Leader‐following consensus of fractional‐order multi‐agent systems via adaptive control

Abstract

Summary This article focuses on the consensus problem of leader‐following fractional‐order multi‐agent systems (MASs) with general linear and Lipschitz nonlinear dynamics. First, the distributed adaptive protocols for linear and nonlinear fractional‐order MASs are constructed, respectively. We allow the control coupling gains to be time varying for each agent. Moreover, the adaptive modification schemes for the control gain are designed, which renders smaller control gains and thus requires smaller amplitude on the control input without sacrificing consensus convergence. Second, based on fractional‐order Lyapunov stability theorem and Barbalat's lemma, two novel sufficient conditions in terms of linear matrix inequalities are provided to ensure that the leader‐following consensus can be obtained in the case for any undirected connected communication graph. Furthermore, we show that the proposed algorithm also works for consensus of agents with intrinsic Lipschitz nonlinear dynamics. As a result, the proposed framework requires no global information and thus can be implemented in a fully distributed manner. Finally, the numerical simulations are given to demonstrate the effectiveness of obtained the theoretical results.

Torsional Vibration Analysis of Shaft in an Induced Draft Fan Due to Variable Frequency Drive

“…In the case of small disturbance, the ESA method is used to determine the stability of the system by obtaining the eigenvalues of the coefficient matrix after linearizing the system. This is based on second Lyapunov stability theorem [17][18].…”

“…16. After the elastic strength of the shaft increases, it can be seen from equation (18) that the NTF increases, and the resonance region is narrowed and shifts to the right. Nonetheless, the resonance region exists, and it is still possible to operate in the resonance region under the condition of wide-range speed regulation.…”

Distributed cooperative fault detection and isolation for uncertain multi‐agent systems based on zonotope theory

“…In recent years, the researches on MASs have received much attention. [14][15][16][17][18][19][20][21] It is worth pointing out that, for a MAS, any trivial fault may cause serious consequences, because the fault appearing in any single agent will be transmitted to the whole system through the connection point of the communication topology, resulting in negative effect on every agent. For this reason, FDI designs for MASs are crucial and significant tasks in order to guarantee the MASs working normally.…”

“…With the development of industry, MASs have been widely applied in various sectors and critical areas, such as flexible manufacturing, 8,9 traffic control, 10,11 sensor networks, 12,13 and so on. In recent years, the researches on MASs have received much attention 14‐21 . It is worth pointing out that, for a MAS, any trivial fault may cause serious consequences, because the fault appearing in any single agent will be transmitted to the whole system through the connection point of the communication topology, resulting in negative effect on every agent.…”

Consensus of nonlinear multi–agent systems with distributed event–triggered impulsive control

“…A large number of consensus control schemes for MASs have been proposed, such as robust control (Gong and Lan, 2018;Xue et al, 2019), distributed optimal control (Tao et al, 2018;Ma et al, 2019aMa et al, , 2019b, and adaptive control (Ji et al, 2020;Gao et al, 2018). Note that these control methods are all continuous, which result in information transaction wastage and low efficiency.…”