Guangbin Liu

Guaranteed-Cost Consensus for Singular Multi-Agent Systems With Switching Topologies

Guaranteed-cost consensus problems for high-order singular multi-agent systems with switching topologies are investigated. Firstly, to achieve a trade-off design object between consensus regulation performances and control energy consumptions, a quadratic cost function is constructed by state errors among agents and control inputs of all agents and guaranteed-cost consensus problems are introduced. Then, based on linear matrix inequality techniques, sufficient conditions for guaranteed-cost consensus and consensualization are presented respectively, which can guarantee the scalability of singular multi-agent systems since the dimensions of all the variables in these conditions are independent of the number of agents. Moreover, an upper bound of the cost function is determined, explicit expressions of consensus functions are given on the basis of the Second Equivalent Form, and it is shown that consensus functions are dependent on the average of initial states of all agents but are independent of switching topologies. Finally, the applications of theoretical results in multi-agent supporting systems are shown.

Leader–follower guaranteed-cost consensualization for high-order linear swarm systems with switching topologies

Abstract Leader–follower guaranteed-cost consensus analysis and design problems for high-order linear time-variant swarm systems with switching topologies are investigated, where two types of switching topologies are considered; that is, each interaction topology in the switching set has a spanning tree, and the union of a series of interaction topologies in a certain time interval has a spanning tree, which is referred to a joint spanning tree. Firstly, the leader–follower guaranteed-cost consensus problem is introduced, which means that all the followers in a swarm system can track the state of the leader and some performance index should be satisfied simultaneously; that is, leader–follower consensus is achieved in a suboptimal manner. Secondly, by the state decomposition, a necessary and sufficient condition for leader–follower consensus is proposed, which only transforms leader–follower consensus problems into asymptotic stability ones but cannot be directly used to determine whether or not swarm systems can achieve leader–follower consensus. Furthermore, in terms of linear matrix inequalities, sufficient conditions of leader–follower guaranteed-cost consensualization for swarm systems with a spanning tree and a joint spanning tree are presented respectively. Finally, two numerical examples are given to demonstrate theoretical 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.

Guaranteed cost consensus for multi-agent systems with time delays

Abstract Guaranteed cost consensus problems for multi-agent systems with time delays are considered. The idea of guaranteed cost control is introduced into consensus problems for multi-agent systems with time delays, where a guaranteed cost function is proposed to simultaneously consider the consensus regulation performance and the energy consumption. For fixed topologies and switching topologies, some sufficient conditions for guaranteed cost consensus are given respectively by the state space decomposition approach and the Lyapunov method. Moreover, an upper bound of the guaranteed cost function and the consensus value are determined respectively for the two cases. Numerical simulations are presented to demonstrate the effectiveness of theoretical results.

Hybrid consensus for swarm systems with discrete-time communication: Time delay approach

Hybrid consensus problems among a group of continuous-time high-order agents with directed communication topology are investigated by a time delay approach, where each agent obtains the communication information from its neighboring agents only at discrete-time instants. Firstly, based on both the continuous-time state information of each agent and the discrete-time communication information with time-varying sampling interval of its neighboring agents, a hybrid discrete/continuous consensus protocol is designed. Secondly, hybrid consensus problems are transformed into simultaneous stabilization problems of multiple sampled control subsystems with low dimensions by the state space decomposition approach. Thirdly, by using the time delay approach and linear matrix inequality (LMI) theory, sufficient conditions for hybrid consensus and consensualization are presented, where four LMI constraints are only included. It should be pointed out that the hybrid consensus for high-order swarm systems depends on the gain matrices, the spectra property of the Laplacian matrix, and the maximum sampling interval. Moreover, the consensus function is determined when swarm systems achieve hybrid consensus. Finally, numerical examples are given to illustrate the effectiveness of the theoretical results.