Distributed finite‐time formation control of multiple Euler–Lagrange systems under directed graphs

Abstract

This paper investigates the finite‐time formation problem of multiple Euler–Lagrange systems subject to model uncertainties and external disturbances under directed graphs. An adaptive distributed control approach is developed by integrating dynamic gain control and adaptive control based on the consensus theory and the finite‐time stability theory. Auxiliary scalar dynamics are constructed to facilitate dynamic gain design. It is shown that finite‐time formation can be achieved via the proposed non‐smooth controller characterized by fractional powers of the auxiliary dynamics, which is significantly different from most existing works on finite‐time controllers where fractional powers of system states are adopted. Moreover, continuity of the proposed controller is guaranteed by adjusting one control parameter, of which range is proven explicitly. In addition, dynamic surface control is improved to remove acceleration information from finite‐time controller design. In the end, the effectiveness of the proposed control approach is verified by numerical simulation.

Resilient Formation Reconfiguration for Leader–Follower Multi-UAVs

“…The belief degree of each assessment grade in each rule is assigned based on empirical knowledge, as shown in Table 5. The antecedent attribute weight δ 11 f , f = 1, 2, and the rule weight θ 11 k , k = 1, . .…”

“…Formation control for multi-UAVs refers to the fact that a group of UAVs can form and maintain a specific geometry in order to collaboratively accomplish a series of goals and can adapt to changes in the external environment by adjusting the geometry [9][10][11]. In general, formation control can be divided into three phases: the initial formation phase, the formation maintenance phase, and the formation reconfiguration phase-the last phase has the most complexity and challenges.…”

“…. , P 11 , is the belief degree of the pth assessment grade D11 p in the kth rule. Here, one assumes that each belief rule of BRB 11 is complete, that is,…”

Robust adaptive finite‐time control design for the generation of stable oscillations in the strict‐feedback form non‐linear systems with input dead‐zone non‐linearity

“…Such advantages have led to receiving a great deal of attention during the past years. Some impressive and important research has been reported on the finite-time control of various classes of dynamical systems such as multi-agent systems, switch systems, time-delay systems, stochastic systems, MIMO systems, and systems with input nonlinearities [6][7][8][9][10]. These studies have led to the achievement of valuable results in the control of different dynamical systems.…”