Collaborative Research: Sequential Predictors for Partial Differential Equation and Delay Systems: Designs, Theory, and Applications

该项目解决了在添加剂制造、电池建模、深井提升机、石油钻探、交通拥堵、海水淡化等工程领域中出现的各种动力系统的反馈控制的可实现性问题。反馈控制涉及使用有关动态系统状态及其周围环境的信息，以决定如何调整系统的行为以实现重要目标，例如确保系统在最少人为干预的情况下安全地收敛到期望的运行模式。该项目通过解决在这一新的合作框架外无法解决的重要跨学科问题，结合了私人投资机构在工程和数学方面的互补专业知识。该项目研究时滞关联系统，其中系统或其周围环境的当前状态可能不能用于反馈控制设计，以及在时滞下极值搜索的相关问题，其中人们希望最小化重要类型的代价标准。通过PIS与工业工程师的联系，该项目将增加工程界使用更严格的方法来获得更好的性能控制，并将为研究生提供跨学科的培训，以强制性的工程应用为指导。该项目为涉及延迟、规定的调节时间和不确定性的关键类别的常微分方程组和常微分方程组提供变革性控制和极值求解算法。输入延迟是由传感器或传输现象引起的，当达到控制目标的最后期限很硬时，就会出现有限时间约束。虽然预测已经得到了广泛的应用，但目前还没有类似的预测方法来预测具有指定调整时间的具有滞后和不确定模型参数的镇定问题。这个项目克服了一般类型的非线性系统的这些挑战，使用了新的顺序预测器、顺序反扩散器、链观测器、带有参数识别的自适应控制以及在延迟或时间约束下的极值搜索，包括只有采样输出测量的情况。开发的控制确保了更好的干扰抑制和对不确定因素的鲁棒性。该项目以前沿工程应用为指导，确保了理论的实用性。它们涉及水下海洋机器人的模型，其中通过长时间的延迟来模拟缓慢的声音通信，减少石油生产中的严重堵塞，以及在线社交网络，其中观点传播由PDE-ODE与扩散的级联来模拟。该项目将包括实验实时实施的一些控制和培养博士生。

This project solves the problem of implementability of feedback controls for a variety of dynamical systems that arise in additive manufacturing, battery modeling, deep mine elevators, oil drilling, traffic congestion, water desalination, and other engineering domains. Feedback control involves the use of information about the states of dynamical systems and about their surroundings, to decide how to adjust the behavior of the systems to realize important objectives such as ensuring that the systems safely converge to a desirable operating mode with minimal human intervention. The project combines the PIs' complementary expertise in engineering and mathematics, by tackling important interdisciplinary problems that could not be solved outside of this new collaborative framework. The project studies interconnected systems with delays, in which the current states of the systems or of their surroundings may not be available for use in the feedback control design, and related problems in extremum seeking under delays, in which one wishes to minimize important types of cost criteria. Through the PIs' contacts with engineers from industry, the project will increase the engineering community's use of more rigorous methods to obtain better performing controls and will also provide interdisciplinary training to graduate students that is guided by compelling engineering applications.The project provides transformative control and extremum seeking algorithms for key classes of ODE and ODE-PDE cascades that involve delays, prescribed regulation times, and uncertainties. Input delays arise from sensor or transport phenomena, and finite time constraints occur when there are hard deadlines for achieving control objectives. While prediction has been used extensively, there are currently no analogs of prediction for stabilization problems with prescribed regulation times where there are delays and uncertain model parameters. This project overcomes these challenges for general classes of nonlinear systems, using new sequential predictors, sequential anti-diffusors, chain observers, adaptive control with parameter identification, and extremum seeking under delays or time constraints, including cases where only sampled output measurements are available. The controls developed ensure better disturbance rejection and robustness against uncertainties. The project is guided by cutting edge engineering applications, to ensure the usefulness of the theory. They involve models for underwater marine robots where slow acoustic communication is modeled through long delays, the reduction of severe slugging in oil production, and online social networks where opinion spreading is modeled by PDE-ODE cascades with diffusion. The project will include experimental real time implementation of some of the controls and train PhD students.