The National Natural Science Foundation of China (61304108),The National Basic Research Program of China (2020YFC2200600)
为了解决高超声速飞行器纵向运动模型的稳定轨迹跟踪控制问题,设计了一种指定时间自适应控制方法.通过引入障碍李雅普诺夫函数,保证速度跟踪误差和高度跟踪误差能够收敛到期望的区域,同时满足系统的瞬态性能和稳态精度. 将自适应控制与实际指定时间稳定理论结合,实现了闭环系统在指定时间稳定,收敛时间可根据实际需求预先指定. 引入的固定时间滤波器对虚拟导数进行求解,避免了传统反步控制中存在的“计算爆炸”问题,提高了收敛速度. 对所设计的控制器利用李雅普诺夫理论给出了严格理论证明,并能够保证系统其它状态变量在指定时间内趋于稳态值. 仿真结果表明,所设计的控制器能够使速度和高度稳定地跟踪参考信号,满足时变的性能约束需求且具有较强的鲁棒性.
A prescribed-time adaptive control method is designed to solve the problem of stable trajectory tracking control of the hypersonic vehicle. The velocity and altitude tracking errors are guaranteed to converge to the desired area by introducing the barrier Lyapunov function while meeting the system's transient performance and steady-state accuracy requirements. By combining the adaptive control with the practically prescribed-time stability theory, the closed-loop system is stable at a prescribed time, and the convergence time can be predefined according to the actual needs. The introduced fixed-time filter is employed to solve the virtual derivative, which avoids the "term of explosion" problem in traditional backstepping control and improves the convergence speed. A rigorous theoretical proof is presented for the designed controller using Lyapunov theory, which can ensure that the other state variables of the system tend to the steady-state value within a specified time. The simulation results show that the designed controller can make the velocity and altitude track the reference signals stably, and meet the time-varying performance constraints robustly.