摘要
本文针对一类在非控制边界带有未知参数的不确定双曲型PDE-ODE级联系统,研究其自适应边界镇定问题.与已有密切相关文献相比,本文系统中带有的未知参数使所得闭环系统是一个非线性系统,从而导致已有的分析系统适定性和稳定性的策略不再适用.为了实现本文的控制目标,关键在于为闭环系统和未知参数选取恰当的能量函数和动态补偿器.具体的,通过利用自适应技术和投影算子,引入一个恰当的动态补偿器处理未知参数.在此基础上借助反推技术成功的设计出所期望的自适应边界控制器.然后,利用非线性发展方程理论和通过构造恰当的能量函数,得到整个闭环系统的适定性和稳定性结果.
Adaptive boundary stabilization is investigated for a class of uncertain hyperbolic PDE–ODE cascade systems which allows an unknown parameter at the uncontrolled boundary. Compared with the most closely related literature, the unknown parameter makes the resulting closed-loop system a nonlinear one, which leads to the existing methods of analyzing the wellposedness and stability of a system no longer applicable. To achieve the control objective of this paper, a dynamic compensation for the unknown parameter and an energy function for the considered closed-loop system must be chosen appropriately. Specifically, by using the adaptive technique and projection operator, a proper dynamic compensation is introduced to deal with the unknown parameter. Based on this and by using the backstepping technique, a desired adaptive boundary controller is successfully constructed for the considered system. Then, by the theory of nonlinear evolution equations and constructing an appropriate energy function, the well-posedness and stability results of the entire closed-loop system are obtained.
引文
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