逐步平衡和部分观测下的最优反馈控制
Optimal feedback control under stepwise equilibration and partial observation
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中文总结 AI 辅助
研究微观机器在部分观测下的最优反馈控制，通过解析求解谐波陷阱在噪声测量下的贝尔曼递归，得出最优协议，其最小功分解为传输成本与提取项，固定干预成本超渐近提取时最优周期数有限，净功非负。
中文摘要 AI 辅助
许多微观机器依靠噪声信号引导非平衡转换并在时间尺度分离的状态下运行。我们考虑反馈协议，即系统在其能量景观的快速、测量条件变化之间达到平衡。在此极限下，部分可观测控制问题精确地简化为哈密顿量更新上的有限时间贝尔曼递归。对于在噪声位置测量下平移到规定目标的谐波陷阱，我们通过解析求解此递归。最优协议平衡其对估计波动的响应与朝着目标的进展，在执行截止日期附近的端点时尽早利用信息。最小功分解为正的热力学长度传输成本和由测量解析的平衡波动分数设定的负的信息启用提取项。当固定干预成本超过每个周期的渐近提取时，它选择有限的最优周期数。我们表明，在这种平移谐波情况下，创建和重置测量记录的最小热力学成本总是超过此阈值，使得最优周期数有限且任何测量通道的净功非负。
英文摘要
Many microscopic machines rely on noisy signals to direct nonequilibrium transformations and operate in a timescale-separated regime. We consider feedback protocols in which a system equilibrates between rapid, measurement-conditioned changes of its energy landscape. In this limit, the partially observable control problem reduces exactly to a finite-horizon Bellman recursion over Hamiltonian updates. For a harmonic trap translated to a prescribed target under noisy position measurements, we solve this recursion analytically. The optimal protocol balances its response to the estimated fluctuation against progress toward the target, exploiting information early while enforcing the endpoint near the deadline. The minimum work decomposes into a positive thermodynamic-length transport cost and a negative information-enabled extraction term set by the fraction of equilibrium fluctuations resolved by the measurement. When a fixed intervention cost exceeds the asymptotic extraction per cycle, it selects a finite optimal number of cycles. We show that, in this translated harmonic case, the minimum thermodynamic cost of creating and resetting the measurement record always exceeds this threshold, making the optimal cycle count finite and the net work non-negative for any measurement channel.
