Consensus and performance optimisation of multi‐agent systems with position‐only information via impulsive control

Abstract

In this study, the consensus problem of second-order multi-agent systems (MAS) with position-only information is studied. Allowable sampling period for which second-order consensus can be achieved is obtained with two impulsive consensus algorithms. It is shown that if there is at least one eigenvalue of the Laplcian matrix with a non-zero imaginary part, consensus cannot be achieved for sufficiently small or large impulsive periods for both algorithms. Furthermore, the convergence performance of the MAS is optimised. Convergence speed, asymptotical decay factor and per-step decay factor of the error energy are utilised to investigate the convergence performance, and the relationship among impulsive period, topology structure and convergence performance is derived. Finally, numerical examples are given to validate our theoretical results.

Multisynchronization for Coupled Multistable Fractional-Order Neural Networks via Impulsive Control

“…It is found that impulsive control is very effective in a wide variety of applications for performance improvement of control process [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Ayati and Khaloozadeh [19] study the adaptive impulsive control to design an observer for nonlinear continuous systems.…”

“…Chen et al [21] show that complex networks can synchronize under the impulsive control policy. It is also demonstrated that second-order consensus can be achieved via impulsive control algorithms [23]. In [24], impulsive control scheme is utilized to improve the performance of differential evolution.…”

Impulsive consensus of multi-agent nonlinear systems with control gain error

“…Compared with these continuous control methods, impulsive control is an efficient method to deal with the dynamical systems which cannot be controlled by continuous control methods [21][22][23][24][25]. In addition, in consensus processes, one node receives the information from its neighbor nodes only at the discrete time instants, which dramatically reduces the amount of synchronization information transmitted between the nodes of multi-agent systems and makes the method more efficient in a large number of real-life applications [26][27][28][29][30][31]. In the literatures dealing with the impulsive consensus problem, several important topics have been addressed, including impulsive consensus with communication delay [32][33][34], some investigations about average consensus [35,36], networks with switching topology [37], etc.…”

Robust regional eigenvalue‐clustering analysis for grey discrete‐time systems with/without state delay

“…However, an unresolved issue is that, to achieve robust and consistent performance, the eigenvalues of a dynamic system must remain within a specified region. Therefore the robust eigenvalue-clustering problem in linear systems has been studied intensively by many researchers [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Eigenvalueclustering or pole-clustering in a specified circular region of a grey discrete-time system was also studied by Liu [23] by applying an approach developed earlier by Chou [9].…”

“…Theorem 2: all eigenvalues for the grey discrete-time system with state delay in (1) are located within a specified region D, if all eigenvalues of the discrete-time system x(k + 1) = Ax(k) are located within a specified region D, and if the following inequality is satisfied r[|(qI − A) −1 |(|M | + |q −l |(|B| + |N |))] < 1 (22) where q ∈ Q and Q denotes the boundary of the specified region D.…”