Consensus Of High-order Multi-agent Systems Research Articles

Scaled Position Consensus of High-Order Uncertain Multiagent Systems Over Switching Directed Graphs.

We investigate the scaled position consensus of high-order multiagent systems with parametric uncertainties over switching directed graphs, where the agents' position states reach a consensus value with different scales. The intricacy arises from the asymmetry inherent in information interaction. Achieving scaled position consensus in high-order multiagent systems over directed graphs remains a significant challenge, particularly when confronted with the following complex features: 1) uniformly jointly connected switching directed graphs; 2) complex agent dynamics with unknown inertias, unknown control directions, parametric uncertainties, and external disturbances; 3) interacting with each other via only relative scaled position information (without high-order derivatives of relative position); and 4) fully distributed in terms of no shared gains and no global gain dependency. To address these challenges, we propose a distributed adaptive algorithm based on a acrlong MRACon scheme, where a linear high-order reference model is designed for every individual agent employing relative scaled position information as input. A new transformation is proposed which converts the scaled position consensus of high-order linear reference models to that of first-order ones. Theoretical analysis is presented where agents' positions achieve the scaled consensus over switching directed graphs. Numerical simulations are performed to validate the efficacy of our algorithm and some collective behaviors on traditional consensus, bipartite consensus, and cluster consensus are shown by precisely choosing the scales of the agents.

Distributed Adaptive Forwarding Finite-Time Output Consensus of High-Order Multiagent Systems via Immersion and Invariance-Based Approximator.

A finite-time output consensus control problem is investigated in this article for an uncertain nonlinear high-order multiagent systems (MASs). For this class of MASs, the order of individual follower is reduced gradually by implementing the immersion and invariance (I&I) control theory repeatedly, and a requirement of solving partial differential equations (PDEs) in I&I control theory is obviated. Furthermore, an I&I-based radial basis function neural network (RBFNN) approximator is developed, where an extra cross term is added in the approximation mechanism, and the form of an update law for weights is transformed into a proportional and integral one. This I&I-based RBFNN approximator does not rely on a cancellation of the perturbation term, and these uncertainties are reconstructed by the I&I manifold adaptively, which is for improvement of approximation behaviors of traditional RBFNNs. On this basis, a distributed adaptive forwarding finite-time output consensus control strategy is proposed by combining a sign function, and the convergence time of the MAS can be adjusted with appropriate finite-time parameters. Finally, two illustrative examples verify the effectiveness of the theoretical claims.

Fast Consensus of High-Order Multiagent Systems

In this paper, the fast consensus problem of high-order multi-agent systems (MASs) under undirected topologies is considered. The direct link between the consensus convergence rate and the control gains is established. A gradient descent based algorithm is proposed to optimize the convergence rate. By applying the Routh-Hurwitz stability criterion, the lower bound on the convergence rate is derived, and explicit control gains are derived as conditions to achieve the optimal convergence rate. Moreover, a protocol with time-varying control gains is designed to achieve the finite-time consensus. Explicit formulas for the time-varying control gains and the final consensus state are given. Numerical examples and simulation results are presented to illustrate the obtained theoretical results.

Lag Group Consensus of High-Order Multiagent Systems in Directed Network Settings

This article studies lag group consensus problems of multiagent systems with directed information transformations. Agents in the network are divided into finite groups, and modeled by high-order systems. Distributed consensus protocols with constant lags are presented to realize the lag group consensus: the states of the agents in a group approach to a consensus value asymptotically, while there exist given ratios between the final values of different groups. Necessary and sufficient criteria for the lag group consensus are obtained by the Laplace transformation. Finally, theoretical results are proved to be effective by several simulation results.

Distributed Adaptive Finite-Time Consensus for High-Order Multi-Agent Systems with Intermittent Communications under Switching Topologies

In this paper, a distributed adaptive finite-time consensus (FTC) control protocol for a high-order multi-agent system (MAS) with intermittent communications under switching topologies is proposed. Meanwhile, considering the problem of heterogeneous unknown nonlinearities and other uncertain disturbances, the adaptive neural network and the sliding mode control method are used to compensate the nonlinearity of each agent separately. The agents are homogeneous, so the system has symmetry. The switching topologies considered in this paper are asymmetric. Compared with consensus protocol for asymptotic convergence, simulation results show that the proposed method can effectively solve the presence of the nonlinear and accelerate the convergence speed of the system so that an FTC can be reached.

Leader selection in networks under switching topologies with antagonistic interactions

In leader–follower networks, leader selection is an important issue, and efficient schemes of selecting a group of leaders are sought to guarantee the desired coordination performance. In this paper, we study the leader selection problem under switching topologies, and aim to minimize the number of leaders to ensure the consensus of high-order multiagent systems with antagonistic interactions, which are usually represented by negative edge weights on a communication graph. First, as the basis of leader selection, sufficient conditions including average dwell time bounds for each possible topology and a mild network connectivity assumption are derived for followers to reach the expected property. Second, by applying the derived consensus criterion, metrics for identifying leaders are established via the submodular optimization method, and the supermodularity of the metrics is proved in the digraph case. Third, by utilizing the established metrics, a leader selection scheme with two polynomial-time algorithms is presented to determine leaders dynamically, and the optimality of the returned solution has a provable guarantee. Finally, the performance of the proposed leader selection scheme is demonstrated by numerical examples.

Fixed-time leader-follower quantized output consensus of high-order multi-agent systems over digraph

This paper is concerned with fixed-time leader-follower consensus of high-order multi-agent system (MAS) under quantized communication and directed communication graph. First, dynamic encoder, quantizer and decoder are presented to encode and quantize the transmitted states at the sending end and decode the transmitted states at the receiving end. Next, a new distributed observer is proposed to estimate the leader’s states within a fixed time under quantized communication environment and directed communication graph. Practical fixed-time convergence of the proposed distributed observer is proved based on nonsmooth stability analysis. Then, a new predefined-time control scheme is developed to achieve practical predefined-time convergence of tracking error dynamics. Finally, simulation results show the validity of the strategy developed in achieving fixed-time leader-follower consensus and formation.

Consensus of High-Order Discrete-Time Multiagent Systems With Switching Topology

The communication cost is generally higher for the consensus of high-order multiagent systems than that for low-order multiagent systems. In this paper, two novel distributed protocols are proposed to address the consensus of high-order discrete-time multiagent systems. By the proposed consensus protocols, each agent only needs to transmit the value of a variable to neighbor agents regardless of the order of agent dynamics. Theoretical analysis shows that the proposed protocols guarantee asymptotic consensus of the agent states in different cases of communication graphs, including jointly connected ones. Simulative examples verify the theoretical results and the efficacy of the proposed protocols.

Asynchronous Distributed Model Predictive Control for Optimal Output Consensus of High-Order Multi-Agent Systems

Considering the extensive applications of the model predictive control (MPC), this paper investigates the MPC problem with an application to the optimal output consensus of high-order multi-agent systems. A synchronous distributed optimization algorithm for the MPC problem is proposed, and we further devise its asynchronous version. The algorithm allows agents to choose the uncoordinate step-sizes depending on local information, which improves the flexibility of multi-agent systems. The convergence of the proposed algorithm is guaranteed if the positive uncoordinate step-sizes satisfy the explicit conditions. Compared with the synchronous version that needs a global clock to control all agents for communication and update, the asynchronous algorithm does not require each agent in the multiagent systems to update and communicate simultaneously, and also converges to the optimal global solution to the problem. The numerical simulations demonstrate the availability of the proposed algorithm and the validity of the theoretical results.

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.

Event-triggered consensus control of high-order multi-agent systems with arbitrary switching topologies via model partitioning approach

This paper investigates the problem of event-triggered consensus control for high-order multi-agent systems with arbitrary switching topologies. To achieve this goal, a novel model partitioning approach is proposed, where the high-order error systems are partitioned into stable subsystems and unstable subsystems through coordinate transformations. By analyzing the unstable subsystems under arbitrary switching, an appropriate controller can be designed to guarantee the subsystems stable. Then the controller gain of the multi-agent systems can be derived through inverse transformations. The designed controller can guarantee the error state convergence under each topology within any time interval, which further ensures the consensus of high-order multi-agent systems under arbitrary switching topologies. Finally, a numerical example is provided to illustrate the feasibility of the theoretical results.

Distributed fuzzy adaptive consensus for high-order multi-agent systems with an imprecise communication topology structure

In this study, we consider the consensus problem for a high-order multi-agent systems (MASs) with an imprecise communication topology structure described by the Takagi–Sugeno fuzzy model. A distributed adaptive control protocol is proposed for the consensus problem comprising MASs with unknown parameters and input disturbances. The proposed protocol can guarantee that the consensus errors asymptotically approach zero under the conditions that the communication topology is fuzzy union connected and the dynamics of the leader are unknown to any agent among the followers. Furthermore, the proposed algorithm is extended to solve the formation control problem for MASs. Sufficient conditions are provided for the consensus and formation problems for MASs based on Lyapunov stability theory. Finally, three simulation examples are presented to illustrate the effectiveness of the proposed control protocol.

Robust Leader-Following Consensus of High-Order Multi-Agent Systems in Prescribed Time

This article addresses the distributed prescribed-time leader-following consensus problem for a class of high-order multi-agent systems (MASs) with perturbed nonlinear agents dynamics and where the topology of the network contains a directed spanning tree, with the leader as the root. Prescribed-time consensus means that an agreement state of the MAS is achieved in a preset time, introduced as a parameter of the control law, and this constant settling time is achieved independently of the agents' initial state. The proposed control method exhibits three main advantages: first, to our best knowledge, it is the first time that prescribed-time convergence in a consensus problem is achieved for agents with high-order nonlinear dynamics, using a robust leader-following protocol, which allows an effective rejection of matched disturbances in the agents' model. Second, the proposed controller provides control signals of lower magnitude than existing approaches. Third, the proposed consensus protocol does not have parameters to be adjusted depending on the connectivity of the considered communication graph.

Nonlinear PI Control for High-Order Agents With Unknown High-Frequency Gain Signs Under Switching Topologies

Existing results on dealing with unknown high-frequency gain signs (UHFGSs) mainly adopt the Nussbaum-type functions. A new kind of control algorithms with nonlinear PI functions are presented to cope with UHFGSs. It is rigorously proven that the proposed algorithms with properly selected nonlinear PI functions can guarantee consensus for high-order multi-agent systems (MASs) under switching topologies with uniformly quasi-strongly $\delta $ -connected graphs (UQSGs). Furthermore, we also investigate the output leaderless consensus of heterogeneous agents with UHFGSs. Finally, the numerical examples are illustrated to show the validity of the proposed results.

Event-triggered bipartite consensus for high-order multi-agent systems with input saturation

In this paper, the bipartite consensus problem for high-order multi-agent systems (MASs) with input saturation is investigated by distributed event-triggered control and low-gain feedback technique. The underlying topological graph of the system is divided into undirected graph and directed graph. Distributed event-triggered control strategy is proposed to guarantee the semi-global bipartite consensus of MASs. The lower bound of time interval between any two consecutive triggering instants ensures that the Zeno behavior can be excluded for each agent. Finally, two simulation examples are presented to illustrate the effectiveness of the theoretical results.

Robust Output Feedback Consensus of High-order Multi-agent Systems with Nonlinear Uncertainties

In this paper, the output feedback consensus problem of high-order multi-agent systems with nonlinear uncertainties is researched by the robust control method. By the dimensional extension of the observation matrix, the consensus control problem is transformed into a stability problem. Then the robust controller is designed by combining the nominal controller and the robust compensator. The nominal controller can obtain desired nominal performance based on the output informations. The robust compensator, which relys on robust signal compensation technology, is order to suppress the nonlinear uncertainties. According to the proposed method, output consensus error can be guaranteed as small as desired. Finally, simulation results are given to illustrate the effectiveness of this control method.

Optimal Output Consensus of High-Order Multiagent Systems With Embedded Technique.

In this paper, we study an optimal output consensus problem for a multiagent network with agents in the form of multi-input multioutput minimum-phase dynamics. Optimal output consensus can be taken as an extended version of the existing output consensus problem for higher-order agents with an optimization requirement, where the output variables of agents are driven to achieve a consensus on the optimal solution of a global cost function. To solve this problem, we first construct an optimal signal generator, and then propose an embedded control scheme by embedding the generator in the feedback loop. We give two kinds of algorithms based on different available information along with both state feedback and output feedback, and prove that these algorithms with the embedded technique can guarantee the solvability of the problem for high-order multiagent systems under standard assumptions.

Consensus for high-order multi-agent systems with communication delay

In this study, consensus problem for general high-order multi-agent systems with communication delay is investigated. Given the unstable agent dynamics and a known communication delay, two consensus protocols are designed to guarantee consensus over undirected network. By jointly researching the effects of agent dynamics and network topology, allowable delay bounds depending on the maxima of concave functions are easy to calculate. Especially, the maximum delay bound is derived when the network topology is completely connected. The main approach for the same involves designing the control gains on the basis of the solution of a parametric algebraic Riccati equation. Finally, the theoretical results are demonstrated via numerical simulations.

Improved delay-dependent consensus stability criteria of high-order multi-agent systems with time delays

This paper studies the consensus of high-order multi-agent systems with communication time delays. In order to get the maximum allowable delay bound, an approach of system transformations is introduced. Through transformation the consensus problem is converted to the robust stability problem of some uncertain state-delayed system. The proposed method employs an improved vector Wirtinger-type inequality for constructing a novel Lyapunov–Krasovskii functional. Based on the Lyapunov stable theory, new sufficient conditions in terms of linear matrix inequalities which contain the feedback gain condition and delay condition are given to guarantee the average consensus under fixed topology and switching connected topologies, respectively. Maximum allowable delay bounds are further obtained for both systems. As long as the delays are less than this bound, there exist linear feedback consensus protocols driving the multi-agent system to achieve consensus. The effectiveness of the proposed method is demonstrated by numerical examples.

Quantized Leaderless and Leader-Following Consensus of High-Order Multi-Agent Systems With Limited Data Rate

Distributed consensus with limited communication data rate is an interesting and important problem and has been studied for multi-agent networks with the first order and second order integrator dynamics. However, the problem remains challenging for higher-order systems due to the complexity of consensus analysis and data rate minimization. In this paper, the leaderless and leader-following quantized consensus for a special kind of high-order systems are considered. Each agent is assumed to be controllable and observable with single input and single output, and its system matrix admits n identical eigenvalues of 1. The special case of n-th order integrator multi-agent system with only the first state variable being measurable is first investigated, and it is shown that for a fixed undirected connected network, n bits of information exchange between agents suffice to guarantee the leaderless and leader-following quantized consensus respectively with an exponential convergence rate by employing a suitable encoding-decoding scheme and perturbation analysis of matrices. The obtained results are then extended to the general case of multi-agent dynamics with n identical eigenvalues of 1 by applying the same encoding-decoding scheme and control protocol to an observer system for each agent. The final consensus value and the application to formation control are also discussed.