Output-feedback Protocol Research Articles

Observer-based positive edge consensus of multi-agent systems with directed graphs

This paper concentrates on the positive edge consensus in directed networks with spanning trees using output feedback protocols. First, a novel positive system observer is established, which introduces a parameter to enhance the design freedom of the observer. Furthermore, sufficient conditions are proposed, which are based solely on the network’s edge count. Specifically, improved consensus and non-negative conditions are obtained by optimizing the constraints on the eigenvalue information. Subsequently, based on positive edge-consensus design conditions, a programming algorithm is developed. Finally, the effectiveness of the proposed control protocol is verified utilizing numerical simulations.

Event-Triggered Multiagent Consensus Under Relative Output Sensing.

Event-triggered (ET) consensus of linear multiagent systems with relative output sensing on undirected graphs is studied. Two output-feedback protocols with static and time-varying coupling strengths, respectively, are proposed, which, different from the existing results in relative output sensing, integrate effective ET strategies to reduce the communication burdens between agents. To ensure the closed-loop consensus, design conditions about the gain matrices, coupling strengths, and event-triggering functions are derived. Zeno behaviors are also shown to be excluded from the triggering process. In addition, recursive algorithms are devised for computing the continuous-time relative signals required by the event-triggering functions, so that continuous monitoring of neighbors is circumvented. Numerical examples finally demonstrate the effectiveness of the proposed design method.

Output consensus robustness and performance of first‐order agents

AbstractIn this article, we study consensus robustness and performance problems for continuous‐time multi‐agent systems. We consider first‐order unstable agents coordinated by an output feedback protocol over a network subject to an unknown, uncertain constant delay. Our objectives are twofold. First, we seek to determine the largest range of delay permissible so that the agents may achieve robustly consensus despite variation of the delay length, herein referred to as the delay consensus margin. Second, we attempt to determine consensus error performance quantified under an norm criterion, which measures the disruptive effect of random nodal noises on consensus. We consider both undirected and directed graphs. For undirected graphs, we obtain analytical results for the delay consensus margin and the consensus error performance, while for directed graphs, we develop computational results and analytical bounds. The results provide conceptual insights and exhibit how the agents' unstable pole, nonminimum phase zero, as well as the network topology and network delay may limit fundamentally the consensus robustness and performance of first‐order agents.

A hybrid time/event-triggered interaction framework for multi-agent consensus with relative measurements

This paper is concerned with the output-feedback consensus problem of linear multi-agent systems on undirected graphs. Our focus is on reducing sensing and communication burdens between agents. Based on relative output measurements, a dynamic output-feedback (DOF) protocol is proposed, which, by leveraging the structure of the closed-loop dynamics, integrates a hybrid time/event-triggered sampling mechanism such that only intermittent interaction between agents is needed. Consensus conditions are established by the Lyapunov method and numerical simulations are provided for illustrating the effectiveness of the protocol. Compared with the existing results, the proposed DOF protocol has the following merits: (1) they rely on relative output measurements but do not need absolute measurements about agents; (2) they only require agents to intermittently interact with neighbors and thus can greatly reduce sensing and communication burdens between agents; and (3) the designed event-triggering conditions do not need to perform extra reconstruction operations that are computationally demanding.

Attack-free protocols design for leader-following consensus of discrete-time multi-agent systems with multiple input delays

The consensus problem for leader-following multi-agent systems (MASs) characterised by discrete-time multiple input delays linear systems with directed communication topologies is investigated. Under reasonable assumptions, full-order observer-based output feedback protocols are first established by using the relative outputs and inputs of neighbouring agents. In order to overcome the impact of potential network attacks, we truncate the relative inputs of the proposed protocols, namely the exchange of communication information between neighbouring agents is forbidden, so that the closed-loop leader-following MAS is inherently immune to being attacked and achieves consensus. Additionally, the improved attack-free protocols not only allow arbitrarily large yet bounded delays, but also only relative output measurement can be available, which reduces the communication burden and thus are easy to implement in practice. A numerical example is worked out to illustrate the effectiveness of the proposed approach.

Fully distributed leader–follower consensus for multi-agent systems based on reduced-order adaptive feedback protocol

This paper addresses the leader–follower consensus problem of linear multi-agent systems by designing reduced-order adaptive output feedback protocol. Using relative output information among neighboring agents, node-based adaptive output feedback control protocol and edge-based adaptive output feedback control protocol are presented, respectively. For both cases, based on Lyapunov analysis and algebraic Riccati equation design, some sufficient conditions are given to achieve leader–follower consensus by applying the proposed adaptive output feedback protocols. Finally, some simulation examples are given to illustrate the validity of the theoretical results.

Fully distributed event-triggered output feedback control for linear multi-agent systems with a derivable leader under directed graphs

This article studies the design method of fully distributed event-triggered output feedback protocol for linear multi-agent systems with a derivable leader under directed graphs. The research on such problems in the existing reference needs complete state feedback and the state variable of the adaptive law used in the literature controller is monotonic and non decreasing, which may make the control input exceed the actual saturation value, thus affecting the practical application. How to design a completely distributed event-triggered adaptive output feedback protocols for multi-agent systems with a derivable leader on directed graphs is an open issue. In order to overcome the difficulty of designing the controller without complete state information, we design the event-triggered output feedback protocol, and with the help of σ-modification techniques, ensure the boundedness of the adaptive law in proposed protocol. The conditions to ensure the realization of the leader–follower consensus and exclude Zeno behavior are given. Furthermore, the control protocol is fully distributed and uses neighbor information only when the event trigger conditions are satisfied. Finally, the availability of the proposed protocol is illustrated by simulation examples.

Appointed-Time and Attack-Free Bipartite Synchronization of Generic Linear Multiagent Systems Over Directed Switching Networks

This article derives a solution to the appointed-time and attack-free bipartite synchronization problem for generic linear multiagent systems over directed switching networks accommodating cooperative and antagonistic interactions. Herein, appointed-time means that the settling time is independent of any parameters and is preappointed in advance. Attack-free requires that the communication channel is protected, which means that no state and observer information exchange is allowed, and only measured relative output information is available when designing protocols. Firstly, by virtue of Pontryagin’s maximum principle, a distributed appointed-time state-feedback protocol is developed for directed switching networks, which tackles the appointed-time bipartite synchronization problem from a motion-planning approach based on sampling measurements, but takes the risk of facing cyber attacks on information exchange channels. Then, to be free of network attacks, a sampling-based attack-free observer using relative output information is designed to observe bipartite synchronization errors at an appointed time. By combining the appointed-time state-feedback protocol with the sampling-based attack-free observer, an attack-free output-feedback protocol is developed without requiring the state or control input information. The attack-free appointed-time bipartite synchronization problem is thus resolved. Both the state-feedback and attack-free protocols show the ability of disturbance rejection to the nonidentical bounded disturbances. To our knowledge, it is the first time to solve the appointed-time and attack-free bipartite synchronization problem for generic linear multiagents based on state- and output-feedback information, respectively. Finally, simulations verify the effectiveness of the two protocols.

Cluster consensus for leader-following high-order linear multiagent systems

<p indent="0mm">Cluster consensus for leader-following high-order linear multiagent systems (MASs) is investigated. Based on the information of an agent and its neighbors, state feedback and output feedback control protocols are designed for each follower, respectively. Sufficient conditions for leader-following cluster consensus are given using tools from the algebraic Riccati equation and matrix analysis. It is shown that if the communication topology of an MAS composed of the leader and followers is interactively balanced and contains a spanning tree, the MAS can achieve leader-following cluster consensus under the proposed control protocols by properly selecting control gains. Particularly, it is found that the leader-following cluster consensus problem based on the output feedback protocol can be transformed into a static output feedback problem using an error system. If the input and output matrices of a follower satisfy a certain rank condition, the MAS can achieve leader-following cluster consensus under the designed output feedback control protocol.

Necessary and Sufficient Conditions of Formation-Containment Control of High-Order Multiagent Systems With Observer-Type Protocols

The analysis and design problems of formation-containment control for high-order linear time-invariant (LTI) multiagent systems (MASs) on directed graphs with observer-based output-feedback protocols are given in this work. To expand the feasibility of state formation configuration, two well-structured compensation signals are introduced for the leaders and followers in the protocols, respectively. Benefitting from the compensation signal of followers, the decoupling between formation control of leaders and containment control of followers is achieved. Thus, a necessary and sufficient condition is first established such that the formation-containment control for high-order LTI MASs can be achieved. Moreover, a heuristic iterative algorithm is developed to compute the controller gains, observer gains, as well as the compensation signals. Finally, two numerical examples are implemented to illustrate the time-varying formation-containment control of high-order MASs, which shows the validity and practicability of the theoretical results and algorithm.

LMI-based consensus of linear multi-agent systems by reduced-order dynamic output feedback

This work proposes new conditions for consensus of homogeneous multi-agent systems subjected to exogenous disturbances in directed communication graphs by dynamic output feedback protocols. The agents under investigation are described as linear dynamics, and the communication network is such that each agent receives as information only the output of neighbor agents. The synchronization problem is rewritten as an output feedback stabilization without requiring the Laplacian matrix to be diagonalizable. As the main appeal, we propose new necessary and sufficient conditions for the design of dynamic output feedback controllers of arbitrary order – including static output feedback as a particular case – and sufficient Linear Matrix Inequalities (LMIs) for H∞ consensus. Numerical experiments illustrate the effectiveness of the proposed approach.

Bipartite Containment Control for Multiagent Systems with Adaptive Quantization Information

In this study, bipartite containment control for multiagent systems (MASs) with quantitative information is investigated. Communication topology is structurally balanced, and the follower’s trajectory is within the area surrounded by the leader by designing distributed error terms. The leader is an external system, and the matrix information of the leader cannot be accessed by followers. Based on an adaptive quantization information distributed observer, the authors introduce an output feedback protocol to study bipartite containment control. Finally, simulations demonstrate the effectiveness of proposed control algorithms.

Practical output consensus of nonlinear heterogeneous multi-agent systems with limited data rate

This paper investigates the consensus problem for nonlinear heterogeneous multi-agent systems with limited communication data rate. Each agent is modeled by a higher-order strict-feedback continuous-time system with unknown nonlinearities and external disturbance, and only the first state variable being measurable. Extended state observers (ESOs) are used to estimate the unmeasurable agent states and the unknown nonlinear dynamics. An ESO-based distributed output feedback protocol with dynamic encoding and decoding is then presented. It is shown that, for a connected undirected network, the proposed protocol guarantees practical output consensus, in which the steady-state consensus error can be made arbitrarily small. The ESO-based protocol also shapes the transient consensus performance, as it is capable of recovering the consensus performance of a linear counterpart with fully measurable states. Furthermore, we prove that for higher-order uncertain nonlinear multi-agent systems, consensus can be achieved with merely one bit information exchange between each pair of adjacent agents at each time step. Finally, simulations on third-order pendulum systems are given, which verify the theoretical results.

Consensus of Multiagent Systems With Relative State Saturations

Within the multiagent systems framework, the relative states between neighbors can be acquired by some on-board sensors, and then the relative state saturations inevitably occur due to the limited sensing capabilities. This paper investigates the consensus problem of nonlinear multiagent systems subject to the relative state saturations. Utilizing the incidence matrix and the edge Laplacian, the consensus problem of nonlinear multiagent systems with the relative state saturations can be cast into the stabilization problem of edge dynamics operating on the constrained set. Three types of protocols, namely continuous, intermittent, and adaptive state feedback protocols are, respectively, proposed for achieving the constrained consensus, and meanwhile yielding consensus values. A consensus analysis is provided by virtue of state saturation theory, switched system theory, adaptive theory, and Lyapunov stability theory. Output feedback protocol is also designed. Finally, the obtained results are applied to connectivity preservation for first-order nonlinear multiagent systems, despite the presence of limited communication range and input constraints. The theoretical results are validated by two simulation examples.

Energy-constraint output formation for swarm systems with dynamic output feedback control protocols

This paper studies the energy-constraint output formation control for swarm systems with leaderless and leader-following topology structures. Most existing results on output formation with the dynamic output feedback protocols focus on the swarm systems without the energy constraint, but it is well known that the energy constraint is critically important for practical applications. In order to analyze the impacts of the energy constraint, a new energy-constraint output formation protocol is proposed. First, by the observable decomposition approach, a dynamic output formation protocol is presented, which contains an energy-constraint term to restrict the whole consumption. Then, sufficient conditions for leaderless energy-constraint output formation are presented via establishing the relationship of the energy constraint and the matrix variables, where it is found that the designed gain matrices of the output formation protocol can ensure that the actual energy consumption is lower than the total energy supply. Especially, a partition checking algorithm is proposed to check those conditions, which can ensure the scalability and solvability of a swarm system. Moreover, the output formation center function is derived to depict the whole macroscopic movement of a swarm system. A nonsingular transformation approach is presented to unify leaderless energy-constraint output formation and energy-constraint output formation tracking into the same framework, which are usually discussed in different theoretical frameworks. Finally, two simulation examples are illustrated to show that the theoretical results about leaderless energy-constraint output formation and energy-constraint output formation tracking are correct.

Consensus of Discrete-Time Multiagent Systems With State, Input, and Communication Delays

In this paper, we study the consensus problem for high-order discrete-time multiagent systems with state, input, and communication delays, where the input and communication delays can be arbitrarily large yet exactly known. Moreover, the communication delays are different for different agents. Nested predictor-based state feedback protocols and full-order/reduced-order observer-based output feedback protocols are established to solve the problem. It is shown that both the input and communication delays can be compensated completely. Furthermore, linear matrix inequalities-based approaches are provided to design state feedback gains and observer gains. A numerical example is worked out to illustrate the effectiveness of the proposed approaches.

Hierarchical Decomposition-Based Distributed Full States Tracking Consensus for High-Order Nonlinear Multiagent Systems

This article studies the distributed adaptive leader-following control for high-order time-varying nonlinear multiagent systems (MASs) with uncertain parameters. The state feedback protocol and output feedback protocol are proposed, respectively, to render all states consensus errors to converge to zero asymptotically. First, the hierarchical decomposition algorithm is used to construct a refreshed communication graph to address the mutual dependence problem of controllers. Then, by introducing a local neighborhood consensus errors-based transformation, the leader-following consensus problem is converted into the stabilization problem for the consensus error system. Using the backstepping method and tuning function technique, the distributed adaptive state feedback controller is designed to render all followers' states to track the leader's ones. Further, by constructing the reduced-order dynamic gain k-filter to estimate unmeasured states, a distributed adaptive output feedback controller is designed. In both controller design methods, the traditional Lipschitz condition need not be satisfied any more for all time-varying nonlinear functions, and different from most of the existing results on the high-order nonlinear MASs, full states consensus can be obtained. Finally, a general numerical example is given to illustrate the effectiveness of the proposed methods.

Consensus of Continuous-Time Linear Multiagent Systems With Discrete Measurements.

This article concerns the robust consensus problem of continuous-time linear multiagent systems (MASs) with uncertainty and discrete-time measurement information, where the output measurement information is in the data-sampled form. Distributed output-feedback protocol with or without controller interaction is proposed for each agent. Specifically, the output-feedback protocol runs in continuous time with an output error correction term mixed with the discrete-time measurement information. The concrete algorithm is given for the construction of the feedback matrices. Then, by using the delay-input approach, sufficient conditions are provided for the robust consensus of this kind of MASs interacting over networks described by the directed graphs. Finally, numerical simulations are given to illustrate the theoretical results.

Leader–follower consensus for multi‐agent systems with external disturbances generated by heterogeneous nonlinear exosystems

AbstractIn this paper, the leader–follower consensus problem is investigated for multi‐agent systems subject to external disturbances generated by heterogeneous nonlinear exosystems. First, the disturbance observers are developed for each follower to effectively estimate the nonlinear disturbances. Then, based on the presented observers, the distributed state and output feedback consensus protocols are proposed to guarantee that the consensus tracking errors converge to zero asymptotically, and meanwhile to reject the nonlinear disturbances. Particularly, the output feedback protocol can be designed and implemented without any global information about the whole network, which means it is fully distributed. Finally, two numerical examples are given to illustrate the effectiveness of the results.

A suboptimality approach to distributed [formula omitted] control by dynamic output feedback

This paper deals with suboptimal distributed H2 control by dynamic output feedback for homogeneous linear multi-agent systems. Given a linear multi-agent system, together with an associated H2 cost functional, the objective is to design dynamic output feedback protocols that guarantee the associated cost to be smaller than an a priori given upper bound while synchronizing the controlled network. A design method is provided to compute such protocols. The computation of the two local gains in these protocols involves two Riccati inequalities, each of dimension equal to the dimension of the state space of the agents. The largest and smallest nonzero eigenvalue of the Laplacian matrix of the network graph are also used in the computation of one of the two local gains. A simulation example is provided to illustrate the performance of the proposed protocols.