标题： 最优性原理与基于神经常微分方程的过程建模用于分布式控制 显示英文标题

标题： Optimality Principles and Neural Ordinary Differential Equations-based Process Modeling for Distributed Control

摘要： 机器学习和过程控制分析的最新进展提出了如何自然地将新的数据驱动方法与经典过程模型和控制相结合的问题。 我们提出了一种过程建模框架，通过一致的拓扑特性和广延量的守恒，实现数据驱动算法的集成。 过程网络单元之间的相互连接通过连通矩阵和网络图表示。 我们推导出系统的自然目标函数，等价于稳态系统中的非平衡熵产生，作为过程动态的驱动力。 我们说明了如何将分布式控制和优化实施到过程网络结构中，以及控制定律和算法如何改变系统的自然平衡，以达到工程目标。 基本要求是流量条件可以用锥形扇区（无源性）条件来表示。 我们的形式化方法允许通过稀疏深度神经网络，将来自拓扑的基本守恒性质与从数据中学习的动态关系结合起来。 我们在一个简单的库存控制系统实际例子中演示了如何将过程的基本拓扑与神经网络常微分方程模型相结合。 系统特定的本构方程未被描述，而是由神经常微分方程算法通过伴随方法结合自适应常微分方程求解器，从合成时间序列数据中学习。 由此产生的神经网络形成一个状态空间模型，可用于例如模型预测控制算法。 显示英文摘要

摘要： Most recent advances in machine learning and analytics for process control pose the question of how to naturally integrate new data-driven methods with classical process models and control. We propose a process modeling framework enabling integration of data-driven algorithms through consistent topological properties and conservation of extensive quantities. Interconnections among process network units are represented through connectivity matrices and network graphs. We derive the system's natural objective function equivalent to the non-equilibrium entropy production in a steady state system as a driving force for the process dynamics. We illustrate how distributed control and optimization can be implemented into process network structures and how control laws and algorithms alter the system's natural equilibrium towards engineered objectives. The basic requirement is that the flow conditions can be expressed in terms of conic sector (passivity) conditions. Our formalism allows integration of fundamental conservation properties from topology with learned dynamic relations from data through sparse deep neural networks. We demonstrate in a practical example of a simple inventory control system how to integrate the basic topology of a process with a neural network ordinary differential equation model. The system specific constitutive equations are left undescribed and learned by the neural ordinary differential equation algorithm using the adjoint method in combination with an adaptive ODE solver from synthetic time-series data. The resulting neural network forms a state space model for use in e.g. a model predictive control algorithm.