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

复杂工程系统的最优实时控制的两个主要挑战来自于这些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基本物理、化学和生物现象的准确理解而产生的固有不确定性。高保真模型通常不适合实时决策，因为它们的计算要求太高。另一方面，模型的不确定性会损害决策的可靠性，从而不利于复杂系统的安全、可靠和优化运行。在这个探索性的研究项目中，一个新的范例学习为基础的最优控制，保证稳定性和鲁棒性的不确定性的非线性系统将开发通过使用近似模型的系统和它的不确定性，同时优化系统性能的更新模型的系统在线学习。 原型的例子将集中在冷大气等离子体射流，可以在材料加工和等离子体医学的新兴领域产生重大影响。拟议的研究是由越来越多的重要性，使用高保真模型的工程系统的最优控制，以及理论上的挑战，解决系统处理的不确定性，非保守的控制性能，并且计算复杂度低。最终的目标是开发一种基于学习的最优控制方法，利用高保真度的不确定系统的知识，确保安全和鲁棒的系统运行中存在的不确定性，减轻保守的控制性能，并适合于实时计算。高保真模型将用于系统地告知设计，并通过不确定性下的闭环模拟验证基于学习的最优控制的性能。该项目的具体目标是：（1）开发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，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对基于学习的最优控制进行性能验证，以及（3）证明基于学习的最优控制对复杂工程系统的潜在好处，即，冷大气等离子体射流试验台所提出的方法可能会发现许多应用程序以外的涉及低温大气等离子体射流。除了在新兴的多学科领域培养研究生外，还将开发一门新的高级本科/研究生课程，整合数据科学、贝叶斯推理以及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，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

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.