Time-varying formation for linear multi-agent systems based on sampled data with multiple leaders

Adaptive Bipartite Fixed-Time Time-Varying Output Formation-Containment Tracking of Heterogeneous Linear Multiagent Systems

This study investigates the bipartite fixed-time time-varying output formation-containment tracking issue for heterogeneous linear multiagent systems with multiple leaders. Both cooperative communication and antagonistic communication between neighbor agents are taken into account. First, the bipartite fixed-time compensator is put forward to estimate the convex hull of leaders' states. Different from the existing techniques, the proposed compensator has the following three highlights: 1) it is continuous without involving the sign function, and thus, the chattering phenomenon can be avoided; 2) its estimation can be achieved within a fixed time; and 3) the communication between neighbors can not only be cooperative but also be antagonistic. Note that the proposed compensator is dependent on the global information of network topology. To deal with this issue, the fully distributed adaptive bipartite fixed-time compensator is further proposed. It can estimate not only the convex hull of leaders' states but also the leaders' system matrices. Based on the proposed compensators, the distributed controllers are then developed such that the bipartite time-varying output formation-containment tracking can be achieved within a fixed time. Finally, two examples are given to illustrate the feasibility of the main theoretical findings.

Hybrid Event-Triggered and Impulsive Control Strategy for Multiagent Systems With Switching Topologies

This article investigates the hybrid event-triggered and impulsive consensus problems for leaderless and leader-following multiagent systems (MASs) with switching topologies. Based on the state information of neighboring agents at event-triggered moments and impulsive instants, a hybrid event-triggered and impulsive control strategy (HETICS) is designed to reduce the communication frequency between neighboring agents and to ensure consensus of leaderless and leader-following MASs. By utilizing the Lyapunov direct method, some consensus criteria are obtained for leaderless and leader-following MASs with switching topologies. It is shown that the HETICS excludes the Zeno behavior. Several numerical examples and simulations are given to illustrate the effectiveness of the proposed consensus strategy and a comparison with previous consensus control methods is given.

Consensus of Second-Order Hybrid Multiagent Systems by Event-Triggered Strategy

In this article, an event-triggered method is proposed to solve the consensus of the second-order hybrid multiagent systems (MASs), which contain discrete-time and continuous-time individuals. First, we give a selection criteria of the coupling gains, the eigenvalues of communication topology, and the event-triggered sampling interval to guarantee the hybrid consensus, which have an impact on system stability, due to the interaction and co-existence of discrete-time and continuous-time individuals. Second, the hybrid second-order consensus under the event-triggered strategy is proven, where the agents communicate with their neighbors and update their controllers only at the triggered instants. Finally, we give some simulation examples to prove the validity of the main results.

Semiglobal Observer-Based Non-Negative Edge Consensus of Networked Systems With Actuator Saturation

The observer-based edge-consensus problem of networked continuous-time dynamical systems with edge state non-negative constraint and actuator saturation is considered in this paper. Based on line graph theory, low-gain output-feedback technique and algebraic Riccati equation (ARE)-based method, two edge-consensus algorithms are designed to achieve the observer-based edge consensus, in which the specific mathematical expressions of the two algorithms are obtained. Meanwhile, sufficient conditions are obtained to meet the bounded inputs and the non-negative edge states by combining with the ARE-based low-gain output-feedback technique and the positive system theory. Moreover, the feedback-gain and observer-gain matrices which must meet the sufficient conditions at the same time are existed and easy to obtain. Finally, two simulation cases are introduced to show the effectiveness of the theoretical results.

An iterative Q-learning based global consensus of discrete-time saturated multi-agent systems

This paper addresses the consensus problem of discrete-time multiagent systems (DTMASs), which are subject to input saturation and lack of the information of agent dynamics. In the previous works, the DTMASs with input saturation can achieve semiglobal consensus by utilizing the low gain feedback (LGF) method, but computing the LGF matrices by solving the modified algebraic Riccati equation requires the knowledge of agent dynamics. In this paper, motivated by the reinforcement learning method, we propose a model-free Q-learning algorithm to obtain the LGF matrices for the DTMASs achieving global consensus. Firstly, we define a Q-learning function and deduce a Q-learning Bellman equation, whose solution can work out the LGF matrix. Then, we develop an iterative Q-learning algorithm to obtain the LGF matrix without the requirement of the knowledge about agent dynamics. Moreover, the DTMASs can achieve global consensus. Lastly, some simulation results are proposed to validate the effectiveness of the Q-learning algorithm and show the effect on the rate of convergence from the initial states of agents and the input saturation limit.

Controllability of heterogeneous multiagent systems with two-time-scale feature

In this paper, we investigate the controllability problems for heterogeneous multiagent systems (MASs) with two-time-scale feature under fixed topology. Firstly, the heterogeneous two-time-scale MASs are modeled by singular perturbation system with a singular perturbation parameter, which distinguishes fast and slow subsystems evolving on two different time scales. Due to the ill-posedness problems caused by the singular perturbation parameter, we analyze the two-time-scale MASs via the singular perturbation method, instead of the general methods. Then, we split the heterogeneous two-time-scale MASs into slow and fast subsystems to eliminate the singular perturbation parameter. Subsequently, according to the matrix theory and the graph theory, we propose some necessary/sufficient criteria for the controllability of the heterogeneous two-time-scale MASs. Lastly, we give some simulation and numerical examples to demonstrate the effectiveness of the proposed theoretical results.