High-order Linear Multi-agent Systems Research Articles

Design Finite-time Consensus Protocol for High-order Linear Multi-agent Systems: A Gain Scheduled Approach⋆

This paper revisits the finite-time consensus problem for high-order linear multi-agent networks by using smooth state-feedback. By following a gain scheduled approach, this paper first presents finite-time consensus protocol with a state-independent parameter, which takes the time-varying solution of parametric Lyapunov equation to design control gain. Note that the state-independent parameter is selected based on the connectivity of topology, which is a piece of global information. To get rid of this dependence, a node-based adaptive parameter is further proposed to achieve fully distributed consensus. Through finite-time stability theory, both the prepared parameters, including state-independent and adaptive parameters, for control protocol make the agents achieve finite-time consensus. Particularly, a specific convergence time is given by following the concept of finite-time escaping function. Finally, we provide a practical simulation on finite-time formation problem of six satellites, demonstrating the validity of theoretical results.

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.

A L2‐gain robust PID‐like protocol for time‐varying output formation‐containment of multi‐agent systems with external disturbance and communication delays

This paper addresses the time-varying output formation-containment control problem for homogeneous high-order linear Multi-Agent Systems (MASs). In this context, a PID-like output-feedback control strategy is proposed capable to guarantee that all followers reach and maintain a time-varying formation reference behaviour, as imposed by the multiple leaders, while keeping a prescribed offset with respect to it. Moreover, the proposed approach allows dealing with both communication impairments and external disturbances acting on agents dynamics. The asymptotic stability of the closed-loop MAS is analytically proved by means of a Lyapunov–Krasovskii approach. Stability conditions are expressed as a feasibility problem with Linear Matrix Inequalities constraints, whose solution provides the proper tuning of the robust PID control gains. Extensive numerical analysis confirms the theoretical framework and discloses the effectiveness of the proposed approach in ensuring the output time-varying formation-containment.

Distributed model reference adaptive containment control of heterogeneous multi-agent systems with unknown uncertainties and directed topologies

In this paper, the containment control problem of heterogeneous uncertain high-order linear Multi-Agent Systems (MASs) is addressed and solved via a novel fully-Distributed Model Reference Adaptive Control (DMRAC) approach, where each follower computes its adaptive control action on the basis of local measurements, information shared with neighbors (within the communication range) and the matching errors w.r.t. its own reference model, without requiring any previous knowledge of the global directed communication topology structure. The approach inherits the robustness of the direct model reference adaptive control (MRAC) scheme and allows all agents converging towards the convex hull spanned by leaders while fulfilling at the same time local additional performance requirements at single-agent level, such as prescribed settling time, overshoot, etc. The asymptotic stability of the whole closed-loop network is analytically derived by exploiting the Lyapunov theory and the Barbalat lemma, hence proving that each follower converges to the convex hull spanned by the leaders, as well as the boundedness of the adaptive gains. Extensive numerical analysis for heterogeneous MAS composed of stable, unstable and oscillating agent dynamics are presented to validate the theoretical framework and to confirm the effectiveness of the proposed approach.

Sliding Mode Control for Robust Consensus of General Linear Uncertain Multi-agent Systems

This paper investigates the robust consensus problem for general high-order linear multi-agent systems with external disturbances and internal uncertainties in coefficient matrices. Distributed protocols based on sliding mode control are proposed to realize the robust consensus under matched uncertainties.

Distributed Time-Varying Formation Control for Multiagent Systems With Directed Topology Using an Adaptive Output-Feedback Approach

This paper addresses fully distributed formation control problems for high-order linear multiagent systems (MASs) with directed communication topology. In order to overcome the shortcomings of designing time-varying formation (TVF) protocols via the global information of the communication network and the full states of all the agents in existing formation results, a novel adaptive TVF protocol is developed. First, dynamic output feedback information and sequential observers are used to construct the adaptive TVF protocol. Then, a distributed algorithm which includes a TVF feasibility constraint is proposed. Only local outputs of neighboring agents are used in the algorithm. Moreover, applying the proposed approach and the Lyapunov stability theory, it is found that the fully distributed TVF can be achieved. Finally, numerical simulations are given to demonstrate the theoretical results.

Finite-Time Consensus and Tracking Control of A Class of Nonlinear Multiagent Systems

In this technical note, we consider the finite-time consensus and tracking problems for a class of nonlinear multiagent systems with directed topology. By using the homogeneous function, we firstly give a finite-time consensus protocol for high-order linear multiagent systems. Then, we present the finite-time consensus and tracking protocols for strict feedback nonlinear multiagent systems. When state information is not available, the finite-time convergent observer is used to estimate each agent’ states, and we give the finite-time consensus and tracking protocols based on the finite-time observers.

Adaptive guaranteed-performance consensus design for high-order multiagent systems

The current paper investigates the distributed guaranteed-performance consensus design problems for high-order linear multiagent systems with leaderless and leader-follower structures, respectively. The information about the Laplacian matrix of the interaction topology or its minimum nonzero eigenvalue is usually required in existing works on the guaranteed-performance consensus, which means that their conclusions are not completely distributed. A new translation-adaptive strategy is proposed to realize the completely distributed guaranteed-performance consensus control by the structure feature of a complete graph in the current paper. For the leaderless case, an adaptive guaranteed-performance consensualization criterion is given in terms of Riccati inequalities and a regulation approach of the consensus control gain is presented by linear matrix inequalities. Extensions to the leader-follower cases are further investigated. Especially, the guaranteed-performance costs for leaderless and leader-follower cases are determined, respectively, which are associated with the intrinsic structure feature of the interaction topologies. Finally, two numerical examples are provided to demonstrate theoretical results.

Distributed fault-tolerant time-varying formation control for high-order linear multi-agent systems with actuator failures

This paper investigates the fault-tolerant time-varying formation control problems for high-order linear multi-agent systems in the presence of actuator failures. Firstly, a fully distributed formation control protocol is presented to compensate for the influences of both bias fault and loss of effectiveness fault. Using the adaptive online updating strategies, no global knowledge about the communication topology is required and the bounds of actuator failures can be unknown. Then an algorithm is proposed to determine the control parameters of the fault-tolerant formation protocol, where the time-varying formation feasible conditions and an approach to expand the feasible formation set are given. Furthermore, the stability of the proposed algorithm is proven based on the Lyapunov-like theory. Finally, two simulation examples are given to demonstrate the effectiveness of the theoretical results.

Distributed Time-Varying Formation Robust Tracking for General Linear Multiagent Systems With Parameter Uncertainties and External Disturbances.

This paper investigates the time-varying formation robust tracking problems for high-order linear multiagent systems with a leader of unknown control input in the presence of heterogeneous parameter uncertainties and external disturbances. The followers need to accomplish an expected time-varying formation in the state space and track the state trajectory produced by the leader simultaneously. First, a time-varying formation robust tracking protocol with a totally distributed form is proposed utilizing the neighborhood state information. With the adaptive updating mechanism, neither any global knowledge about the communication topology nor the upper bounds of the parameter uncertainties, external disturbances and leader's unknown input are required in the proposed protocol. Then, in order to determine the control parameters, an algorithm with four steps is presented, where feasible conditions for the followers to accomplish the expected time-varying formation tracking are provided. Furthermore, based on the Lyapunov-like analysis theory, it is proved that the formation tracking error can converge to zero asymptotically. Finally, the effectiveness of the theoretical results is verified by simulation examples.

Discrete-time consensus strategy for a class of high-order linear multiagent systems under stochastic communication topologies

Achieving consensus in a class of high-order discrete-time multiagent systems is studied. It is supposed that the network topology is dynamic and the existence of a communication link between each two agents is stochastic. Based on the concept of discrete-time super-martingales, we propose a Lyapunov-based high-order protocol which guarantees achieving almost sure consensus in the network in the presence of some conditions. The main contribution of the paper compared with existing results for consensus control of high-order multiagent systems under stochastic networks is that the proposed consensus protocol in this paper requires no knowledge on the set of feasible topologies (topologies with nonzero probabilities), and can be designed without computing the eigenvalues of the coupling matrices associated with the feasible topologies. In this condition, the computational costs of the consensus protocol design will be decreased significantly. The results are validated via a numerical example.

Stochastic averaging approach to leader-following consensus of linear multi-agent systems

Recently, consensus of high-order linear multi-agent systems (MAS) has received much attention by many researchers, putting emphasis mainly on dealing with fixed network topology, with relatively few attention on the case of switching topology. The averaging method proposed in Ni et al. (2012, 2013) [26,27] was shown to be a powerful tool to investigate consensus problem of deterministic switching high-order MAS. This paper aims at extending the deterministic averaging method to the stochastic case which includes communication white noises and Markovian switching network topology, where the commonly used assumptions in existing literature on the decreasing gain and the balance of the underlying graph were abandoned. The stochastic averaging based method can tackle the challenge problem of investigating the joint effect of the stochastic network topology, the high-order dynamics of the agents and the noisy communication among agents on the consensus. Extension to observer-based leader-following consensus is also explored and stochastic version of separation principle is 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.

Consensus of High-Order Linear Multiagent Systems with Multitype Switching Topologies Based on the Dynamic Dwell Time Approach

This paper investigates the consensus problem of high-order continuous-time linear multiagent systems (LMASs) with multitype switching topologies which include both consensusable and unconsensusable communication topologies. A linear transformation is introduced, which equivalently transforms the consensus problem into the stability problem of a corresponding switched system, along with a necessary and sufficient condition to analyze the consensus problem. This paper is aimed at studying the impact of a switching rule on communication topologies for consensus of LMASs. Based on the dynamic dwell time method, a sufficient condition is derived for consensus of LMASs. It is shown that, with switching signals that satisfy this switching rule, LMASs can achieve consensus under directed switching communication topologies. A numerical example is provided to illustrate the effectiveness of the theoretical results.

Consensus of delayed multi‐agent systems by reduced‐order observer‐based truncated predictor feedback protocols

For high-order linear multi-agent systems with large input and communication delays, a predictor feedback approach is established to design reduced-order observer-based output feedback protocols. This approach can compensate arbitrarily large delays but will lead to infinite dimensional protocols. Under the assumption that the open-loop dynamics is at most polynomially unstable, the proposed predictor feedback protocols is truncated by removing the distributed terms, resulting in a finite dimensional reduced-order observer-based output feedback protocols, which will be referred to as truncated predictor feedback (TPF) protocols. Compared with the predictor feedback protocols, the main advantage of the TPF protocols is that it is very easy to implement. Two numerical examples are worked out to demonstrate the effectiveness of the proposed approaches.

Partial Stability Approach to Consensus Problem of Linear Multi-agent Systems

A linear transformation is proposed to deal with the consensus problem of high-order linear multi-agent systems (LMASs). In virtue of the linear transformation, the consensus problem is equivalently translated into a partial stability problem. We discuss three issues of the LMASs under a generalized linear protocol: 1) to find criteria of consensus convergence; 2) to calculate consensus function; 3) to design gain matrices in the linear consensus protocol. Precisely, we provide a necessary and sufficient criterion of consensus convergence in terms of Hurwitz stability of a matrix and give an analytical expression of the consensus function. In addition, we set up a relation between the gain matrices in the protocol and the convergence time and consensus accuracy of the agents, and then design the gain matrices with respect to a pre-specified convergence time and a required consensus accuracy.

Consensus of output-coupled high-order linear multi-agent systems under deterministic and Markovian switching networks

Consensus problem for high-order multi-agent systems is considered under deterministic and Markovian switching topologies. Only relative output information of agents is assumed to be available through the networks. First, a necessary and sufficient condition for achieving a consensus under a fixed communication network is presented. Based on this result and the stability of switched systems, a high-order multi-agent system with the proposed low-gain controller is shown to reach a consensus under deterministic switching network if the total time when the network is disconnected is, in some senses, smaller than the total time of the network being connected. Furthermore, the conditions sufficient for a high-order multi-agent system to reach an almost sure and mean-square consensus, under Markovian switching networks, are presented. Finally, illustrative examples are given to demonstrate the results.

Swarm stability for high-order linear time-invariant singular multi-agent systems

Swarm-stability and swarm-stabilisation problems for high-order linear time-invariant singular multi-agent systems with directed networks are investigated. First, necessary and sufficient conditions for swarm stability and asymptotic swarm stability are proposed, which are independent of the dimensions of Jordan blocks of the Laplacian matrix of the interaction topology. Then, an approach is given to determine the absolute motion as a whole, and it is shown that the absolute motion is completely determined by initial states if the interaction topology is balanced. Furthermore, an approach is presented to determine gain matrices for asymptotic swarm stabilisation. Moreover, leader-following swarm-stability and swarm-stabilisation problems are investigated. Finally, numerical examples are given to demonstrate theoretical results.

State Consensus Analysis and Design for High-Order Discrete-Time Linear Multiagent Systems

The paper deals with the state consensus problem of high-order discrete-time linear multiagent systems (DLMASs) with fixed information topologies. We consider three aspects of the consensus analysis and design problem: (1) the convergence criteria of global state consensus, (2) the calculation of the state consensus function, and (3) the determination of the weighted matrix and the feedback gain matrix in the consensus protocol. We solve the consensus problem by proposing a linear transformation to translate it into a partial stability problem. Based on the approach, we obtain necessary and sufficient criteria in terms of Schur stability of matrices and present an analytical expression of the state consensus function. We also propose a design process to determine the feedback gain matrix in the consensus protocol. Finally, we extend the state consensus to the formation control. The results are explained by several numerical examples.

Consensusabilization for Continuous-Time High-Order Multiagent Systems with Time-Varying Delays

For the consensus problems of high-order linear multiagent systems with time-varying delays in directed topologies, the LMI based-consensus criterion and NLMI-based consensusabilization (protocol parameters design that makes the multiagent systems achieve consensus) are investigated. Improved Lyapunov-Krasovskii functional is used for establishing the consensus convergence criteria and deriving the corresponding consensus protocol. In order to reduce the conservativeness, some proper free-weighting matrices are added into the derivative of Lyapunov-Krasovskii functional and that only keeps one necessary zoom. The numerical and simulation examples are given to demonstrate the effectiveness of the theoretical results. Compared with existing literatures, the convergence criterion and protocol design proposed have lower conservativeness.