A globally fixed-time solution of distributed formation control for multiple hypersonic gliding vehicles

Abstract

This paper investigates the distributed formation control problem for multiple hypersonic gliding vehicles (HGVs) under direct communication topology. Based on a formation flight framework of multiple HGVs, a globally fixed-time formation control scheme is proposed by using the fixed-time stability and the hierarchical control theory. Firstly, a fixed-time consensus law is addressed in the three-dimensional formation flight dynamics to generate the virtual control inputs. In order to design appropriate actual control inputs to track the virtual control commands rapidly and accurately, a composite fixed-time feedback control law is then put forward, where a new fixed-time tracking differentiator is designed to obtain the information on the time derivatives of virtual control inputs. Following, the problem of “explosion of complexity” can be resolved effectively. Finally, the globally fixed-time convergence is achieved in spite of the initial conditions of HGV's states, where the upper bound of the settling time can be estimated in advance by only using the control parameters and the direct communication topology. The desired formation configuration can be established within a prescribed convergence time. Extensive numerical simulations are performed to demonstrate the effectiveness and superiority of the proposed formation control strategy.