Improving global optimization methods for dynamic process models

工程、化学和物理中的许多应用都涉及到具有时变行为的系统。这些动态系统包括通过复杂的化学反应系统从较低价值的原材料生产高价值特种化学品、生物制品和药品的间歇过程，通过防止系统偏离轨道来保持安全和质量的自动控制政策，细胞生长等生物过程，以及机器人。所提出的研究计划的目标是改进动态系统过程模型的全局优化方法。*系统的全局优化涉及确定能够产生最佳性能的参数或运行条件，并验证没有替代方案的性能会更好。这项任务在数学上具有挑战性，因为它需要提取关于复杂系统行为的全局知识，同时严格将次优参数排除在考虑之外。动态行为给优化方法带来了更多的障碍，使系统的局部知识更难获得。因此，目前的全局动态优化方法在实际应用中仅限于小系统。然而，一些实际问题需要动态系统的全局优化，包括验证安全约束被强健地满足，验证过程模型充分地描述了底层系统，以及提高经济性能。首先，将开发新的技术来提供优越的全局边界信息，以减少总体优化方法所需的迭代次数。其次，将开发新的数值方法来更有效地处理这种边界信息，以加快统筹法的速度。这些途径将通过利用全球优化和模型开发中几个最近和独立的进展之间尚未开发的协同作用来实现，包括我在博士后工作中开发的用于提取有用的全球边界信息的数值方法。这项研究将使更多的动态模型在实践中得到优化，对上述实际科学和工程应用产生深远的影响。特别是，这项工作将为提高加拿大特种化学和制药部门的间歇化学过程的经济表现提供技术。还将启用更强大的自动控制政策，并将帮助设计安全、环境友好的化学工艺。最终，拟议研究计划的长期目标是开发新的理论和数值工具，以促进实际应用中在全局优化方面的进一步进步。

Many applications in engineering, chemistry, and physics involve systems with time-varying behavior. These dynamic systems include batch processes for production of high-value specialty chemicals, bioproducts, and pharmaceuticals from lower-value raw materials through complex systems of chemical reactions, automatic control policies that maintain safety and quality by preventing systems from drifting off-course, biological processes such as cell growth, and robotics. The goal of the proposed research program is to improve global optimization methods for process models of dynamic systems. ******Global optimization of a system involves determining parameters or operating conditions that produce the best possible performance, and verifying that no alternative would perform better. This task is mathematically challenging, since it requires extracting global knowledge about a complicated system's behavior, while rigorously excluding suboptimal parameters from consideration. Dynamic behavior introduces further obstacles into optimization methods, by making local knowledge of the system more difficult to acquire. As a result, current methods for global dynamic optimization are restricted to small systems in practice. Nevertheless, several practical problems require global optimization of dynamic systems, including verification that safety constraints are satisfied robustly, verification that a process model describes the underlying system adequately, and improvement of economic performance.******The proposed program of research pursues two avenues for improving global dynamic optimization methods. First, new techniques will be developed to furnish superior global bounding information, to reduce the number of iterations required by an overarching optimization method. Second, new numerical methods will be developed process this bounding information more efficiently, to speed up the overarching method. These avenues will be pursued by exploiting untapped synergies between several recent and independent advances in global optimization and model development, including a numerical method developed in my postdoctoral work for extracting useful global bounding information. This research will allow more dynamic models to be optimized in practice, with far-reaching impact across the practical science and engineering applications mentioned above. In particular, this work will provide techniques for improving the economic performance of batch chemical processes in the specialty chemical and pharmaceutical sectors of Canada. More robust automatic control policies will also be enabled, and the design of safe, environmentally friendly chemical processes will be aided. Ultimately, the long-term goal of the proposed research program is to develop new theoretical and numerical tools to foster further advances in global optimization for practical applications.