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

该项目解决了在增材制造、电池建模、深部矿井升降机、石油钻井、交通拥堵、海水淡化和其他工程领域出现的各种动态系统的反馈控制的可实施性问题。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，来决定如何调整系统的行为以实现重要目标，例如确保系统在最小的人为干预下安全地收敛到理想的运行模式。该项目结合了pi在工程和数学方面的互补专业知识，通过解决在这个新的合作框架之外无法解决的重要跨学科问题。该项目研究具有延迟的互联系统，其中系统或其周围环境的当前状态可能无法用于反馈控制设计，以及延迟下极值寻求的相关问题，其中希望最小化重要类型的成本标准。通过pi与工业界工程师的联系，该项目将增加工程界对更严格方法的使用，以获得更好的性能控制，并将为研究生提供跨学科的培训，以引人注目的工程应用为指导。该项目为涉及延迟、规定的调节时间和不确定性的ODE和ODE- pde级联的关键类别提供了转换控制和极值搜索算法。输入延迟是由传感器或传输现象引起的，当实现控制目标有严格的最后期限时，就会出现有限的时间限制。虽然预测已经被广泛使用，但目前还没有类似的预测来解决具有规定调节时间的稳定问题，这些问题存在延迟和不确定的模型参数。该项目克服了一般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、带参数识别的自适应控制以及延迟或时间约束下的极值搜索，包括只有采样输出测量可用的情况。所开发的控制确保了更好的抗干扰性和对不确定性的鲁棒性。该项目以前沿工程应用为指导，以确保理论的实用性。其中包括水下机器人的模型，其中缓慢的声学通信通过长时间延迟建模，减少石油生产中的严重段塞，以及在线社交网络，其中意见传播通过PDE-ODE级联扩散建模。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.