Fixed-time flocking formation of nonlinear multi-agent system with uncertain state perturbation

Hierarchical predefined‐time bipartite tracking of Euler–Lagrange systems over a signed graph

“…Algorithm Characteristic This manuscript Estimation of the tracking errors More convenient for the design of controller and reduce the problem. Reference [8,30] Estimation for the leader's states Traditional and complex for the calculation.…”

“…where θi = 𝜃 i − e i , ζi = 𝜁 i − ̇ei , Equations ( 5) correspond to the local control algorithm and Equations (8) show the distributed estimator layer, the parameters of the local control layer are selected as…”

“…Additionally, distributed cooperative control has captured wide attention, owing to its notable advantages such as better feasibility, stronger robustness, and reduced resource consumption [5,6], and so on. It follows the extensive employment of distributed algorithms in applications involving consensus control [7], flocking [8], and formation [9]. Consensus tracking control, as discussed in Han et al [10], is widely acknowledged as a critical and prominent subject in the field of cooperative control for MASs.…”

“…Please see Table 1 and Table 2 for details. • Different from the traditional observer [8,30], it is the tracking errors between followers and leader that is estimated in this paper, which let the tracking problem reduce to stability problem after the distributed estimator layer.…”

“…A hierarchical predefined‐time control (HPTC) algorithm is proposed and offers three main contributions, which are as follows: To effectively tackle predefined‐time tracking problem of ELSs with bipartite interactions, outer disturbance and dynamic uncertainties, a HPTC algorithm with novel nonsingular terminal sliding mode is employed. In comparison to the finite‐ and fixed‐time control algorithms [19, 26] described before, the proposed HPTC framework provides the possibility of explicitly designing convergence time's upper bound of settling time as a specific control parameter within the algorithm. Please see Table 1 and Table 2 for details. Different from the traditional observer [8, 30], it is the tracking errors between followers and leader that is estimated in this paper, which let the tracking problem reduce to stability problem after the distributed estimator layer. …”