Robust Optimization of Nonlinear Dynamical Systems

在制造业、国防和能源应用等领域，越来越多的人强调健壮的系统设计，这促使设计工程师使用高保真模型来考虑复杂的非线性行为和参数值的不确定性。该研究项目将为工程师开发新颖的方法和易于使用的软件，以考虑设计阶段的不确定性。这些产品将极大地提高几乎所有行业的设计能力，从而实现更安全、更可靠、更强大、更经济的工程系统设计。作为该研究项目的一部分，研究生将接受前沿研究方面的培训。此外，我们将开发一个新的动力系统鲁棒设计模块，通过研究生在线课程“不确定性分析、鲁棒设计和优化”，向工业系统工程师介绍不确定性下的正式动力系统。本研究项目的目标是解决系统建模为初值问题的稳健设计问题，该问题被表述为双级，最大/最小和/或半无限优化问题。解决这一问题需要建立新的理论数学、数值分析和将动态仿真与确定性全局优化相结合的高速软件实现。提出了基于mccormick的隐式函数松弛的发展，用于全局边界信息的确定性全局优化框架。这些开发将在一个用Julia编程语言编写的软件库中实现，以实现高速和可访问性。改进的系统设计带来了更高的安全性，通过减少灾难性操作故障的影响或完全消除它们，从而造福社会。改进的设计也导致降低生产成本和减少环境影响，通过效率的提高，直接造福社会，通过降低产品的成本（例如，商品，能源，消费品，运输等）。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 increasing emphasis on robust system designs for manufacturing, defense, and energy applications, among others, is motivating design engineers to use high-fidelity models that account for complex nonlinear behavior and uncertainty in parameter values. This research project will develop novel methods and easy-to-use software for engineers to account for uncertainty at the design stage. These products will dramatically improve the design capabilities in nearly every industry, resulting in safer, more reliable, more robust, and more cost-effective designs of engineered systems. As part of this research project a graduate student will be trained in cutting edge research. Also, a new module on the robust design of dynamical systems will be developed to introduce formal dynamical systems under uncertainty to systems engineers from industry through a graduate online course on Uncertainty Analysis, Robust Design, and Optimization.The objective of this research project is to solve the robust design problem for systems modeled as initial value problems which is formulated as a bi-level, max/min, and/or semi-infinite optimization problem. Solving this problem requires establishing new theoretical mathematics, numerical analysis, and high-speed software implementations for combining dynamic simulation and deterministic global optimization. The development of McCormick-based relaxations of implicit functions is proposed for use within deterministic global optimization frameworks for global bounding information. These developments will be implemented in a software library written in the Julia programming language for high speed and accessibility. Improved systems design results in greater safety and security which benefits society by reducing the impacts of catastrophic operational failures or eliminating them altogether. Improved designs also result in reduced production costs and reduced environmental impact through efficiency improvements which directly benefit society by reducing costs of products (e.g., commodities, energy, consumer goods, transportation, etc.).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.