Adaptive prescribed performance control for wave equations with dynamic boundary and multiple parametric uncertainties
Adaptive prescribed performance control for wave equations with dynamic boundary and multiple parametric uncertainties
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DOI：
10.3934/math.2024148
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发表时间：
2024
期刊：
影响因子：
2.2
通讯作者：
Zaihua Xu;Jian Li
中科院分区：
文献类型：
--
作者：
Zaihua Xu;Jian Li
在现代工程中，许多实际问题的动力学可以用双曲分布参数系统来描述。由于实际中不确定性是不可避免的，本文致力于一类典型的不确定双曲分布参数系统的自适应规定性能控制。所讨论的系统同时具有未知的域内空间变化阻尼系数和未知的边界常数阻尼系数。此外，本文还考虑了动态边界条件。这些特点使得本文的控制问题与相关作品中的控制问题有本质的不同。为了解决这个问题，利用基于投影算子的自适应技术、为常微分方程和李亚普诺夫稳定性理论开发的反步方法，提出了一种强大的自适应规定性能控制方案，成功地保证了所得闭环系统的所有状态都是有界的，并且原始系统状态收敛到原点的任意规定小邻域。与现有结果相比，所开发的控制方案不仅能够有效处理严重的不确定性，而且克服了动态边界条件带来的无限维反步控制设计方法的技术难点，保证了预定的性能。
In modern engineering, the dynamics of many practical problems can be described by hyperbolic distributed parameter systems. This paper is devoted to the adaptive prescribed performance control for a class of typical uncertain hyperbolic distributed parameter systems, since uncertainties are inevitable in practice. The systems in question simultaneously have unknown in-domain spatially varying damping coefficient and unknown boundary constant damping coefficient. Moreover, dynamic boundary condition is considered in the present paper. These characteristics make the control problem in the paper essentially different from those in the related works. To solve the problem, using adaptive technique based projection operator, backstepping method developed for ODEs and Lyapunov stability theories, a powerful adaptive prescribed performance control scheme is proposed to successfully guarantee that all states of the resulting closed-loop system are bounded, furthermore, the original system state converges to an arbitrary prescribed small neighborhood of the origin. Compared with the existing results, the developed control schemes can not only effectively handle the serious uncertainties, but also overcome the technical difficulties in the infinite-dimensional backstepping control design method caused by the dynamic boundary condition and guarantee prescribed performance.