阶数自适应分布式积分控制
Order-Adaptive Distributed Integral Control
- College of Artificial Intelligence, Nankai University（南开大学人工智能学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对分布式动态协调中目标复杂度未知时控制器阶数选择的权衡问题，开发阶数自适应分布式积分控制器（OADIC），通过嵌套候选控制器结构实现阶数自适应，保证系统稳定性并明确临界阶数的拒绝时间。
AI中文摘要：
我们解决分布式动态协调中的一个结构权衡问题：当目标复杂度未知时，低阶控制器可节省状态，但可能留下持续的跟踪误差；而高阶控制器可改善跟踪性能，但可能给每个智能体带来不必要的动态负担。为在不采用计算上更复杂的非线性反馈或易产生颤振的非光滑反馈的前提下消除这一选择，我们开发了阶数自适应分布式积分控制器（OADIC）。具体而言，我们从比例反馈开始，仅当局部可测量的相对误差表明当前阶数不足时，才添加积分状态。同时，我们将候选控制器组织为嵌套形式，从而保留现有状态和增益，并在阶数转换期间保持连续的控制输入。为给该设计提供理论基础，我们首先刻画增广智能体-目标图上规定相对位移的一致性。接下来，我们构造增益以稳定所有可容许的固定阶子系统，并为变维闭环系统建立一致的输入-状态稳定性界。此外，我们证明OADIC会在有限个决策区间后拒绝所有不足的阶数，并明确界定临界阶数的拒绝时间。
英文摘要：
We address a structural tradeoff in distributed dynamic coordination: when the target complexity is unknown, a low controller order saves states but may leave a persistent tracking error, whereas a high order improves tracking but may burden every agent with unnecessary dynamics. To remove this choice without resorting to computationally more involved nonlinear feedback or chattering-prone nonsmooth feedback, we develop an order-adaptive distributed integral controller (OADIC). Specifically, we start with proportional feedback and add integral states only when locally measurable relative errors show that the current order is inadequate. Meanwhile, we organize the candidate controllers in a nested form, thereby preserving the existing states and gains and maintaining continuous control inputs during order transitions. To provide a theoretical basis for this design, we first characterize the consistency of prescribed relative displacements on the augmented agent--target graph. Next, we construct gains that stabilize all admissible fixed-order subsystems and establish a uniform input-to-state stability bound for the variable-dimension closed loop. Furthermore, we prove that OADIC rejects every insufficient order after finitely many decision intervals and explicitly bound the rejection time of the critical order.
