Leader-following Output Consensus Research Articles

Distributed Fault Detection and Dynamic Event-Triggered Consensus for Heterogeneous Multiagent Systems Under Deception Attacks

This paper focuses on the problem of distributed fault detection and leader-following output consensus for heterogeneous multiagent systems subject to deception attacks. During the information exchange and dissemination, a malicious attacker can make full use of specialized computer technology and launch stochastic deception attacks against some vulnerable agents over the network. The attack signals in actual operation tend to be energy-constrained, and Bernoulli distribution can be used to describe the random features. Taking the attack information into account, the distributed fault detection observer and the dynamic consensus compensator are designed in two separate steps. In order to reduce unnecessary information transmission, a dynamic event-triggered mechanism with output-dependent threshold is introduced to the adjustment of consensus protocol. According to Lyapunov stability theory and linear matrix inequality (LMI) techniques, sufficient conditions are derived for developing the model gains of the observer and the compensator. Finally, a simulation example of RLC circuit systems is provided to illustrate the effectiveness of the obtained theoretical results.

Distributed Adaptive Output Consensus of Unknown Heterogeneous Non-Minimum Phase Multi-Agent Systems

This article addresses the leader-following output consensus problem of heterogeneous linear multi-agent systems with unknown agent parameters under directed graphs. The dynamics of followers are allowed to be non-minimum phase with unknown arbitrary individual relative degrees. This is contrary to many existing works on distributed adaptive control schemes where agent dynamics are required to be minimum phase and often of the same relative degree. A distributed adaptive pole placement control scheme is developed, which consists of a distributed observer and an adaptive pole placement control law. It is shown that under the proposed distributed adaptive control scheme, all signals in the closed-loop system are bounded and the outputs of all the followers track the output of the leader asymptotically. The effectiveness of the proposed scheme is demonstrated by one practical example and one numerical example.

Semiglobal Leader-Following Output Consensus of Discrete-Time Heterogeneous Linear Systems Subject to Actuator Position and Rate Saturation

Motivated by the fact that physical systems are usually subject to actuator position and rate saturation, we consider in this article the semiglobal leader-following output consensus problem of a group of discrete-time heterogeneous linear systems with position and rate-limited actuators by output feedback control law. Distributed observers are designed for followers to estimate the state of the leader and the follower itself, based on which a novel distributed control law is proposed. We show that, via the low gain feedback design technique and output regulation theory, the semiglobal leader-following output consensus of discrete-time heterogeneous linear systems can be achieved by the consensus protocol if each follower is reachable from the leader in a directed communication topology.

Leader-Following Consensus of Heterogeneous Linear Multiagent Systems With Communication Time-Delays via Adaptive Distributed Observers.

This article investigates the leader-following consensus problem of heterogeneous linear multiagent systems under switching and directed topologies. It is assumed that the communication between agents suffers from time-varying delays and only the neighboring agents of the leader are able to get access to the information of the leader agent, including its agent matrices. A key technical lemma on the input to state stability of time-delayed systems is first established with which the main results of this article can be obtained. An adaptive distributed observer, taking into consideration of communication time delays, is proposed for each follower to estimate the leader's system matrices and its state. Then, a distributed controller based on this adaptive observer is developed. We show that the resulting closed-loop multiagent system achieves the leader-following output consensus. Two examples are finally given to illustrate the effectiveness of the proposed controller.

Leader-following almost output consensus for discrete-time heterogeneous multi-agent systems in the presence of external disturbances

In this paper, we consider the problem of leader-following almost output consensus for discrete-time multi-agent systems with heterogeneous follower agents. Conditions on agent dynamics, the communication topology and how the disturbance enters the agent dynamics are established under which leader-following almost output consensus can be achieved, that is, the leader-following output consensus can be reached with any pre-specified level of accuracy and the effect of the disturbance on the leader-following consensus can be attenuated to any pre-specified level. A family of state feedback consensus protocols are constructed by using the low gain feedback design technique and a modified discrete-time Riccati equation. These consensus protocols are shown to achieve leader-following almost output consensus. Additional conditions are identified under which output feedback results are established. Simulation results demonstrate the effectiveness of the proposed consensus protocols.

An Improved Distributed Nonlinear Observers for Leader-Following Consensus via Differential Geometry Approach

This article is concerned with the leader-following output consensus problem in the framework of distributed nonlinear observers. Instead of certain hypotheses on the leader system, a group of geometric conditions is put forward to develop a novel distributed observers strategy, thereby definitely improving the applicability of the existing results. To be more specific, the improved distributed observers can precisely handle consensus problems for some nonlinear leader systems, which are invalid for the traditional strategies with a certain assumption, such as elastic shaft single linkage manipulator (ESSLM) systems and most of the first-order nonlinear systems. We prove the sufficient conditions for the exponential stability of our distributed observers’ error dynamic by proposing two pioneered lemmas to show the relationship between the maximum eigenvalues of two matrices appearing in Lyapunov type matrices. Then, a partial feedback linearization method with zero dynamic proposed in differential geometry is employed to design the purely decentralized control law for the affine nonlinear multiagent system. With this advancement, the existing results can be regarded as a specific case owing to that the followers can be chosen as an arbitrary minimum phase affine smooth nonlinear system. At last, the novel distributed observers and the improved purely decentralized control law are applied in the distributed control framework to construct a closed-loop system. We also prove the stability of the closed-loop system to achieve leader-following consensus. Our method is illustrated by the ESSLM system and Van der Pol system as leaders.

Leader-Following Almost Output Consensus for Linear Heterogeneous Multiagent Systems With Disturbance-Affected Unstable Zero Dynamics by Output Feedback

A novel design of observer-based output feedback consensus protocols in a low-and-high gain feedback framework is proposed for a linear heterogeneous multiagent system, where the unstable zero dynamics of the follower agents is affected by disturbances. Conditions on the graph that represents the connectivity among the agents and on how the disturbances enter the zero dynamics of the follower agents are identified, under which the leader-following almost output consensus can be attained with the proposed protocols. More specifically, the proposed protocols achieve leader-following output consensus to an arbitrarily high level of accuracy, and the effect of the disturbances on the consensus errors is attenuated to an arbitrarily low level.

Leader-following output consensus of T-S fuzzy switched multi-agent systems under bumpless transfer control and event-triggered communication

This paper studies the leader-following output consensus problem of a class of nonlinear switched multi-agent systems described by the T-S fuzzy models. A sufficient condition on the leader-following output consensus and the bumpless transfer performance is developed via co-design of the observer-based bumpless transfer fuzzy controllers and the agent-dependent switching law, which the local stabilizability of all the fuzzy subsystems of each agent is not required. By using the distributed dynamic event-triggered rule, the fuzzy estimator for each agent is constructed to estimate the state of leader. Besides, Zeno behaviour is ruled out via discussing the existence of the lower bound on inter-event intervals. Finally, two examples are given to validate the effectiveness of our results.

Semi-global leader-following output consensus of heterogeneous systems subject to actuator position and rate saturation

We study in this paper a semi-global leader-following output consensus problem for multiple heterogeneous linear systems in the presence of actuator position and rate saturation over a directed topology. For each follower, via the low gain feedback design technique and output regulation theory, both a state feedback consensus protocol and an output feedback consensus protocol are constructed. In the output feedback case, different distributed observers are designed for the informed followers and uninformed followers to estimate the state of the leader and the follower itself. We show that the semi-global leader-following output consensus of heterogeneous linear systems can be achieved by the two consensus protocols if each follower is reachable from the leader in the directed communication topology.

Leader-Following Output Consensus of Heterogeneous Uncertain Linear Multiagent Systems With Dynamic Event-Triggered Strategy

This article investigates the leader-following output consensus problem of heterogeneous linear multiagent systems, where the nonidentical followers are subject to norm bounded parameter uncertainties. Two novel distributed event-triggered consensus strategies based on state feedback and output feedback, respectively, are proposed to solve the leader-following output consensus problem. A dynamic event-triggering mechanism which involves internal state variables is proposed to determine the next triggering instant. It should be noted that the controllers can be designed without the knowledge of some global graph information, such as the eigenvalues of the Laplacian matrix associated with the corresponding communication graph and the number of agents. In addition, the interevent time can be prolonged and the Zeno behavior can be excluded with the proposed dynamic triggering mechanism. Finally, an example is presented to illustrate the effectiveness of the proposed controllers.

Distributed control of heterogeneous multi-agent systems with unknown control directions via event/self-triggered communication

This paper investigates the leader-following output consensus of heterogeneous multi-agent systems (MASs) with unknown and nonidentical control directions under switching topology. To save the communication resources, a distributed adaptive control protocol together with an event-triggered communication scheme is proposed to achieve the output consensus. A self-triggered communication strategy is further given to prevent the continuous monitoring of neighbors states. Moreover, we prove that the proposed event/self-triggered strategies are Zeno-free. The obtained results are successfully applied to design the output formation controller. Finally, the effectiveness of the proposed theoretical results is demonstrated by two numerical examples.

Finite-time leader-following output consensus for multi-agent systems via extended state observer

In this paper, the finite-time leader-following output consensus problem is investigated for a multi-agent system subjected to directed topology and disturbance. Firstly, a distributed finite-time extended state observer (DFTESO) is designed to provide estimate for unmeasured consensus errors and disturbances. The sufficient condition is provided in terms of linear matrix inequality (LMI) to ensure that the error dynamics of the DFTESO is convergent in finite time. Then, based on the designed observer, the leader-following consensus protocol based on dynamic gain method is proposed under the directed topology. Finally, an example on the multi-spacecraft system is provided to illustrate the effectiveness of the proposed methodology.

Distributed Adaptive Output Consensus for High-Order Multiagent Systems with Input Saturation and Uncertain Nonlinear Dynamics

This paper deals with the leader-following output consensus problem for a class of high-order affine nonlinear strict-feedback multiagent systems with unknown control gains and input saturation under a general directed graph. Nussbaum gain function technique is used to handle the unknown control gains, and the uncertain nonlinear dynamics of each agent is approximated by radial basis function neural networks. Distributed adaptive controllers are designed via the backstepping technique as well as the dynamic surface control approach. It is proved that the closed-loop multiagent systems are semiglobally uniformly ultimately bounded, and the output consensus error can converge to a small region around the origin. Finally, the theoretical results are supported by a numerical simulation.

Semi-global leader-following output consensus for heterogeneous fractional-order multi-agent systems with input saturation via observer-based protocol

In this paper, semi-global leader-following output consensus problem for heterogeneous fractional-order multi-agent systems with input saturation and external disturbances is investigated. The case where the dynamics are integer-order can be viewed as a special case of fractional-order systems. First, a novel observer-based consensus algorithm is designed to solve the semi-global output consensus problem. It is worth noting that the consensus is semi-global since the set of initial states is bounded. Then, the low gain feedback technique is utilized based on the solution of a parametric algebraic Riccati equation. Moreover, sufficient conditions of output consensus for heterogeneous fractional-order multi-agent systems are derived by using algebraic graph theory, matrix theory and the stability theory of fractional-order systems. It can be proven that the output signals of followers can reach synchronization with the leader’s. Finally, numerical examples are provided to illustrate the effectiveness of our conclusions.

Reduced-order observer-based robust leader-following control of heterogeneous discrete-time multi-agent systems with system uncertainties

In this paper, the leader-following control of heterogeneous discrete-time multi-agent systems (HD_MASs) in the presence of system uncertainties under directed topology is addressed. It aims to achieve reference tracking, disturbance rejection and robust control while the references and disturbances are generated by an autonomous exosystem. In practice, these agents are often different types of devices, thus they have different internal dynamics. Moreover, it is difficult to measure all states of each aircraft due to high cost or technical limitation. In this case, a novel leader-following output consensus problem is formulated and solved in this paper. Firstly, an appropriate linear transformation is proposed to divide the state information of each agent into measurable and unmeasurable parts. Then the reduced-order observer is designed only for unmeasurable parts. Based on the designed observer, the distributed feedback controller is proposed such that the outputs of all followers reach the same trajectory with the leader. In light of the internal model principle and discrete-time algebraic Riccati equation, the robust leader-following consensus of HD_MASs is achieved. Furthermore, this paper extends the results to continuous-time multi-agent systems. Finally, several simulation experiments are presented to verify the effectiveness of the theoretical results.

Distributed Control of Nonlinear Multiagent Systems With Unknown and Nonidentical Control Directions via Event-Triggered Communication.

In this paper, the leader-following output consensus problem for a class of uncertain nonlinear multiagent systems with unknown control directions is investigated. Each agent system has nonidentical dynamics and is subject to external disturbances and uncertain parameters. The agents are connected through a directed and jointly connected switching network. A novel two-layer distributed hierarchical control scheme is proposed. In the upper layer, to save the communication resources and to handle the switching networks, an event-triggered communication scheme is proposed, and a Zeno-free event-triggered mechanism is designed for each agent to generate the asynchronous triggering time instants. Furthermore, to avoid the continuous monitoring of the system states, a Zeno-free self-triggering algorithm is proposed. In the lower layer, to handle the unknown control directions problem and to achieve the output tracking of the local references generated in the upper layer, the Nussbaum-type function-based technique is combined with internal model principle. With the proposed two-layer distributed hierarchical controller, the leader-following output consensus is achieved. The obtained result is further extended to the formation control problem. Finally, three numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

Semi-global/global output consensus for nonlinear multiagent systems with time delays

Under a fixed directed graph, the leader-following output consensus problem is investigated for a class of nonlinear time delay multiagent systems with the less conservative condition on nonlinear functions. It is the first time that the output feedback consensus algorithms are proposed for nonlinear multiagent systems with time delays on the state. Moreover, the proposed algorithms have a simple design procedure and can be used to address the consensus problem of nonidentical multiagent systems. A novel dynamic compensator is designed for each follower and the distributed memoryless controller is constructed based on the compensator. The controller is independent of time delays, which depends only on the follower output and the relative output information of its neighbor agents, and it can render that all outputs of the agents achieve a consensus. Furthermore, it is proved that the resulting closed-loop system is stable in the sense of semi-global (global) boundedness. Finally, the effectiveness of the output feedback distributed consensus algorithms is demonstrated by a simulation example.

Leader-Following Output Consensus for High-Order Nonlinear Multiagent Systems

This technical note focuses on the leader-following output consensus problem for a class of high-order nonlinear multiagent systems under a fixed directed graph. To obtain the global result of output feedback control for the system with the less conservative condition on nonlinear terms than traditional Lipschitz one, the novel reduced-order dynamic compensator is constructed. By introducing an appropriate state transformation, a new fully distributed output feedback control method is proposed, which greatly simplifies the design procedure compared with the backstepping method. The distributed linear-like controller with a dynamic gain is designed for each agent based only on the relative output measurements of neighboring agents. The condition that the orders of all agents should be the same is not needed anymore with the proposed method; thus, the novel result will have extensive applications. Finally, the theoretical results are supported by a numerical simulation.

Leader-Following Output Consensus for High-Order Nonlinear Multi-Agent Systems by Distributed Event-Triggered Strategy via Sampled Data Information

In this paper, the observer-based leader-following output consensus problem is investigated for high-order nonlinear multi-agent systems with a distributed event-triggered mechanism. The system dynamics are described as a strict-feedback form and satisfy the Lipschitz condition. Both the event-triggered communication scheme and the sampled-based communication scheme are considered to solve the output consensus problem. First, a distributed event-triggered strategy is developed by using the dynamic output-feedback control method for the event-triggered communication scheme. With the complicated event-triggered strategy, some critical techniques are used to achieve that all the sampling intervals have a positive lower bound. Thus, Zeno behavior is excluded. Then, an event-triggered output consensus protocol is proposed with a sampled-based monitoring scheme, where the monitoring instants only happen at the sampling instants. By using the Lyapunov stability theorem, it is proved that all the output tracking errors converge to zero exponentially when the design parameters are chosen properly for both these two cases. Also, we get that it does not need all agents to be triggered synchronously. Finally, the two simulation examples are considered to show the efficiency of the consensus protocols.

Semi-Global Cooperative Output Regulation Problem for Heterogeneous Swarm Systems With Input Saturation Under Switching Network

In this paper, the semi-global cooperative output regulation problem of heterogeneous swarm systems subject to saturation under switching network is investigated. Like the common consensus problems, the swarm systems consist of some followers cannot access the state of the leader directly. But the difference is that some even cannot measure the state of the leader all the time. By utilizing the distributed output feedback control method, the low-gain feedback technique and the output regulation theories, we establish two sets of consensus control laws, respectively, based on the state feedback method and the output feedback method, to solve the output consensus problems in this kind. Besides, the global leader-following output consensus problem under switching network is proved to be a special case of semi-global cooperative output regulation problem under switching network, and as a consequence, it can also be solved by our method. A simulation example is proposed to illustrate the results very well.