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于这类系统的高保真基本模型的计算复杂性和由于缺乏对控制系统行为的潜在的物理、化学和生物现象的准确理解而产生的内在不确定性。高保真模型通常无法进行实时决策，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、可靠和优化运行。在这一探索性研究项目中，将开发一种新的基于学习的最优控制范例，通过使用系统及其不确定性的近似模型来确保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的更新模型来优化系统性能。典型的例子将集中在冷大气等离子体射流，它可以在材料加工和新兴的等离子体医学领域产生重大影响。拟议的研究是由于使用高保真模型进行工程系统最优控制的日益重要的重要性，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性的相关理论挑战。最终目标是开发一种基于学习的最优控制方法，该方法利用不确定系统的高保真知识，确保系统在存在不确定性的情况下安全和鲁棒地运行，降低保守的控制性能，并且易于实时计算。高保真模型将被用来系统地为设计提供指导，并通过不确定情况下的闭环仿真来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)发展一种特别适合于使用具有任意概率不确定性的非线性高保真模型来验证基于学习的最优控制性能的不确定性传播方法；(3)展示基于学习的最优控制在一个复杂的工程系统上的潜在好处。除了涉及低温大气等离子体喷流的应用外，拟议的方法可能会有许多应用。除了在新兴的多学科领域培训研究生外，还将开发一门新的高级本科生/研究生课程，整合数据科学、贝叶斯推理和复杂化学和生物分子系统的稳健优化的基本概念。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.