Descriptor Multi-agent Systems Research Articles

Design of distributed observer-based controllers for bipartite containment of discrete-time descriptor MASs over signed digraphs

In this article, the bipartite containment control problem is considered for discrete-time linear descriptor multi-agent systems (DMASs) with multiple dynamic leaders under fixed signed digraph topology, in which each leader can be autonomous or evolving dynamically via communicating with other leaders in its neighbourhood. Based upon the properties of the solutions to discrete-time modified generalised algebraic Riccati equations(MGAREs), three different types of distributed observer-based protocols utilising only available local information are devised. Algorithms for constructing the devised protocols are also presented. Moreover, sufficient conditions ensuring the bipartite containment of the DMASs are established. Finally, the effectiveness of the presented protocols is validated by numerical simulations.

Output containment control for heterogeneous discrete-time linear descriptor multi-agent systems by a feedforward output regulation approach

This paper studies the cooperative output containment control of the heterogeneous linear discrete-time descriptor multi-agent systems based on the output regulation theory. First, the output containment control problem is transformed into a standard cooperative output regulation problem. Second, since only a portion of the followers can directly obtain the information of the leaders, a new distributed observer is designed for each follower to estimate the combinations of the leaders’ states by using the local state containment errors. Third, two types of distributed control algorithms, as well as the corresponding sufficient conditions, are provided to ensure the achievement of the output containment control. Finally, numerical simulation results illustrate the validity of the proposed method.

Leader-Following Exponential Consensus of Fractional-Order Descriptor Multiagent Systems With Distributed Event-Triggered Strategy

In this article, the leader-following exponential consensus problem of fractional-order descriptor multiagent systems (FOD-MASs) with event-triggered control (ETC) protocol is investigated, which includes integer-order descriptor multiagent systems as the special case. Two classes of control schemes and the corresponding event-triggered conditions are presented, respectively. First, a distributed state feedback ETC protocol is developed to reach the leader-following exponential consensus. The leader-following exponential consensus is achieved in the sense of the Mittag-Leffler stability of fractional-order systems. Second, when full-state measurements are not available, a novel observer-type output feedback ETC strategy with some desirable characteristics is provided. For two distributed ETC protocols, consensus conditions are derived and convergence rate of the system can be adjusted. Also, the integral inequality is applied to get the fact that Zeno behavior is excluded, which verifies the feasibility of ETC schemes. Finally, the effectiveness of conclusions is demonstrated by the examples.

Admissible Consensus for Homogenous Descriptor Multiagent Systems

This paper addresses the admissible consensus problem for homogenous descriptor multiagent systems with undirected graphs and disturbances. First, to achieve the consensus objective and attenuate the effects of disturbances, the distributed controllers are formulated and the admissible consensus problems are formulated. Another improvement emphasizes that the proposed approach can simplify the complexity of the admissible consensus analysis by using the state transformation during the admissible analysis and disturbances suppression analysis. Moreover, based on Riccati inequalities and linear matrix inequalities, two necessary and sufficient conditions are presented to ensure the admissible consensus and disturbances suppression objectives. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed approaches.

Optimal output regulation for heterogeneous descriptor multi-agent systems

This paper studies the cooperative optimal output regulation problem for general heterogeneous descriptor multi-agent systems under a directed topology containing a spanning tree. First, a distributed observer is presented for each agent to estimate the state information of the exogenous system. Then, the optimal state feedback control and the optimal output feedback control based on a reduced-order normal observer are designed respectively to make the output of each agent track to the reference output and minimize given performance functions simultaneously. Under some standard assumptions and employing some appropriate coordinate transformations, it’s shown that both distributed protocols can solve the optimal output regulation problems, and the optimal feedback gains are obtained by solving a set of generalized Riccati equations. Finally, two numerical examples demonstrate the effectiveness of the proposed approach.

Bipartite containment of descriptor multi‐agent systems via an observer‐based approach

This study considers the bipartite containment problem for a class of descriptor multi-agent systems (MASs) under a structurally balanced graph. A new bipartite containment control protocol acting on each follower is proposed on the basis of designing a singular observer, where relative output information is utilised. By employing the stability theory of descriptor systems and multiple Lyapunov function technique, some sufficient criteria are derived to guarantee observer-based bipartite containment of descriptor MASs. The feasibility of obtained theoretical results is finally verified via performing simulations.

Consensus conditions for higher-order descriptor multi-agent systems with communication time-delays

In this paper, the consensus problem for higher-order descriptor multi-agent systems (DMASs) with time-delays is investigated. Firstly, a distributed consensus protocol based on output feedback is proposed. Secondly, the state transformation is presented to convert the consensus problem into the stability problem. Based on the Lyapunov theory and the linear matrix inequality (LMI) method, sufficient conditions in terms of LMIs are derived to ensure that consensus of DMASs can be achieved. Moreover, the consensus problem for higher-order DMASs with delays is solved under two cases where interaction topologies are undirected and directed, which is more complicated and challenging. Finally, numerical simulations are provided to demonstrate the effectiveness of our results.

Limited-Budget Output Consensus for Descriptor Multiagent Systems With Energy Constraints.

This article deals with limited-budget output consensus for descriptor multiagent systems with two types of switching communication topologies, that is, switching connected ones and jointly connected ones. First, a singular dynamic output feedback control protocol with switching communication topologies is proposed on the basis of the observable decomposition, where an energy constraint is involved and protocol states of neighboring agents are utilized to derive a new two-step design approach of gain matrices. Then, limited-budget output consensus problems are transformed into asymptotic stability ones and a valid candidate of the output consensus function is determined. Furthermore, sufficient conditions for limited-budget output consensus design and analysis for two types of switching communication topologies are proposed, respectively, and an explicit expression of the output consensus function is given, which is identical for two types of switching communication topologies. Finally, two numerical simulations are shown to demonstrate theoretical conclusions.

Bipartite Consensus for Descriptor Multiagent Systems With Antagonistic Interactions

This brief investigates the bipartite consensus problem for descriptor multi-agent systems under a communication graph with positive and negative weights links. Necessary and sufficient conditions are established for descriptor multi-agent systems to achieve admissible bipartite consensus, which are related to the interaction topology and the properties of each agent dynamics. To ensure admissible bipartite consensus and minimize a local performance index, an optimal distributed state feedback control is designed by adopting the linear quadratic regulator (LQR) optimal technique. Finally, simulation results illustrate the effectiveness of the proposed method.

Cooperative optimal control for descriptor multi-agent systems

Abstract This paper provides a theory analysis of cooperative optimal control problem for leader-follower descriptor multi-agent systems. Based on the linear quadratic regulator theory, the state feedback controller is designed to guarantee the consensus of multi-agent systems and minimize a local performance index, which is independent of the graph topology, the control gain matrix is obtained by solving a generalized Riccati equation. Because the local optimal protocol devised cannot guarantee the global optimality of the entire system, the inverse optimal control theory is applied to design distributed control protocols that ensure consensus and global optimality with respect to some global performance index. The defined performance index is related to the interaction topology, whose Laplacian matrix is constrained to be diagonalizable. Finally, two numerical examples and comparisons are supplied to verify the effectiveness of the theoretical results.

Admissible H∞ control of linear descriptor multi-agent systems with external disturbances

This paper is concerned with the admissible H∞ control problem for descriptor linear multi-agent systems with external disturbances. A distributed dynamical control strategy is developed based on the relative output measurements between agents and self feedbacks. The coupled descriptor network multi-agent systems are converted into N independent systems with the same dimension. In addition, admissible H∞ performance equivalence between the coupled systems and the isolated systems is proved. Furthermore, a sufficient condition for designing the admissible H∞ controller of the coupled systems is given. Overall, the contributions in this work are to extend the existing results on admissible H∞ control of normal linear multi-agent to descriptor linear multi-agent systems, and the results are only relate to the maximum and minimum eigenvalues of Laplacian matrix. Finally, effectiveness of the proposed method is verified through some simulation examples.

Admissible Consensus for Descriptor Multi-Agent Systems with Exogenous Disturbances.

In this paper, we study the admissible consensus for descriptor multi-agent systems (MASs) with exogenous disturbances that are generated by some linear systems. The topology among agents is represented by a directed graph. For solving the admissible consensus problem, the exogenous disturbance observer and distributed control protocol are proposed. With the help of the graph theory and the generalized Riccati equation, some conditions for admissible consensus of descriptor MASs with exogenous disturbances are obtained. Finally, we provide a numerical simulation to effectively illustrate the results we have reached before.

Cooperative optimal preview tracking for linear descriptor multi-agent systems

In this paper, a cooperative optimal preview tracking problem is considered for continuous-time descriptor multi-agent systems with a directed topology containing a spanning tree. By the acyclic assumption and state augmentation technique, it is shown that the cooperative tracking problem is equivalent to local optimal regulation problems of a set of low-dimensional descriptor augmented subsystems. To design distributed optimal preview controllers, restricted system equivalent (r.s.e.) and preview control theory are first exploited to obtain optimal preview controllers for reduced-order normal subsystems. Then, by using the invertibility of restricted equivalent relations, a constructive method for designing distributed controller is presented which also yields an explicit admissible solution for the generalized algebraic Riccati equation. Sufficient conditions for achieving global cooperative preview tracking are proposed proving that the distributed controllers are able to stabilize the descriptor augmented subsystems asymptotically. Finally, the validity of the theoretical results is illustrated via numerical simulation.

Admissible consensus for descriptor multi-agent systems via distributed observer-based protocols

In this paper, the admissible consensus problem of descriptor multi-agent systems via distributed observer-based protocols is considered. The dynamics of agents is modeled by the general form of continuous-time linear descriptor systems, and the interaction topology among the agents is modeled by a directed graph. It is assumed that the output information but not the state information of the agents is available. To achieve control objective, two types of state observers are adopted for the agents to estimate its states and the related state disagreements respectively, by which two different architectures of connecting observers and controllers are proposed. Based on the generalized Riccati equation and Lyapunov admissible theory, a sufficient admissible consensus condition is established for the descriptor multi-agent systems. The full-order and reduced-order observer-based consensus protocols can be unified in our proposed framework. Based on the special solutions of the established condition, some full-order and reduced-order observer-based consensus protocols can be obtained. Finally, a simple simulation example is provided to illustrate our established result.

Leader-following consensus for discrete-time descriptor multi-agent systems with observer-based protocols

In this paper, the leader-following consensus problem of discrete-time descriptor multi-agent systems is considered. Each agent’s dynamics is modelled by a discrete-time linear descriptor system, and the interaction topology among the agents is assumed to be directed. To solve the multi-agent consensus problem, three different architectures of connecting observers and controllers are used to construct the consensus protocols. A kind of modified generalized algebraic Riccati equation is provided to design the protocol’s gain matrices. Based on graph theory, matrix theory and the Lyapunov method, some sufficient convergence conditions are established to guarantee the descriptor multi-agent system achieves consensus. Finally, a simulation example is provided to illustrate the obtained results.

Distributed observer-based consensus protocol for descriptor multi-agent systems

In this paper, the consensus problem of descriptor multi-agent systems is considered. Each agent’s dynamics is given in the general form of a continuous-time linear descriptor system, and the communication topology among the agents is assumed to be directed in fixed topology case and balanced in switching topology case, respectively. Three kinds of distributed observer-based consensus protocols are proposed to solve the descriptor multi-agent consensus problem. Multi-step algorithms are provided to design the gain matrices and coupling constants involved in the protocols. The design approach is based on the generalized Riccati equation, and Lyapunov stability theory. Some sufficient consensus conditions are established to guarantee that the descriptor multi-agent system achieves consensus under the directed fixed topology and balanced switching topology. Furthermore, the state variable feedback consensus problem and the observer-based consensus problem with a desired decay rate are discussed. Finally, a simulation example is provided to illustrate the obtained results.

Admissible consensus for heterogeneous descriptor multi-agent systems

This paper focuses on the admissible consensus problem for heterogeneous descriptor multi-agent systems. Based on algebra, graph and descriptor system theory, the necessary and sufficient conditions are proposed for heterogeneous descriptor multi-agent systems achieving admissible consensus. The provided conditions depend on not only the structure properties of each agent dynamics but also the topologies within the descriptor multi-agent systems. Moreover, an algorithm is given to design the novel consensus protocol. A numerical example demonstrates the effectiveness of the proposed design approach.

Consensus of descriptor multi‐agent systems via dynamic compensators

This study deals with the consensus problem via dynamic output feedback (dynamic compensator) for descriptor (singular) multi-agent systems with fixed topologies and agents described by general linear systems. Only output information of each agent can be delivered from its neighbour agents. Based on graph, algebra and descriptor linear system theory, the necessary and sufficient conditions are proposed for the existence of dynamic compensators solving the considered problem. The given conditions depend on both the topologies within descriptor multi-agent systems and the structure properties of each agent dynamics. According to non-zero eigenvalues of the Laplacian matrix of the weighted digraph are the same or different, two consensus algorithms via dynamic compensators are proposed, respectively. The provided examples demonstrate the effectiveness of the proposed consensus algorithms.

Necessary and Sufficient Consensus Conditions of Descriptor Multi-agent Systems

For descriptor multi-agent systems with fixed topology and agents described by general descriptor linear time-invariant systems, necessary and sufficient conditions of consensusability with respect to a set of admissible consensus protocols are proposed using the tools of algebra, graph and descriptor linear system theory. The consensusability conditions depend on both the structure properties of each agent's dynamics and the topology within the descriptor multi-agent systems. Designing an output feedback control law can guarantee that the studied descriptor multi-agent system is consensusable with respect to a given admissible set. A provided example indicates the applicability of the proposed approach.