Fixed-time leader-following flocking and collision avoidance of multi-agent systems with unknown dynamics

Abstract

The fixed-time flocking of multi-agent systems with a virtual leader is investigated in this paper. The motion dynamics of the agents are assumed to be unknown and only satisfy the boundedness, which does not need to be modelled by the Lipschitz condition. To achieve the flocking and collision avoidance for all agents in the fixed time, a control protocol in the high-dimensional space is developed by using the graph theory and the theoretical properties of differential equations. Moreover, the upper bound of the settling time only depending on the control protocol and the topology of network is estimated. Numerical examples are used to verify the theoretical results, and show that the proposed method provides an applicable method for the control of the nonlinear dynamic systems.

Fixed-time leader-following synchronization in delayed network via non-chattering nonlinear control

“…Remark 8: The purpose of choosing function g ( · ) and h ( · ) satisfying Assumptions 1 and 2 is to clearly show the effectiveness of the proposed controller. In practice, those controllers may also be suitable for the systems that do not meet these assumptions (Yan et al, 2021).…”

“…In order to enhance convergence, the fixed-time approaches can be used to drive the system quick convergence within a fixed settling time which is independent of the initial conditions (Chen et al, 2020;Polyakov, 2012). In the most existing fixed-time approaches (Liu and Chen, 2016;Yan et al, 2021;Yin et al, 2020), controller usually include the following terms: u(t) =À ke(t) À h 1 sgn(e)jej e À h 2 sgn(e)jej j . The disadvantages of this control are as follows:…”

“…In order to enhance convergence, the fixed-time approaches can be used to drive the system quick convergence within a fixed settling time which is independent of the initial conditions (Chen et al, 2020; Polyakov, 2012). In the most existing fixed-time approaches (Liu and Chen, 2016; Yan et al, 2021; Yin et al, 2020), controller usually include the following terms: u ( t ) = − κ e ( t ) − η 1 sgn ( e ) | e | ε − η 2 sgn ( e ) | e | ξ . The disadvantages of this control are as follows: (1) it includes the sign function of the error which may have the chattering phenomena; (2) it has the absolute values of the error which may result in the sudden changes of the signals at some time instants and produce the undesirable effects; and (3) the convergence is not high (Yang et al, 2017).…”

Cooperative target search and tracking for multi-UAVs based on control barrier functions

“…On the basis of Ganganath et al (2016), a semi-flocking algorithm for multiple target tracking and area coverage is employed by Yuan et al (2018), which enables mobile nodes to realize self-organization based on perceived information through information exchange between neighbor nodes. For precise flocking and collision avoidance of the multi-agent system, Yan et al (2021) present a control protocol in the high-dimensional space developed using the graph theory and the theoretical properties of differential equations, which ensures a precise security distance between UAVs. In recent years, target enclosing control for mobile agents has been widely investigated in literature, such as Muslimov and Munasypov (2020), Yao et al (2015), Dou et al (2020), and Yang et al (2020).…”

Unmanned aerial vehicle formation obstacle avoidance control based on light transmission model and improved artificial potential field

“…At the same time, UAV formation with obstacle avoidance function can adapt to various and complex flight environments, which have good application prospects in civilian fields such as plant protection, power inspection, security, and logistics. However, obstacle avoidance for UAV formation under uncertain and complex flying environments is still a challenge so far (Singla et al, 2021; Sui et al, 2021; Yan et al, 2021; Yang et al, 2021).…”