EAGER/Collaborative Research: Real-Time: Hybrid Control Architectures Combining Physical Models and Real-time Learning

机器学习作为许多复杂工程问题的有效解决方案，已经成为众多研究者关注的焦点。机器学习的核心是为计算机提供使用可用数据进行学习的方法。人工神经网络（ANN）传统上一直是机器学习方法的支柱。虽然这些学习系统肯定有其优势，但它们在控制工程的背景下也有局限性。例如，基于物理的模型通常为电网、自动驾驶汽车和机器人的控制系统设计提供关键的物理见解。因此，在基于学习的控制系统的背景下完全丢弃这些模型通常会适得其反。EARLY概念探索性研究（EAGER）项目旨在开发一种新的，基础的和创新的控制架构，该架构将基于模型的设计方法与实时学习方法的优势相结合。该架构是基于动态系统的数学建模的最新进展。虽然非常适合工程，生物和生态学中的各种应用，但目标应用是智能电网的安全可靠控制。 后者显然对未来的经济发展和国家不断发展的能源分配系统的安全至关重要。项目成果将为复杂的能源管理问题提供切实可行的解决方案，这些问题涉及不确定的电力需求、能源限制和可再生资源的使用，同时保持电网的稳定性和可靠性。它们的输出之间的测量差异定义了一个误差系统。其关键思想是使用一个通用的输入输出表示称为陈Fliess函数系列来描述这个未知的误差系统。通过最小均方误差估计器实时估计级数系数。有效地，传统的人工神经元在这里被这种新型的学习单元所取代，以近似误差系统。控制问题是通过预测控制使用假设的模型和学习误差系统来解决的。使能技术是最近在Chen-Fliess级数的数值逼近方面的进展，这使得在离散时间内实现该方案成为可能。该项目的具体目标是（1）推进支持控制应用实时学习的理论基础，包括这些新的深度学习学习单元的级联（2）优化和调整智能电网实时控制的新理论结果，以提供先验性能保证。这里的主要问题在于，除了可再生资源的作用外，电网的动态过于简化/模型化不佳带来的不确定性。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Machine learning has become a focus of many researchers as effective solution to many complex engineering problems. At its core machine learning are the methods that provide computers ways to learn using available data. Artificial neural networks (ANN) have traditionally been the backbone of machine learning methods. While these learning systems certainly have their strengths, they also have limitations in the context of control engineering. For example, physics based models often provide key physical insight into the design of control systems for power grids, autonomous vehicles, and robots. So completely discarding such models in the context of learning based control systems is often counterproductive. This EArly-concept Grant for Exploratory Research (EAGER) project aims to develop a new, foundational and innovative control architecture which combines the advantages of model based design methods with those of real-time learning. The architecture is based on recent advances in the mathematical modeling of dynamical systems. While well suited for a variety of applications in engineering, biology, and ecology, the target application is the safe and reliable control of smart grids. The latter are clearly of vital importance for future economic development and the security of the nation's constantly evolving energy distribution system. Project outcomes will provide practical solutions to complex energy management problems involving uncertain power demands, energy limits, and use of renewable resources while at the same time maintaining grid stability and reliability.The hybrid control architecture involves a given system and an assumed physical model both driven by the same control input. The measured difference between their outputs defines an error system. The key idea is to use a generic input-output representation known as a Chen-Fliess functional series to describe this unknown error system. The series coefficients are estimated in real-time via a minimum mean-square error estimator. Effectively, the conventional artificial neuron is replaced here by this new type of learning unit to approximate the error system. The control problem is solved via predictive control using the assumed model and the learned error system. The enabling technology is recent advances in the numerical approximation of Chen-Fliess series which make it possible to implement the scheme in discrete-time. The specific objectives of the project are to (1) advance the theoretical foundations that underpin real-time learning for control applications, including the cascading of these new learning units for deep learning (2) optimize and adapt the novel theoretical results for real-time control of smart grids to provide a priori performance guarantees. The main problem here lies in the uncertainty coming from the over-simplified/poorly modeled dynamics of the grid in addition to the action of renewable resources.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.