EAGER: Real-Time: Learning-based Optimal Control of Stochastic Nonlinear Systems

复杂工程系统最优实时控制的两个主要挑战来自这些系统的高保真基本模型的计算复杂性，以及由于缺乏对控制系统行为的潜在物理、化学和生物现象的精确理解而产生的固有不确定性。高保真模型通常不利于实时决策制定，因为它们对计算的要求太高。另一方面，模型的不确定性会影响决策的可靠性，从而不利于复杂系统的安全、可靠和最优运行。在这个探索性的研究项目中，将通过使用系统及其不确定性的近似模型来开发一种新的基于学习的最优控制范式，以保证不确定非线性系统的稳定性和鲁棒性，同时根据在线学习的系统更新模型来优化系统性能。原型将集中在冷大气等离子体射流上，它可以在材料加工和等离子体医学新兴领域产生重大影响。提出的研究的动机是使用高保真模型进行工程系统最优控制的重要性日益增加，以及在统一的最优控制公式中解决系统处理不确定性，非保守控制性能和低计算复杂度相关的理论挑战。最终目标是开发一种基于学习的最优控制方法，该方法利用对不确定系统的高保真知识，确保在存在不确定性的情况下系统运行的安全性和鲁棒性，减轻保守控制性能，并且适合实时计算。高保真模型将用于系统地为设计提供信息，并通过不确定条件下的闭环仿真验证基于学习的最优控制的性能。该项目的具体目标是：(1)发展基于学习的最优控制的理论和公式，(2)开发一种不确定性传播方法，该方法特别适用于使用具有任意概率不确定性的非线性高保真模型进行基于学习的最优控制的性能验证，以及(3)展示基于学习的最优控制在复杂工程系统（即冷大气等离子体射流试验台）上的潜在好处。除了涉及低温大气等离子体射流之外，所提出的方法可能会找到许多应用。除了在新兴的多学科领域培养研究生外，还将开发一个新的高级本科/研究生课程，该课程整合了数据科学，贝叶斯推理以及复杂化学和生物分子系统的鲁棒优化的基本概念。该奖项反映了美国国家科学基金会的法定使命，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。

The two main challenges in optimal real-time control of complex engineering systems arise from the computational complexity of high-fidelity fundamental models of such systems and the inherent uncertainty stemming from lack of exact understanding of the underlying physical, chemical, and biological phenomena governing the system behavior. High-fidelity models are often prohibitive for real-time decision making because they are too computationally demanding. On the other hand, model uncertainty can compromise the reliability of decision making thus can be detrimental to safe, reliable, and optimal operation of complex systems. In this exploratory research project, a new paradigm for learning-based optimal control that guarantees stability and robustness of uncertain nonlinear systems will be developed by using approximate models of the system and its uncertainty, while optimizing the system performance with respect to an updated model of the system learned online. The prototypical example will focus on cold atmospheric plasma jets that can have significant impact in materials processing and in the emerging field of plasma medicine.The proposed research is motivated by the growing importance of using high-fidelity models for optimal control of engineering systems as well as the theoretical challenges associated with addressing systematic handling of uncertainties, non-conservative control performance, and low computational complexity in a unified optimal control formulation. The ultimate objective is to develop a learning-based optimal control method that leverages high-fidelity knowledge of an uncertain system, ensures safe and robust system operation in the presence of uncertainties, mitigates conservative control performance, and is amenable to real-time computations. High-fidelity models will be used to systematically inform the design and verify the performance of learning-based optimal control via closed-loop simulations under uncertainty. The specific aims of the project are: (1) develop theory and formulations for learning-based optimal control, (2) develop an uncertainty propagation method that is especially suited for performance verification of learning-based optimal control using nonlinear high-fidelity models with arbitrary probabilistic uncertainties, and (3) demonstrate the potential benefits of learning-based optimal control on a complex engineering system, i.e., a cold atmospheric plasma jet testbed. The proposed methodology may find numerous applications beyond the ones involving low-temperature atmospheric plasma jets. In addition to training a graduate student in an emerging multi-disciplinary field, a new upper level undergraduate/graduate course will be developed that integrates basic concepts from data science, Bayesian inference, and robust optimization of complex chemical and biomolecular systems.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.