可规定性能的输入受限非线性系统反步控制

Prescribed performance backstepping control of nonlinear systems with input saturation

摘要:

针对具有不可直接测量状态和控制方向未知的输入受限非线性系统的跟踪问题,提出一种基于模糊状态观测器的反步控制方法.首先采用模糊状态观测器估计被控系统中的不可测量状态；然后利用具有光滑特性的双曲正切函数和Nussbaum增益函数对控制器的饱和问题进行处理，根据可规定误差面性能技术对输出跟踪误差的边界进行限定；最后将反步法和动态面法相结合设计鲁棒控制器.运用Lyapunov理论对系统的稳定性能进行了分析，证明闭环系统的所有信号最终半全局一致有界.以具有参数不确定性和存在外界未知有界干扰的高超声速飞行器纵向运动为仿真模型，仿真结果验证了所提算法的有效性.

Abstract:

The tracking problem of the nonlinear system with input saturation is investigated by using a backstepping approach based on fuzzy state observer, where the underline system contains immeasurable states and unknown control directions. Firstly, a fuzzy state observer is designed to estimate the immeasurable states. Then, the Hyperbolic tangent function with smooth property and a Nussbaum function are used to handle the input saturation. The bound of the output tracking error is set by the prescribed performance methodology. A robust controller is designed combining the backstepping approach and the dynamic surface method. The Lyapunov theory is applied to analyze the stability of the system. It is proved that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded(SGUUB). Finally, the longitudinal dynamics as the simulation model is given to show the effectiveness of the proposed control approach.