Fault-tolerant finite-time dynamical consensus of double-integrator multi-agent systems with partial agents subject to synchronous self-sensing function failure

Abstract

This paper investigates fault-tolerant finite-time dynamical consensus problems of double-integrator multi-agent systems (MASs) with partial agents subject to synchronous self-sensing function failure (SSFF). A strategy of recovering the connectivity of network topology among normal agents based on multi-hop communication and a fault-tolerant finite-time dynamical consensus protocol with time-varying gains are proposed to resist synchronous SSFF. It is proved that double-integrator MASs with partial agents subject to synchronous SSFF using the proposed strategy of network topology connectivity recovery and fault-tolerant finite-time dynamical consensus protocol with the proper time-varying gains can achieve finite-time dynamical consensus. Numerical simulations are given to illustrate the effectiveness of the theoretical results.

Fixed-time group consensus of second-order multi-agent systems based on event-triggered control

“…Theorem 2 Under the control protocol (11) with σ 1 , σ 2 , σ 3 , σ 4 , σ 5 > 0, 0 < d < σ 3 , σ ≫ 1, and m ∈ (0, 1), n, r ∈ (1, ∞) are the ratio of positive odd numbers, if 0 < δ < σ 5 (1 − ι), where ι ∈ (0, 1), and assumptions 1 and 2 hold, then MAS (1) achieves fixed-time event-triggered group consensus, and the settling time T satisfies…”

“…Theorem 3 For MAS (1), if the condition in Theorem 2 holds, then no Zeno behavior occurs under the event-triggered controller (11) with the event-triggered function (13).…”

“…There is t j k+1 − t j k ≥ σ 5 ι ω > 0. Hence, there is no Zeno behavior under the event-triggered controller (11) with the eventtriggered function (13).…”

“…Remark 2 If design control protocols based on sign function as usual, when the state error of agents in the system tends to 0, it will cause the control input to oscillate. Therefore, softsign function is introduced to replace the sign function in the control protocol, and it turns out that no Zeno behavior exists under the designed event-triggered controller (11) with the event-triggered function ( 13), which will be further illustrated in simulation examples.…”

“…In recent years, much attention was paid to the consensus problem for the first-order multi-agent system (MAS). [6][7][8] Compared with the first-order MAS, problems considered in second-order MASs [9][10][11][12][13] are more complex. In Ref.…”