Discrete-time Linear Multi-agent Systems Research Articles

Consensus analysis of switching multi-agent systems with fixed topology and time-delay

Abstract This paper investigates the average consensus problems of the discrete-time Markov switching linear multi-agent systems ( LMAS ) with fixed topology and time-delay. Firstly, we introduce a concept of the average consensus to adapt the stochastic systems. Secondly, a time-delay switching consensus protocol is proposed. By developing a new signal mode, the switching signal of the systems and the time-delay signal of the controller can be merged into one signal. Thirdly, by Lyapunov technique, two LMIs criteria of average consensus are provided, and they reveal that the consensus of the multi-agent systems relates to the spectral radius of the Laplacian matrix. Furthermore, by our results and CCL -type algorithms, we can get the gain matrices. Finally, a numerical example is given to illustrate the efficiency of our results.

Consensusability of discrete-time linear multi-agent systems over analog fading networks

This paper studies the consensusability problem of discrete-time linear multi-agent systems over analog fading networks. It aims to decide whether there exists a distributed controller such that the underlying multi-agent system can achieve mean square consensus over analog fading channels. Conditions to ensure mean square consensus are derived for the scenarios of undirected communication topologies with identical fading networks, balanced directed communication topologies with identical fading networks, and undirected communications topologies with non-identical fading networks, respectively. For scalar systems, the sufficient condition is shown to be necessary. The results indicate that the effect of fading networks on consensusability is determined by the statistics of channel fading. Finally, simulations are conducted to validate the theoretical results.

Leader-Following Consensus of Discrete-Time Multiagent Systems With Encoding–Decoding

The leader-following consensus of general linear discrete-time multiagent systems with a limited communication data rate and a directed fixed topology is investigated. The consensus protocol is designed for each agent, which is given in terms of states of its encoder and decoders with time-varying quantization levels. A rigorous analysis for the consensus convergence is provided. A finite lower bound of the communication data rate between each pair of adjacent agents is obtained to ensure consensus. A numerical example is presented to demonstrate the validity of the results obtained.

Consensus of high-order discrete-time linear networked multi-agent systems with switching topology and time delays

In this paper, the consensus problem for high-order discrete-time networked multi-agent systems (D-NMAS) is investigated by distributed feedback protocols. By constructing the self-feedback matrix and the neighbouring feedback matrix for networks, consensus protocols are designed under three different cases and the corresponding convergence analysis is provided. Consensus convergence results of networks are provided by three final consensus values, which are related to self-feedback matrices, initial states of networks and the topology of networks, not related to time delays. In the first case where a directed network with a fixed topology is concerned, the high-order discrete-time consensus problem is studied as an example, and a sufficient and necessary condition is obtained. In the scenario with directed networks with switching topology, a sufficient condition guaranteeing the consensus of high-order D-NMAS is derived, after the consensus analysis is transformed into stability analysis. As for directed networks with switching topology and time delays, the discrete-time stability model with time delays is converted into a general discrete-time stability model by an augmented method and the sufficient condition is provided to achieve consensus for directed networks. Furthermore, the sufficient conditions determining the neighbouring feedback matrix are independent of the number of agents. Two numerical examples are provided to demonstrate the correctness and effectiveness of the theoretical results.

Output consensus of networked multi-agent systems with time-delay compensation scheme

The output consensus problem of linear discrete-time multi-agent systems (DTMASs) with heterogeneous dynamics and a communication delay is investigated in this paper. In order to remove the negative effects of the communication delay, the networked predictive control scheme is introduced to compensate for the network delay actively. A novel distributed protocol is proposed with the predictions of agents׳ outputs at current time, instead of available outdated data. For DTMASs with heterogeneous agents and a constant communication delay, the sufficient conditions of output consensus are obtained while agents׳ states are not measurable. Simulation results are further presented to demonstrate the effectiveness of the theoretical results.

Consensus of linear discrete-time multi-agent systems based on full-dimensional state observer

This paper considers consensus of linear discrete-time multi-agent systems (MASs) based on full-dimensional state observer. Compared to Cheng et al. (2011), a new consensus protocol for the discrete-time MASs with virtual communication network topology is proposed and has faster convergence speed. Under the new consensus protocol, each agent gets not only its own state through the full-dimensional observer, but also the states of its neighbours and its instantaneous neighbours to reach consensus. Necessary and sufficient conditions of consensus for the MASs are presented. Finally, an example is provided to illustrate the effectiveness of the proposed method, and extended to directed topology case.

Consensus of linear discrete-time multi-agent systems based on full-dimensional state observer

This paper considers consensus of linear discrete-time multi-agent systems (MASs) based on full-dimensional state observer. Compared to Cheng et al. (2011), a new consensus protocol for the discrete-time MASs with virtual communication network topology is proposed and has faster convergence speed. Under the new consensus protocol, each agent gets not only its own state through the full-dimensional observer, but also the states of its neighbours and its instantaneous neighbours to reach consensus. Necessary and sufficient conditions of consensus for the MASs are presented. Finally, an example is provided to illustrate the effectiveness of the proposed method, and extended to directed topology case.

Observer-based semi-global consensus of discrete-time multi-agent systems with input saturation

This paper deals with the low-gain output feedback cooperative control for discrete-time linear multi-agent systems subject to actuator saturation. Based on the algebraic Riccati equations, semi-global exponential consensus is demonstrated for multi-agent system networks with a switching topology that is known or unknown to the agents. The combinational measurements are utilized to design the state observer. The estimated combinational states are used for controller design and Lyapunov stability analysis. The theoretical results are illustrated by a numerical example.

Controllability of heterogeneous multi-agent systems under directed and weighted topology

ABSTRACTThis paper considers the controllability problem for both continuous- and discrete-time linear heterogeneous multi-agent systems with directed and weighted communication topology. First, two kinds of neighbour-based control protocols based on the distributed protocol of first-order and second-order multi-agent systems are proposed, under which it is shown that a heterogeneous multi-agent system is controllable if the underlying communication topology is controllable. Then, under special leader selection, the result shows that the controllability of a heterogeneous multi-agent system is solely decided by its communication topology graph. Furthermore, some necessary and/or sufficient conditions are derived for controllability of communication topology from algebraic and graphical perspectives. Finally, simulation examples are presented to demonstrate the effectiveness of the theoretical results.

LQR-Based Optimal Distributed Cooperative Design for Linear Discrete-Time Multiagent Systems.

In this paper, a novel linear quadratic regulator (LQR)-based optimal distributed cooperative design method is developed for synchronization control of general linear discrete-time multiagent systems on a fixed, directed graph. Sufficient conditions are derived for synchronization, which restrict the graph eigenvalues into a bounded circular region in the complex plane. The synchronizing speed issue is also considered, and it turns out that the synchronizing region reduces as the synchronizing speed becomes faster. To obtain more desirable synchronizing capacity, the weighting matrices are selected by sufficiently utilizing the guaranteed gain margin of the optimal regulators. Based on the developed LQR-based cooperative design framework, an approximate dynamic programming technique is successfully introduced to overcome the (partially or completely) model-free cooperative design for linear multiagent systems. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methods.

Distributed consensus control for discrete-time linear multi-agent systems with reduced-order observer

In this paper, we investigate multi-agent consensus problem with discrete-time linear dynamics under directed interaction topology. By assumption that all agents can only access the measured outputs of its neighbor agents and itself, a kind of distributed reduced-order observer-based protocols are proposed to solve the consensus problem. A multi-step algorithm is provided to construct the gain matrices involved in the protocols. By using of graph theory, modified discrete-time algebraic Riccati equation and Lyapunov method, the proposed protocols can be proved to solve the discrete-time consensus problem. Furthermore, the proposed protocol is generalized to solve the model-reference consensus problem. Finally, a simulation example is given to illustrate the effectiveness of our obtained results.

Distributed-observer-based cooperative control for synchronization of linear discrete-time multi-agent systems

This paper considers output synchronization of discrete-time multi-agent systems with directed communication topologies. The directed communication graph contains a spanning tree and the exosystem as its root. Distributed observer-based consensus protocols are proposed, based on the relative outputs of neighboring agents. A multi-step algorithm is presented to construct the observer-based protocols. In light of the discrete-time algebraic Riccati equation and internal model principle, synchronization problem is completed. At last, numerical simulation is provided to verify the effectiveness of the theoretical results.

Containment control of discrete-time general linear multi-agent systems under dynamic digraph based on trajectory analysis

This paper devotes itself to the containment tracking problem of general linear time-varying discrete-time multi-agent systems (MASs). The convergence analysis is based on trajectory analysis rather than Lyapunov method. Nonnegative matrix theory, in particular the row-stochastic matrix properties, together with the relation between matrix and graph topology, are explored to handle the containment control problem. Based on a technical lemma concerning norm estimation of infinite product of row-stochastic matrices, we show that the followers can exponentially tend to the dynamical convex hull spanned by the leaders, i.e. the containment can be achieved under the very relaxed conditions: strictly instability of the individual-system of each agent (without interactions with other agents) is allowable and the graph topology is only required to be jointly having directed spanning forest frequently enough. Moreover, the least convergence rate is explicitly specified. Simulation is also provided to demonstrate the effectiveness of our result.

Synchronization Reachable Topology and Synchronization of Discrete-Time Linear Multi-Agent Systems

In this note, we consider the synchronization problem for discrete-time linear multi-agent systems with time-varying network topology. To describe a new joint connectivity condition for synchronization, the concept of synchronization reachable topology is introduced. Under the conditions that agent dynamics is neutrally stable and network topology is synchronization reachable, a synchronization and an exponential synchronization result are obtained using paracontraction theory. The two results generalize in a natural way the classical results for the consensus of first-order discrete-time multi-agent systems. Finally, the effectiveness of the results is illustrated by a simulation example.

Output Consensus of Heterogeneous Linear Discrete-Time Multiagent Systems With Structural Uncertainties.

This paper investigates the output consensus problem of heterogeneous discrete-time multiagent systems with individual agents subject to structural uncertainties and different disturbances. A novel distributed control law based on internal reference models is first presented for output consensus of heterogeneous discrete-time multiagent systems without structural uncertainties, where internal reference models embedded in controllers are designed with the objective of reducing communication costs. Then based on the distributed internal reference models and the well-known internal model principle, a distributed control law is further presented for output consensus of heterogeneous discrete-time multiagent systems with structural uncertainties. It is shown in both cases that the consensus trajectory of the internal reference models determines the output trajectories of agents. Finally, numerical simulation results are provided to illustrate the effectiveness of the proposed control schemes.

Coordination of Linear Systems with Finite Data Rate and Time-Varying Undirected Topologies

This paper focuses on the synchronization of discrete-time linear multi-agent systems with finite communication data rate and switching undirected topology flows. Quantizedobserver based communication schemes and adaptive encoder-decoders are proposed. We show that there exist such protocols leading to synchronization exponentially fast with only finite bits of information exchanged per step, if the agents' dynamics satisfies some simultaneously stabilizable conditions and network topology flows are frequently connected. For first-order dynamics, the number of bits are related to the unstable mode of agent dynamics, the number of agents, the frequency of connectivity and the Laplacian eigenvalue ratio of the switching topology flow.

Consensus tracking of linear multi‐agent systems under a networked detectability condition with reduced‐order protocols

This study addresses the consensus tracking problem of linear multi-agent systems under a networked detectability condition with reduced-order protocols. The communication subgraph among followers is undirected and connected. It is assumed that only partial relative state information of the leader can be obtained by each follower. The networked detectability condition only requires that the leader is jointly detectable to all followers, without any detectability requirement on an individual follower. Under the assumption that the system is neurally stable, distributed observer-type consensus protocols are constructed for both continuous- and discrete-time linear multi-agent systems. By using tools from matrix theory and linear system analysis, some sufficient conditions are derived to reach consensus tracking. One favourable feature of this study is that the traditional detectability condition for an individual system is extended to the networked case and in contrast to the relevant available results, reduced-order observers are presented to reduce information redundancy. Simulation examples are given to illustrate the theoretical results.

Average Dwell-time Conditions for Consensus of Discrete-time Linear Multi-agent Systems with Switching Topologies and Time-varying Delays

This paper investigates the consensus problem of discrete-time linear multi-agent systems (DLMASs) with directed switching information topologies and time-varying delays. First, we transform the consensus problem to an asymptotic stability problem of a corresponding time-delayed switched linear system (TDSLS) via a proper linear transformation. Then by using a constructed Lyapunov functional and the average dwell-time scheme, we establish a novel delay-dependent sufficient condition for the solvability of the consensus problem in terms of linear matrix inequalities (LMIs) for two cases, respectively: 1) all of the given information topologies are consensusable; 2) some of the given information topologies are consensusable. Finally, numerical examples are given to show the validness of the established results.

Consensus of discrete-time linear multi-agent systems with Markov switching topologies and time-delay

This paper investigates the average consensus problems of the discrete-time linear multi-agent systems (LMAS) with Markov switching topologies. The average consensus protocol is a time-delay feedback switching controller. Compared with existing controllers, it is switching with time-delay. The constant time-delay exists in the signal feedback, and the time-varying time-delay exists in the state feedback. Firstly, we introduce a concept of the average consensus in this stochastic system. Then, we develop a new signal mode to simplify this challenging problem. By Lyapunov technique, two LMIs determinate theorems of average consensus are provided. Then we can find a controller to solve such problems effectively by these theorems. And the last theorem also reveals that we can determinate consensus by the maximum and minimum nonzero eigenvalues of the Laplacian matrices. Finally, a numerical example is given to illustrate the efficiency of our results.

On Discrete-Time Convergence for General Linear Multi-Agent Systems Under Dynamic Topology

This note aims to develop the nonnegative matrix theory, in particular the product properties of infinite row-stochastic matrices, which is widely used for multiple integrator agents, to deal with the convergence analysis of general discrete-time linear multi-agent systems (MASs). With the proposed approach, it is finally shown both theoretically and by simulation that the consensus for all the agents can be reached exponentially fast under relaxed conditions, i.e. the individual uncoupled system is allowed to be strictly unstable (in the discrete-time sense) and it is only required that the joint of the communication topologies has a spanning tree frequently enough. Moreover, a least convergence rate as well as an upper bound for the strictly unstable mode, which are independent of the switching mode of the system, are specified as well.