to solve the consensus of the second-order hybrid multiagent systems (MASs), which contain discrete-time and continuous-time individuals. First, we give a selection criteria of the coupling gains, the eigenvalues of communication topology, and the event-triggered sampling interval to guarantee the hybrid consensus, which have an impact on system stability, due to the interaction and co-existence of discrete-time and continuous-time individuals. Second, the hybrid second-order consensus under the event-triggered strategy is proven, where the agents communicate with their neighbors and update their controllers only at the triggered instants. Finally, we give some simulation examples to prove the validity of the main results.

Semiglobal Observer-Based Non-Negative Edge Consensus of Networked Systems With Actuator Saturation

The observer-based edge-consensus problem of networked continuous-time dynamical systems with edge state non-negative constraint and actuator saturation is considered in this paper. Based on line graph theory, low-gain output-feedback technique and algebraic Riccati equation (ARE)-based method, two edge-consensus algorithms are designed to achieve the observer-based edge consensus, in which the specific mathematical expressions of the two algorithms are obtained. Meanwhile, sufficient conditions are obtained to meet the bounded inputs and the non-negative edge states by combining with the ARE-based low-gain output-feedback technique and the positive system theory. Moreover, the feedback-gain and observer-gain matrices which must meet the sufficient conditions at the same time are existed and easy to obtain. Finally, two simulation cases are introduced to show the effectiveness of the theoretical results.

Second-Order Consensus for Multiagent Systems via Intermittent Sampled Position Data Control

In this paper, a second-order consensus for multiagent systems with a directed communication topology is studied. A novel consensus strategy is first proposed, where a periodic intermittent control strategy only with casual sampled position data is used, which not only decreases the operating time and the update rates of conditioners for every individual but also responds effectively to the case of missing velocity information. A necessary and sufficient consensus condition based on the coupling gains, the sampling period, the communication width, and the spectrum of the Laplacian matrix is established to reach the consensus, and the right intervals of the sampling period are given. Furthermore, a delay-induced consensus protocol is designed, and a necessary and sufficient condition is also given, by which the sampling period and the communication width can easily be chosen to achieve the consensus. At last, some simulation examples are given to verify the correctness of the theoretical results.

Controllability of Two-Time-Scale Discrete-Time Multiagent Systems

In this paper, the controllability problem is addressed for a two-time-scale discrete-time system with multiple agents. First, the system is described by a singularly perturbed difference equation expressed on fast timescale. Then, to eliminate the singular perturbation parameter, by using the iterative method and approximate approach, the two-time-scale system is separated into slow and fast subsystems. Subsequently, some sufficient and/or necessary conditions of controllability for the systems are derived by using matrix theory. Moreover, under three special network topologies, the necessary criteria for controllability are proposed via graph theory. Finally, we give a simulation example to illustrate the effectiveness of the proposed theoretical results.

Positive edge consensus of networked systems with input saturation

This paper studies the edge consensus problems of undirected networked systems with positivity constraint and input saturation. Based on a given nodal network, the definition of edge network is introduced, and the edge dynamics is described by positive systems subject to input saturation. With the connections between the edge network and the nodal network, the lower and upper bounds of the nonzero eigenvalues of the edge Laplacian matrix are presented. Rigorous convergence analysis is carried out. Based on the special properties of positive systems, sufficient conditions of positive edge consensus with input saturation are given without using global topology information, that is, the topology information in the given results only relates to the edge and vertex number of the nodal network. Furthermore, the nonnegative edge consensus problem with uncertain parameters is also studied based on the properties of Metzler matrix. Different from many consensus problems with input saturation which achieve semi-global consensus, the results in this paper are global consensus. The feedback matrix can be computed by solving linear matrix inequality. Some illustrative numerical and practical simulation examples are finally introduced to verify the proposed methods in this paper.

A Stochastic Sampling Mechanism for Time-Varying Formation of Multiagent Systems With Multiple Leaders and Communication Delays

The time-varying formation problem for multiagent systems (MASs) with stochastic sampling and multiple leaders is studied in this paper, in which communication delays are taken into account. All the agents are divided into the set of the follower group and the set of the leader group. Under the proposed stochastic sampling mechanism for time-varying formation of the MASs with communication delays, the followers are driven to achieve time-varying formation where the center of the formation is the convex combination of the states of the leaders. In the theoretical analysis, sufficient conditions for the MASs achieving time-varying formation in mean square under stochastic sampling with multiple leaders and communication delays are derived. Moreover, some corollaries are also given in this paper. Finally, the theoretical analysis is verified by a given simulation example.

Semi-Global Output Consensus for Discrete-Time Switching Networked Systems Subject to Input Saturation and External Disturbances

The semi-global output consensus problem for multiagent systems depicted by discrete-time dynamics subject to external disturbances and input saturation over switching networks is investigated in this paper. Assume that only a small part of subsystems have directly received the output of the exosystem. The distributed consensus algorithms are proposed by adopting the low-gain state feedback and the modified algebraic Riccati equation. Then, the outputs of all subsystems can reach synchronization asymptotically with those of the exosystem by using the proposed consensus protocols on some preconditions. Both the connected switching networks and the jointly connected switching networks are considered for the semi-global output consensus problem, respectively. Some numerical simulation results are shown to validate the theoretical analysis.

An iterative Q-learning based global consensus of discrete-time saturated multi-agent systems

This paper addresses the consensus problem of discrete-time multiagent systems (DTMASs), which are subject to input saturation and lack of the information of agent dynamics. In the previous works, the DTMASs with input saturation can achieve semiglobal consensus by utilizing the low gain feedback (LGF) method, but computing the LGF matrices by solving the modified algebraic Riccati equation requires the knowledge of agent dynamics. In this paper, motivated by the reinforcement learning method, we propose a model-free Q-learning algorithm to obtain the LGF matrices for the DTMASs achieving global consensus. Firstly, we define a Q-learning function and deduce a Q-learning Bellman equation, whose solution can work out the LGF matrix. Then, we develop an iterative Q-learning algorithm to obtain the LGF matrix without the requirement of the knowledge about agent dynamics. Moreover, the DTMASs can achieve global consensus. Lastly, some simulation results are proposed to validate the effectiveness of the Q-learning algorithm and show the effect on the rate of convergence from the initial states of agents and the input saturation limit.

Controllability of heterogeneous multiagent systems with two-time-scale feature

In this paper, we investigate the controllability problems for heterogeneous multiagent systems (MASs) with two-time-scale feature under fixed topology. Firstly, the heterogeneous two-time-scale MASs are modeled by singular perturbation system with a singular perturbation parameter, which distinguishes fast and slow subsystems evolving on two different time scales. Due to the ill-posedness problems caused by the singular perturbation parameter, we analyze the two-time-scale MASs via the singular perturbation method, instead of the general methods. Then, we split the heterogeneous two-time-scale MASs into slow and fast subsystems to eliminate the singular perturbation parameter. Subsequently, according to the matrix theory and the graph theory, we propose some necessary/sufficient criteria for the controllability of the heterogeneous two-time-scale MASs. Lastly, we give some simulation and numerical examples to demonstrate the effectiveness of the proposed theoretical results.