• 论文 •

### 一类不确定双曲型PDE-ODE级联系统的自适应镇定控制

1. 1. 山东大学控制科学与工程学院,济南 250061;2. 烟台大学数学与信息科学学院,烟台 264005
• 出版日期:2018-02-25 发布日期:2018-03-22

XU Zaihua, LIU Yungang1,LI Jian. Adaptive Stabilizing Control for a Class of Uncertain Hyperbolic PDE-ODE Cascade Systems[J]. Journal of Systems Science and Mathematical Sciences, 2018, 38(2): 147-162.

### Adaptive Stabilizing Control for a Class of Uncertain Hyperbolic PDE-ODE Cascade Systems

XU Zaihua1 ,LIU Yungang1 ,LI Jian2

1. 1. School of Control Science and Engineering, Shandong University, Jinan 250061; 2. School of Mathematics and Information Science, Yantai University, Yantai 264005
• Online:2018-02-25 Published:2018-03-22

Adaptive stabilizing control is investigated for a class of uncertain second-order hyperbolic PDE-ODE cascade systems. Essentially different from the results in the existing related literature, an unknown parameter is allowed to appear in the boundary condition of the considered system, which leads to that the existing control design methods are difficult to be applied to solve the problem in this paper. For this, by using the adaptive technique that based on the projection operator, a proper dynamic compensator is introduced to deal with the unknowns of the parameter. Based on this and by using the backstepping technique, a desired adaptive boundary controller is successfully constructed for the considered system, which guarantees that all the states of the closed-loop system are uniformly bounded and ultimately converge to a small neighborhood of the origin. It is necessary to point out that the introduction of dynamic compensator makes the resulting closed-loop system have strong nonlinearity. Therefore, by the theory of nonlinear evolution equations and constructing an appropriate energy function, a more general method of analyzing the well-posedness and stability of a system is presented. At last, by taking an overhead crane with flexible cable as an example, numerical results are given to illustrate the effectiveness of the theoretical results.

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