通过互信息正则化，实现线性系统状态分布的可控调控。
Mutual Information Optimal Density Control of Linear Systems and Generalized Schrödinger Bridges with Reference Refinement
- 用互信息约束控制策略随机性，提升安全性。
- 在特定时间点施加高斯分布约束，精确管理状态不确定性。
- 算法与广义薛定谔桥问题交替优化一致，理论闭环。
我们研究离散时间线性系统的互信息（MI）正则化最优密度控制问题。MI最优控制作为最大熵控制的扩展，可在控制性能与随机输入带来的优势之间权衡。然而，MI正则化会引入策略随机性，限制其在安全关键场景的应用。为此，我们在特定时间点施加高斯密度约束，直接控制状态不确定性。针对该问题，我们提出一种交替优化算法，并推导出每一步的闭式解。此外，我们发现该交替优化过程与关联于离散时间线性系统的广义薛定谔桥问题完全一致。
原文摘要 · Abstract (English)
We consider a mutual information (MI) regularized version of optimal density control of a discrete-time linear system. MI optimal control has been proposed as an extension of maximum entropy optimal control to trade off between control performance and benefits provided by stochastic inputs. MI regularization induces stochasticity in the policy, which poses challenges for applications of MI optimal control in safety-critical scenarios. To remedy this situation, we impose Gaussian density constraints at specified times to directly control state uncertainty. For this MI optimal density control problem, we propose an alternating optimization algorithm and derive the closed form of each step in the algorithm. In addition, we reveal that the alternating optimization of the MI optimal density control problem coincides with that of the so-called generalized Schrödinger bridge problem associated with the discrete-time linear system.
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