标题： 一种改进的自适应数据启用策略优化控制方法以解决状态扰动 显示英文标题

标题： A Modified Adaptive Data-Enabled Policy Optimization Control to Resolve State Perturbations

摘要： 本文提出了对数据使能策略优化（DeePO）算法的修改，以减轻状态扰动。 DeePO是一种自适应的数据驱动方法，旨在迭代计算等效于确定性等价LQR增益的反馈增益。 与其他基于Willems基本引理的数据驱动方法类似，DeePO需要持续激励的输入信号。 然而，来自LQR设计的线性状态反馈增益本身无法生成此类输入。 为了解决这个问题，通常会向控制信号中添加探测噪声以确保持续激励。 然而，添加的噪声可能会引起不期望的状态扰动。 我们首先识别了在未添加探测噪声时危及DeePO期望性能的两个关键问题：状态收敛到平衡点，以及控制器收敛到其最优值。 为了在不依赖探测噪声的情况下解决这些挑战，我们基于两个基本原理提出了无扰动DeePO（PFDeePO）。 首先，在DeePO过程中，当系统状态接近平衡点时，算法暂停控制增益的更新。 其次，当控制器收敛时，它应用一个乘法噪声，该噪声由$1$的均值作为控制信号的增益。 这种方法在系统接近平衡时最小化噪声的影响，同时保持稳定性。 我们通过仿真展示了PFDeePO的有效性，展示了其在保持系统性能和稳定性的同时消除状态扰动的能力。 显示英文摘要

摘要： This paper proposes modifications to the data-enabled policy optimization (DeePO) algorithm to mitigate state perturbations. DeePO is an adaptive, data-driven approach designed to iteratively compute a feedback gain equivalent to the certainty-equivalence LQR gain. Like other data-driven approaches based on Willems' fundamental lemma, DeePO requires persistently exciting input signals. However, linear state-feedback gains from LQR designs cannot inherently produce such inputs. To address this, probing noise is conventionally added to the control signal to ensure persistent excitation. However, the added noise may induce undesirable state perturbations. We first identify two key issues that jeopardize the desired performance of DeePO when probing noise is not added: the convergence of states to the equilibrium point, and the convergence of the controller to its optimal value. To address these challenges without relying on probing noise, we propose Perturbation-Free DeePO (PFDeePO) built on two fundamental principles. First, the algorithm pauses the control gain updating in DeePO process when system states are near the equilibrium point. Second, it applies a multiplicative noise, scaled by a mean value of $1$ as a gain for the control signal, when the controller converges. This approach minimizes the impact of noise as the system approaches equilibrium while preserving stability. We demonstrate the effectiveness of PFDeePO through simulations, showcasing its ability to eliminate state perturbations while maintaining system performance and stability.