AI 中文总结
本文提出一种有限时域自举方法，使数据驱动策略迭代无需初始稳定策略即可启动，通过移位系统评估和离策略数据实现，并验证了其在连续时间线性系统中的有效性。
AI 中文摘要
本文研究了连续时间线性系统在不需要初始稳定策略的情况下的数据驱动策略迭代（PI）。标准无限时域PI无法自启动，因为其策略评估步骤仅在反馈增益稳定时才是适定的。然而，当系统矩阵未知时，验证这一性质是困难的。为消除这一要求，我们开发了一种有限时域自举方法。关键思想是对一个移位系统在紧区间上执行策略评估，其中评估方程对任意有界时变策略都是良定义的。我们证明，对于足够长的时域，移位有限时域问题的初始时刻最优增益，当作为恒定反馈增益应用时，能为原始系统实现规定的稳定裕度。然后，我们基于沿原始被控对象轨迹评估的离策略恒等式，推导出数据驱动的实现。我们使用基函数逼近来重构有限时域值矩阵和策略，并通过扰动策略改进递推来刻画由此产生的误差。进一步引入数据驱动的李雅普诺夫证书，以在候选增益用于初始化无限时域PI之前验证其可容许性。对间歇反应器和两质量弹簧系统的数值研究证明了所提出的自举方法的有效性。
英文摘要
This article investigates data-driven policy iteration (PI) for continuous-time linear systems without requiring an initially stabilizing policy. Standard infinite-horizon PI is not self-starting because its policy-evaluation step is well posed only when the feedback gain is stabilizing. However, verifying this property is difficult when the system matrices are unknown. To remove this requirement, we develop a finite-horizon bootstrap method. The key idea is to perform policy evaluation over a compact interval for a shifted system, where the evaluation equation is well defined for arbitrary bounded time-varying policies. We show that, for a sufficiently long horizon, the initial-time optimal gain of the shifted finite-horizon problem, when applied as a constant feedback gain, achieves a prescribed stability margin for the original system. We then derive a data-driven implementation from an off-policy identity evaluated along trajectories of the original plant. We use basis-function approximations to reconstruct the finite-horizon value matrix and policy, and we characterize the resulting error through a perturbed policy-improvement recursion. A data-driven Lyapunov certificate is further introduced to verify admissibility of the candidate gain before it is used to initialize infinite-horizon PI. Numerical studies of a batch reactor and a two-mass-spring system demonstrate the effectiveness of the proposed bootstrap method.
