Distributed Consensus Tracking Research Articles

Fully Distributed Consensus Tracking of Multiagent Systems With a High-Dimensional Leader and Directed Communication Topology

We study the asymptotic consensus tracking problem for multiagent systems (MASs) with uncertain dynamics under directed communication topology, where the leader has higher dimensional dynamics than followers. In our approach, the uncertainties are approximated by a neural network with arbitrary accuracy in compact regions. To remove the effects of leader’s high dimensional dynamics on consensus, a compensation controller with adaptive coupling strengths is designed. Moreover, to eliminate the effects of uncertain dynamics and external disturbances on consensus, a discontinuous feedback controller with neuro-adaptive law is given. Furthermore, we show fully distributed asymptotic consensus tracking of the considered MAS under the designed compensator plus the feedback controller can be achieved if the communication topology contains a directed spanning tree with the leader being the root. In addition, a theorem is given under the undirected topology. Finally, we perform a simulation to validate the theoretical result.

Robust distributed consensus tracking control for high‐order uncertain nonlinear MASs with directed topologies

AbstractThis paper addresses the robust distributed consensus tracking problem for leader‐follower multi‐agent systems (MASs) with nonlinear dynamics and external disturbances under directed graph topologies. The nonlinear uncertainties are not required to be continuous or meet the matching conditions. The backstepping design method combined with signal compensation approach is proposed to design robust controllers in order to guarantee the consensus tracking property between the followers and the one leader. Moreover, the dynamic surface control technique is used to deal with the 'explosion of complexity' problem. It is proven that the robust distributed consensus tracking property of the MASs can be guaranteed. Furthermore, the consensus tracking errors can be designed as small as required and the convergence speed can be chosen arbitrarily. Finally, two examples are presented to show the validity of the proposed consensus tracking control protocols.

Distributed low-complexity fault-tolerant consensus tracking of switched uncertain nonlinear pure-feedback multi-agent systems under asynchronous switching

This paper addresses a distributed low-complexity design problem for ensuring preassigned fault-tolerant consensus tracking quality of uncertain switched nonlinear pure-feedback multi-agent systems under arbitrary and asynchronous switching. Switched non-affine nonlinearities and unexpected nonlinear and actuator faults of each system are assumed to be unknown. Compared with existing results in the literature, the main contribution of this paper is to provide a simplified robust control strategy to deal with asynchronously switched nonlinearities and faults among systems in the consensus tracking field. Using nonlinearly transformed error surfaces and the common Lyapunov function method, a common robust consensus tracking design strategy is established to ensure the preassigned fault-tolerant consensus tracking performance and the system reliability on the switched faults, without using any adaptive fault compensation techniques based on neural networks or fuzzy logic systems. It is shown that the distributed consensus tracking errors remain within preselected bounds even at switching and fault occurrence instants and finally converge to a preselected neighborhood of the origin.

Distributed consensus tracking of unknown nonlinear chaotic delayed fractional-order multi-agent systems with external disturbances based on ABC algorithm

In this paper, the distributed consensus tracking of unknown nonlinear chaotic delayed fractional-order multi-agent systems (FOMASs) with external disturbances is investigated, where the fractional orders and system parameters are unknown. Firstly, in order to identify the unknown parameters of the delayed nonlinear FOMASs, an efficient artificial bee colony algorithm (ABC)-based parameters estimation approach is put forward. Secondly, based on the estimated parameters, by using fractional derivative inequality and comparison principle of linear fractional equation with delay, a discontinuous distributed control protocol is proposed to make the tracking errors converge to zero asymptotically. Thirdly, to overcome the undesirable chattering phenomenon caused by the discontinuous controller, a continuous distributed control algorithm is further designed and uniformly ultimately bounded (UUB) tracking errors can be obtained and reduced as small as desired. Finally, numerical simulations are given to test the effectiveness of the proposed parameters estimation scheme and the deigned control algorithms.

Consensus Tracking for Heterogeneous Interdependent Group Systems.

This paper is concerned with the consensus tracking problem for heterogeneous interdependent group systems with fixed communication topologies. First, the interdependent model of the heterogeneous system is built from the perspective of the difference of the individual characteristic and the difference of the subgroup topology structure. A class of distributed consensus tracking control protocol is proposed for realizing the consensus tracking of the heterogeneous interdependent group system via using local information. Then, for fixed communication topologies, some corresponding sufficient conditions are given to ensure the achievement of the consensus tracking. Two parameters are defined, which denote, respectively, the proportion of interdependence individual and the redundancy of interdependence. The effects of these parameters are analyzed on the consensus tracking of group systems. Numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

Robust consensus tracking of second-order nonlinear systems using relative position information by K-filter and disturbance observer based control

ABSTRACTThis work considers the problem of distributed consensus tracking control of second-order uncertain nonlinear systems under a directed communication graph which contains a spanning tree, where the leader node is the root. It is assumed that the followers receive only the relative positions from the neighbours. For the purpose of consensus tracking controller design, in each follower, a group of K-filters is introduced so that the necessity of velocity estimating is avoided. Then we can express each follower's tracking error dynamics as a second-order system with mismatched uncertainties. And hence we can design a robust consensus tracking controller for each follower by using the combination of the backstepping design and the disturbance observer based control using only relative position information. Theoretical analysis is performed to show that the DOBs' estimation errors can be made to decay to be sufficiently small very quickly before the system states escape from the feasible region. Then we show that all the followers' states track those of the leader with arbitrarily small ultimate error bounds. And simulation examples are provided to demonstrate the performance of the proposed method.

Consensus Tracking for Teleoperating Cyber-physical System

In this paper, we investigate the consensus tracking problem for teleoperating cyber-physical system (TCPS) under time-varying delay and actuator saturation constraints. Due to the introduction of communication network, variable propagation time delays are considered in cyber element. In addition, actuator saturation problem is investigated in physical element, which is caused by the physical restrictions on robots. Then, a novel distributed consensus tracking controller is proposed in the presence of time-varying delay and actuator saturation. Meanwhile, sufficient conditions are provided to show that the consensus tracking controller can stabilize the master-slave TCPS. Finally, simulations and experiments are performed to validate our proposed results. It is shown that the consensus controllers can guarantee the asymptotic stability of single-master-multi-slave TCPS.

Swarming Behavior of Multiple Euler-Lagrange Systems With Cooperation-Competition Interactions: An Auxiliary System Approach.

In this paper, the swarming behavior of multiple Euler-Lagrange systems with cooperation-competition interactions is investigated, where the agents can cooperate or compete with each other and the parameters of the systems are uncertain. The distributed stabilization problem is first studied, by introducing an auxiliary system to each agent, where the common assumption that the cooperation-competition network satisfies the digon sign-symmetry condition is removed. Based on the input-output property of the auxiliary system, it is found that distributed stabilization can be achieved provided that the cooperation subnetwork is strongly connected and the parameters of the auxiliary system are chosen appropriately. Furthermore, as an extension, a distributed consensus tracking problem of the considered multiagent systems is discussed, where the concept of equi-competition is introduced and a new pinning control strategy is proposed based on the designed auxiliary system. Finally, illustrative examples are provided to show the effectiveness of the theoretical analysis.

Distributed consensus tracking of a class of asynchronously switched nonlinear multi-agent systems

This paper addresses the distributed consensus tracking problem for a class of switched nonlinear multi-agent systems in pure-feedback form under directed communication networks. For a practical environment, switched non-affine nonlinearities for followers are unknown and their switching signals are assumed to be arbitrary and asynchronous. Compared with existing results in the literature, the main contribution of this paper is to provide a universal control strategy to deal with asynchronously switched nonlinear multi-agent systems in the consensus tracking field. By using the function approximation technique, an approximation-based novel recursive design approach for asynchronously switched followers is presented to design local common adaptive controllers without requiring the knowledge on the signs of control gain functions and on the leader’s velocity. From the common Lyapunov function method, it is shown that the consensus tracking errors are asymptotically bounded and converge to a neighborhood of the origin. A simulation example is included to demonstrate the effectiveness of the proposed methodology.

Neutral Networks-Based Adaptive Fixed-Time Consensus Tracking Control for Uncertain Multiple AUVs

This paper is concerned with the fixed-time consensus tracking problem for multi-AUV (autonomous underwater vehicle) systems with uncertain parameters and external disturbances. Firstly, a fixed-time terminal sliding mode is proposed, which can avoid the singularity problem. Then, a continuous distributed consensus tracking control law is designed based on Neutral Network approximation technique, which can guarantee the consensus tracking errors converge to the desired regions in fixed time. A simulation example is given to show the effectiveness of proposed methods.

Distributed adaptive fixed-time consensus tracking for second-order multi-agent systems using modified terminal sliding mode

This paper investigates the fixed-time consensus tracking problems for second-order multi-agent systems with unknown external disturbances. Firstly, a fixed-time terminal sliding mode (FTTSM) is proposed, which can avoid the singularity problem. Then, two continuous distributed consensus tracking control laws with adaptive updating laws are designed respectively, in which the upper bounds of external disturbances are not required. It is proved that the two control laws can both guarantee the consensus tracking errors converge into the desired regions including the origin in fixed time. A simulation example is given to demonstrate the effectiveness of proposed methods.

Distributed Tracking of Nonlinear Multiagent Systems Under Directed Switching Topology: An Observer-Based Protocol

This paper deals with a consensus tracking problem for multiagent systems (MASs) with Lipschitz-type nonlinear dynamics and directed switching topology. Unlike most existing works where the relative full state measurements of neighboring agents are utilized, it is assumed that only the relative output measurements of neighboring agents are available for coordination. To achieve consensus tracking in the considered MASs, a new class of observer-based protocols is proposed. By appropriately constructing some topology-dependent multiple Lyapunov functions, it is theoretically shown that distributed consensus tracking in the closed-loop MASs equipped with the designed protocols can be ensured if each possible topology contains a directed spanning tree rooted at the leader and the dwell time for the switchings among different topology is less than a derived positive quantity. Interestingly, it is found that the communication topology for observers’ states may be independent with that of the feedback signals. The derived results are further extended to the case of directed switching topology with only average dwell time constraints. Finally, the effectiveness of the analytical results is demonstrated via numerical simulations.

Minimal-Approximation-Based Distributed Consensus Tracking of a Class of Uncertain Nonlinear Multiagent Systems With Unknown Control Directions.

A minimal-approximation-based distributed adaptive consensus tracking approach is presented for strict-feedback multiagent systems with unknown heterogeneous nonlinearities and control directions under a directed network. Existing approximation-based consensus results for uncertain nonlinear multiagent systems in lower-triangular form have used multiple function approximators in each local controller to approximate unmatched nonlinearities of each follower. Thus, as the follower's order increases, the number of the approximators used in its local controller increases. However, the proposed approach employs only one function approximator to construct the local controller of each follower regardless of the order of the follower. The recursive design methodology using a new error transformation is derived for the proposed minimal-approximation-based design. Furthermore, a bounding lemma on parameters of Nussbaum functions is presented to handle the unknown control direction problem in the minimal-approximation-based distributed consensus tracking framework and the stability of the overall closed-loop system is rigorously analyzed in the Lyapunov sense.

Distributed consensus tracking with stochastic quantization via pulse-modulated intermittent control

This paper studies the consensus tracking problem of the multi-agent system with bandwidth limitation. The stochastic quantization scheme is adopted to transmit information among agents. The multi-agent system with both velocity-measurable and velocity-unmeasurable are considered. Two pulse-modulated intermittent control are proposed to ensure consensus tracking of the multi-agent system. Based on the stability theory, discretization approaches and algebraic graph theory, some necessary and sufficient conditions are obtained to ensure consensus tracking of the controlled system with and without velocity measurement. Some simulation results are given to show that the followers can well track the dynamic leader by obeying the proposed control laws.

Leader-Following Consensus for High-Order Nonlinear Stochastic Multiagent Systems.

This paper considers the distributed consensus tracking problem for a class of high-order stochastic multiagent systems with uncertain nonlinear functions under a fixed undirected graph. Through the recursive method, the novel nonlinear distributed controllers are designed. By constructing a kind of special form for the virtual controller in the first step of recursive design, we realize that the state variables of every agent are separated except the outputs of the adjacency agents. The designed controller of each agent only depends on its own state variables and the outputs of the adjacent multiagents. With the proposed method, it is not required any more that the orders of the agents are same. This makes the designed controller be easier to be implemented and the proposed method be applicable for a wider class of multiagent systems. The efficiency of the design approach is illustrated by a simulation example.

Distributed adaptive asymptotically consensus tracking control of nonlinear multi-agent systems with unknown parameters and uncertain disturbances

Different from traditional centralized control, one major challenge of distributed consensus tracking control lies in the constraint that the desired reference trajectory is only accessible by part of the subsystems. Currently, most existing schemes require the availability of partial knowledge of the reference trajectories to all of the subsystems or information exchange of local control inputs. In this paper, we investigate distributed adaptive consensus tracking control without such requirements for nonlinear high-order multi-agent systems subjected to mismatched unknown parameters and uncertain external disturbances. By introducing compensating terms in a smooth function form of consensus errors and certain positive integrable functions in each step of virtual control design, a new backstepping based distributed adaptive control protocol is proposed. An extra estimator is designed in each subsystem to handle the parametric uncertainties involved in its neighbors’ dynamics, which avoids information exchange of local neighborhood consensus errors among connected subsystems. It is shown that global uniform boundedness of all the closed-loop signals and asymptotically output consensus tracking can be achieved. Simulation results are provided to verify the effectiveness of our scheme.

Distributed consensus tracking for the fractional-order multi-agent systems based on the sliding mode control method

Distributed consensus tracking for the fractional-order multi-agent systems is mainly studied in this paper. Firstly, the simple Lyapunov candidate function is discussed to judge the validity of the proposed controller. Secondly, according to the sliding mode control method, a controller is designed to achieve the consensus tracking problem when the followers are described by the fractional-order linear dynamics. Thirdly, the case when the dynamics of followers own the intrinsic nonlinear function is discussed, it proves that the designed sliding mode controller is still valid for this case under the certain conditions. For the above two parts, the systems stabilities are judged based on the result of the first part. Finally, several simulations are presented to verify the obtained results.

Robust adaptive distributed dynamic surface consensus tracking control for nonlinear multi-agent systems with dynamic uncertainties

This paper proposes an adaptive distributed consensus tracking control approach for uncertain nonlinear multi-agent systems in pure-feedback form under a directed topology where each follower is dominated by dynamic uncertainties and unmeasured states. Radial basis function neural networks (RBFNNs) are employed to compensate the unknown nonlinear functions obtained by recursive design procedure for followers. The distributed dynamic surface controllers are able to eliminate the condition in which the approximation error of the traditional neural networks is bounded. By introducing an available dynamic signal and two smooth scalar functions, the obstacle caused by unmodeled dynamics is conquered. The main advantage of the proposed method is that for M pure-feedback nonlinear followers, only one learning parameter needs to be updated online. It is also shown that the proposed consensus controller can guarantee cooperatively semi-global uniform ultimate boundedness (CSUUB) of all the signals, and the consensus errors converge to an adjustable neighborhood of the origin.

Robust consensus tracking control of higher‐order uncertain non‐linear systems via cascaded finite‐time estimation of reference states

This work considers the problem of distributed consensus tracking control of higher-order uncertain non-linear systems on a directed graph which contains a spanning tree with the leader node being the root. To facilitate controller design, in each agent of the network, a group of distributed and cascaded finite-time estimators is constructed for estimating the reference trajectory and its higher-order derivatives by information exchange among the local neighbours. Only the highest-order derivative estimator is discontinuous, whereas the estimators of the other reference states are continuous. Finite-time convergence property of each estimator is analysed. Then by utilising the estimated reference states, in each agent, a robust controller composed of some non-linear damping terms, a disturbance observer and a sliding mode control term is designed, so that the agent's states track the estimated reference states with an arbitrarily small ultimate error bound. The tracking performance is theoretically analysed. And simulation examples are provided to demonstrate the performance of the finite-time reference estimators and the tracking controllers.

Neuro-Adaptive Consensus Tracking of Multiagent Systems With a High-Dimensional Leader

This paper is concerned with the distributed consensus tracking problem of uncertain multiagent systems with directed communication topology and a single high-dimensional leader. Compared with existing related works, the dynamics of each follower in the present framework are subject to unmodeled dynamics and unknown external disturbances, which is more practical in various applications. Furthermore, the dimensions of leader's dynamics may be different with those of the followers' dynamics. Under the mild assumption that each follower can directly or indirectly sense the output information of the leader, a distributed robust adaptive neural network controller together with a local observer are designed to each follower to ensure that the states of each follower ultimately synchronize to the leader's output with bounded residual errors under a fixed topology. By appropriately constructing some multiple Lyapunov functions, the derived results are further extended to consensus tracking with switching directed communication topologies. The effectiveness of the analytical results is demonstrated via numerical simulations.