AI 中文总结
针对受控输出为无源输出积分的线性无限维无源系统，提出带动态增益监督器的非线性递归漏斗控制器，证明相关性能并以欧拉-伯努利梁验证，实现指定性能位置跟踪。
AI 中文摘要
我们研究线性无限维无源系统的漏斗控制问题，这类系统的受控输出由无源输出积分得到。在机械应用中，这对应基于测得的无源速度输出进行位置控制。在系统-节点框架内，我们针对具有分布式或边界控制与观测的系统，提出一种带动态增益监督器的非线性递归漏斗控制器。当归一化递归误差接近指定监测水平时，监督器会自动增大阻尼增益。控制器使用跟踪误差及其导数，其中导数直接从无源输出获取，而非通过数值微分得到。我们证明了闭环轨迹的全局存在性与唯一性、指定漏斗性能，以及导数跟踪误差和无源输出的全局有界性。在附加的位置兼容严格耗散性条件下，监督增益仅有限次增大，最终变为常数。因此，增益、内部状态和控制输入全局有界，且递归误差漏斗裕度随时间保持一致。该结果通过具有均匀正分布阻尼的边界驱动欧拉-伯努利梁得到验证。
英文摘要
We study funnel control for linear infinite-dimensional passive systems whose controlled output is obtained by integrating the passive output. In mechanical applications, this corresponds to position control based on a measured passive velocity output. Within the system-node framework, we propose a nonlinear recursive funnel controller with a dynamic gain supervisor for systems with distributed or boundary control and observation. The supervisor automatically increases a damping gain whenever the normalized recursive error approaches a prescribed monitoring level. The controller uses the tracking error and its derivative, with the latter obtained directly from the passive output rather than by numerical differentiation. We prove global existence and uniqueness of the closed-loop trajectory, prescribed funnel performance, and global boundedness of the derivative tracking error and the passive output. Under an additional position-compatible strict dissipativity condition, the supervised gain is increased only finitely many times and eventually becomes constant. Consequently, the gain, the internal state, and the control input are globally bounded, and the recursive-error funnel margin is uniform in time. The results are illustrated by a boundary-actuated Euler-Bernoulli beam with uniformly positive distributed damping.
