Analyzing and controlling system entropy is a powerful tool for regulating predictability of control systems. Applications benefiting from such approaches range from reinforcement learning and data security to human-robot collaboration. In continuous-state stochastic systems, accurate entropy analysis and control remains a challenge. In recent years, finite-state abstractions of continuous systems have enabled control synthesis with formal performance guarantees on objectives such as stage costs. However, these results do not extend to entropy-based performance measures. We solve this problem by first obtaining bounds on the entropy of system discretizations using traditional formal-abstractions results, and then obtaining an additional bound on the difference between the entropy of a continuous distribution and that of its discretization. The resulting theory enables formal entropy-aware controller synthesis that trades predictability against control performance while preserving formal guarantees for the original continuous system. More specifically, we focus on minimizing the linear combination of the KL divergence of the system trajectory distribution to uniform -- our system entropy metric -- and a generic cumulative cost. We note that the bound we derive on the difference between the KL divergence to uniform of a given continuous distribution and its discretization can also be relevant in more general information-theoretic contexts. A set of case studies illustrates the effectiveness of the method.

翻译：分析与控制系统熵是调节控制系统可预测性的有力工具。受益于此类方法的应用范围广泛，涵盖强化学习、数据安全及人机协作等领域。在连续状态随机系统中，精确的熵分析与控制仍具挑战性。近年来，基于连续系统有限状态抽象的控制综合方法已能对阶段成本等目标提供形式化性能保证，但这些成果尚未扩展至基于熵的性能度量。本研究通过以下途径解决该问题：首先利用传统形式化抽象结果获得系统离散化的熵界，进而推导连续分布熵与其离散化熵之间差异的附加边界。所得理论实现了形式化的熵感知控制器综合，可在保持原始连续系统形式化保证的前提下，权衡可预测性与控制性能。具体而言，我们专注于最小化系统轨迹分布与均匀分布之间的KL散度（作为系统熵度量）与通用累积成本的线性组合。需要指出的是，我们所推导的给定连续分布及其离散化对均匀分布KL散度差异的边界，在更广泛的信息论语境中亦具参考价值。系列案例研究验证了该方法的有效性。