Stochastic spatio-temporal processes are prevalent across domains ranging from the modeling of plasma, turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by describing them as evolutionary processes on Hilbert spaces, and in doing so, derives a framework for spatio-temporal manipulation from fundamental thermodynamic principles. This approach yields a variational optimization framework for controlling stochastic fields. The resulting scheme is applicable to a wide class of spatio-temporal processes and can be used for optimizing parameterized control policies. Our simulated experiments explore the application of two forms of this approach on four stochastic spatio-temporal processes, with results that suggest new perspectives and directions for studying stochastic control problems for spatio-temporal systems.

中文翻译：

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利用随机性进行时空系统的开环和模型预测控制

随机时空过程在从等离子体建模、流体湍流到量子系统的波函​​数等领域普遍存在。这封信通过将这些系统描述为希尔伯特空间上的进化过程来研究对这些系统的测度理论描述，并在此过程中从基本热力学原理推导出时空操纵框架。这种方法产生了一个用于控制随机场的变分优化框架。由此产生的方案适用于广泛的时空过程，可用于优化参数化控制策略。我们的模拟实验探索了这种方法的两种形式在四个随机时空过程中的应用，