This paper studies the discrete-time linear-quadratic optimal control problem (LQOCP) for time-delayed descriptor systems in a real Hilbert space, and obtains some novel sufficient conditions for the solvability of the discrete-time LQOCP by the generalized inverse theory and space decomposition technique. Especially, the proposed methods are simpler, easier to verify and compute, and can solve the LQOCP without imposing any range inclusion condition. In addition, our work is verified by some numerical examples.

This paper studies the group consensus problem of second-order multi-agent systems (MASs) with switching communication topology. Unlike most existing papers concerning the consensus issue of MASs under arbitrary switching topology or Markovian switching topology, our paper tries to design a switching signal such that MAS can achieve group consensus under a designed switching signal set. First, using a state transformation method, the group consensus problem of MASs can be equivalently transformed into the asymptotical stability of a corresponding switched system. Then, two sufficient criteria are established by using Lyapunov function method and average dwell time (ADT) approach, where the minimum ADT [Formula: see text] is given clearly. Finally, simulation examples are given to show the effectiveness of our theoretical analysis.

Generally speaking, the complete controllability of multi-agent systems refers to transferring the remaining agents of such system from any arbitrary initial state to any final state by controlling dynamics of a small amount of agents under exchanged information between each other, which makes the system reflect the effect of a whole, that is the complete controllability. Comparing with the complete controllability of multi-agent systems, in reality, it may not be necessary to actuate all agents to the desired configuration. This paper concentrates on the partial controllability problems of discrete-time multi-agent systems with a leader and time-delay on the fixed topology, gives the general definition of the partial controllability, establishes partial controllability criteria. Numerical example and simulations are proposed to illustrate the theoretical results.

This paper investigates the asynchronous consensus of second-order multi-agent systems with directed networks and measurement time-delays via impulsive control. It is assumed that each agent receives the measurements of the information from its neighboring agents and itself according to its own sampling clock, and different agents can have independent sampling times. The controller of agent is designed in impulsive framework and changes agent’s state instantaneously. By transforming the consensus problem into static consensus and using common Lyapunov function, it is proved that there exist protocol parameters ensuring consensus. Also, the design of the parameters is given in a specific form. Finally, simulation examples are drawn to illustrate the effectiveness of the theoretical results.

This paper studies the group consensus tracking issues of discrete time second-order multi-agent systems (MASs) with directed fixed and Markovian switching topologies, respectively. For MASs with m leaders, we first introduce a method to divide the whole MASs into m subgroups. Based on the subgroup-divided method, the condensation directed graph G of the communication topology of the whole MASs becomes a directed acyclic graph (DAG). Then, for MASs with fixed/Markovian switching topology, some sufficient/necessary and sufficient group consensus tracking criteria are established. Finally, simulation examples are given to illustrate the effectiveness of our results.

This study involves an examination of the dynamic consensus problem for networks of double-integrator agents with aperiodic impulsive protocol and fixed topology. With respect to each agent, the control law is designed based on relative state measurements (i.e. position and velocity) between the agent and the neighbouring agents at a few discrete times. Additionally, these state measurements can include time-varying measurement delays. The theory of impulsive differential equations is used to prove that the dynamic consensus can be achieved under the condition of a graph with a spanning tree and to provide the consensus state finally reached by all agents. Furthermore, the study establishes algebraic inequalities that should be satisfied by the control gains, the bounds of impulsive interval lengths, and the upper bound of delays. Two numerical examples are illustrated to validate the main results.

Generally speaking, controllability of multi-agent systems refer to transferring the remaining agents of such system from any arbitrary initial state to any final state by controlling dynamics of a small amount of agents under exchanged information between each other, which makes the system reflect the effect of a whole, that is the complete controllability. Comparing with the complete controllability of the general multi-agent systems, in reality, it may not be necessary to actuate all nodes to the desired configuration. This paper addresses the partial controllability of the discrete-time multi-agent system with a leader under fixed topology, proposes the concept of controllable node group. Some necessary and sufficient conditions are given for partial controllability of the discrete-time multi-agent system with a single leader. Moreover, the partial controllability criteria of some special cases are given. Finally, an numerical example and simulations are given to illustrate the correctness of the theoretical results.

The complete controllability of multi-agent systems are mainly focused on the whole system referring to transferring the remaining agents of such system from any arbitrary initial state to any final state by controlling dynamics of a small amount of agents under exchanged information between each other, which makes the system reflect the effect of a whole. However, in practice, it may not be necessary to ensure all nodes be controllable. This paper mainly investigates the partial controllability of multi-agent systems under undirected fixed topology. The concept of partial controllability is proposed and some sufficient and necessary conditions are proposed for the partial controllability of continuous-time multi-agent systems with multiple leaders. Numerical example and simulations are presented to illustrate the theoretical results.

This paper studies the consensus problem of second-order multi-agent systems with constant time-delay, fixed topology and impulsive algorithm based on periodic sampling. First, by theory of impulsive differential equations, it is proved that the consensus is achieved if and only if some matrix has a simple 1 eigenvalue and all the other eigenvalues are in the unit circle. Meanwhile, the consensus state of the system is obtained, which indicates that the positions and the velocities of all agents reach, respectively, a constant state and zero. Hence we say a static consensus is achieved for multiple second-order agents. Then, by stability of polynomials, we establish a necessary and sufficient condition from the perspective of topology and protocol parameters, which provides the range of allowable time-delay and the choice of impulse period. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results.

This paper considers the group consensus problem for a class of discrete-time heterogeneous multi-agent systems composed of first-order and second-order agents with directed topology. The discrete-time heterogenous multi-agent systems reaching group consensus is proved and the convergent points of such system are found. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Controllability is a fundamental issue concerning control of multi-agent networks and a very important research topic in the modeling, analysis and coordination control of multi-agent systems. Group controllability problem is a further extension of the controllability problem of the general multi-agent systems, which mainly studies the cooperation and control of multi-agent systems with multiple sub-groups or multiple intelligence clusters. Comparing with the controllability of the general multi-agent systems, the group controllability is not only to consider the information interaction among the groups, but also to consider the information interaction between different groups, which makes the system reflect the effect of a whole and also the internal structure of the sub-groups. This paper addresses the group controllability problems of discrete-time multi-agent systems with time-delay, in which both switching topology and fixed topology are considered. This paper also proposes the general definition of the group controllability, as well as establishes group controllability criteria from the algebraic and graphical perspectives. Numerical examples and simulations are proposed to illustrate the theoretical results.

Consensus problem for a group of double-integrator agents is investigated, under impulsive protocol and communication time-delays. For each agent, the relative information of position and the one of velocity are utilized for the control input. These information are both suffered communication time-delays caused by transmission on networks. We employ state transformation to build equivalent condition of consensus solving, that is protocol parameters, impulsive period, and time-delay satisfy some algebraic inequalities, and topology owns spanning tree. The consensus state where all the agents reach finally is also provided. Simulations on directed topology and undirected topology are worked out.

This paper focuses on the consensus problem for second-order multi-agent systems with impulsive algorithm and communication time-delays. By introducing a state transformation, the consensus of the system is translated into the asymptotical stability of a reduced-order discrete-time system. Based on the properties of Laplacian matrix of graphs and a given invertible matrix, necessary and sufficient conditions are established for the consensus convergence in the cases of directed and undirected topologies. Two numerical simulations are worked out to illustrate the effectiveness of the theoretical results.

This paper focuses on the consensus problem for high-order multiagent systems (MAS) with directed network and asymmetric time-varying time-delays. It is proved that the high-order multiagent system can reach consensus when the network topology contains a spanning tree and time-delay is bounded. The main contribution of this paper is that a Lyapunov-like design framework for the explicit selection of protocol parameters is provided. The Lyapunov-like design guarantees the robust consensus of the high-order multiagent system with respect to asymmetric time-delays and is independent of the exact knowledge of the topology when the communication linkages among agents are undirected and connected.

This paper focuses on the consensus problem for high-order multi-agent systems (MAS) with directed interactions and asymmetric time-varying communication delays. By introducing an orthogonal linear transformation, we prove that the consensus of such MAS is achieved if and only if each solution of an equivalent reduced-order system converges to zero. Based on this nature and Lyapunov-Krasovskii functional approach, we then establish several sufficient convergence conditions which are characterized by linear matrix inequalities. Furthermore, we give a Lyapunov-like design for the explicit selection of protocol parameters, which is robust to asymmetric time-varying delays and fixed or switching directed topologies. Also, we show that the solutions of these linear matrix inequalities always exist under the assumptions on network topology and protocol parameters. As application, we construct a state-feedback controller for the consensus of MAS with agent modeled by a completely controllable single-input linear time-invariant system.

This paper studies the consensus problems for a group of agents with switching topology and time-varying communication delays, where the dynamics of agents is modeled as a high-order integrator. A linear distributed consensus protocol is proposed, which only depends on the agent’s own information and its neighbors’ partial information. By introducing a decomposition of the state vector and performing a state space transformation, the closed-loop dynamics of the multi-agent system is converted into two decoupled subsystems. Based on the decoupled subsystems, some sufficient conditions for the convergence to consensus are established, which provide the upper bounds on the admissible communication delays. Also, the explicit expression of the consensus state is derived. Moreover, the results on the consensus seeking of the group of high-order agents have been extended to a network of agents with dynamics modeled as a completely controllable linear time-invariant system. It is proved that the convergence to consensus of this network is equivalent to that of the group of high-order agents. Finally, some numerical examples are given to demonstrate the effectiveness of the main results.

This paper focuses on the controllability of multi-agent systems with fixed topology based on agreement protocols. We analyze three models of agents: single integrator, double integrator and high-order integrator. For a group of single-integrator agents, controllability is studied in a unified framework for both networks with leader-following structure and networks with undirected graph. Some new necessary/sufficient conditions for controllability of networks of single-integrator agents are established. For networks of double-integrator agents, we prove that controllability of the networks is equivalent to that of networks of single-integrator agents under the same topology and same prescribed leaders. This result is further extended to the case of networks of high-order-integrator agents. Moreover, two influencing factors of controllability of networks are investigated, that is, the selection of leaders and the link weights of graphs.

This paper investigates the consensus problem for a group of high-order-integrator agents with fixed topology. A linear distributed consensus protocol is proposed, which only depends on the agent's own information and its neighbors' partial information. A necessary and sufficient condition for convergence to consensus is established. It is proved that the topology having a spanning tree is a necessary condition for convergence to consensus. Based on the consensus protocol for networks of high-order-integrator agents, a consensus controller is provided for a group of identical agents with dynamics described by a completely controllable single-input linear time-invariant (LTI) system. It is shown that the consensus of this kind of networks is equivalent to that of networks of high-order-integrator agents. Finally, the parameter design of the protocol is discussed.