Collaborative Research: Designs and Theory of State-Constrained Nonlinear Feedback Controls for Delay and Partial Differential Equation Systems

合作研究：时滞和偏微分方程系统的状态约束非线性反馈控制的设计和理论

基本信息

批准号：
1408295
负责人：
Michael Malisoff
金额：
$ 22万
依托单位：
Louisiana State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2014
资助国家：
美国
起止时间：
2014-09-01 至 2018-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1408295&HistoricalAwards=false
关键词：
Collaborative Research Designs Theory State

项目摘要

Collaborative Research: Designs and Theory of State-Constrained Nonlinear Feedback Controls for Delay and Partial Differential Equation SystemsControl systems are used to model many important engineering systems, such as electronics manufacturing processes involving lasers, marine robots that can monitor water pollution, oil drilling and refining, and rehabilitation mechanisms for patients with mobility disorders. However, many of these engineering applications involve input delays, state constraints, and uncertainties that can put them outside the scope of existing controller designs and theory. State constraints occur when the control objectives include avoiding undesirable situations such as collisions with obstacles, while input delays often arise from sensor designs or transport phenomena that make it difficult to measure the current state of the system. Also, it is inherent in many engineering applications that the control mechanisms must be autonomous. One important technique for ensuring autonomy is by using feedback control, which means that the control values must be determined from past values of the state of the system. This project will develop cutting edge feedback control designs and theory that can help address the preceding challenges, and will demonstrate the techniques in real time experiments. One key technique will involve prediction, which provides a way to use past observations from the control system to compute future states of the dynamics and future control values, even when the system involves long input delays or considerable uncertainty. As reflected in the backgrounds of the PIs, the project combines insightful engineering with sophisticated mathematics, with the goal of producing practically useful controls that have rigorous performance guarantees under delays or state constraints. The problems to be addressed are among the most challenging and significant ones in the control engineering community. The project will strive for transformative methods, and will pursue three theoretical strategies. The first will seek generalized Lyapunov function constructions for partial differential equations, which can include extensions of current approach for building strict Lyapunov functions for ordinary differential equations to much more difficult hyperbolic partial differential equation cases. The second strategy will involve representing robust predictive controls as solutions of integral delay equations, and a dual representation in terms of perturbed first-order hyperbolic partial differential equations. Combined with the Lyapunov function constructions, this can provide robust tracking for predictively controlled nonlinear ordinary differential equations and robustness results for the corresponding partial differential equations. The third strategy will use robust forward invariance, which involves specifying the state constraints to facilitate computing maximal allowable perturbation sets to ensure safe operation under uncertainty. The project will be guided by cutting edge engineering applications, to help ensure the practical usefulness of all of the project results. The ordinary differential equation applications will involve neuromuscular electrical stimulation, which is a rehabilitation method that can help restore movement in humans with motor neuron disorders, and the control of a class of autonomous marine robots that are used for bathymetric surveys or to monitor water quality. The partial differential equation applications will involve laser pulse shaping systems that are used in the manufacture of flat panel displays or in photolithography, and a multi-phase flow system that can help mitigate the adverse effects of slugging in oil production.

协作研究：针对延迟和部分微分方程系统延迟和部分微分方程系统的设计和理论用于建模许多重要的工程系统，例如涉及激光器的电子制造过程，以及用于活动障碍患者的康复机制。但是，这些工程应用中的许多应用程序都涉及输入延迟，状态限制和不确定性，这些延迟可能使它们超出现有控制器设计和理论的范围。当控制目标包括避免使用障碍物碰撞等不良情况时，就会发生状态限制，而输入延迟通常是由传感器设计或运输现象引起的，这使得难以测量系统的当前状态。同样，在许多工程应用中，控制机制必须是自治的。确保自主权的一种重要技术是使用反馈控制，这意味着控制值必须从系统状态的过去值确定。该项目将开发尖端的反馈控制设计和理论，以帮助应对前面的挑战，并将在实时实验中证明这些技术。一种关键技术将涉及预测，该技术提供了一种使用控制系统的过去观察结果来计算动态和未来控制值的未来状态，即使系统涉及长输入延迟或相当大的不确定性。正如PI的背景所反映的那样，该项目将有见地的工程与精致的数学结合在一起，并将实际上有用的控件产生，这些控制在延迟或州限制下具有严格的性能保证。要解决的问题是控制工程社区中最具挑战性和最重要的问题之一。该项目将努力争取变革性方法，并将追求三种理论策略。第一个将为部分微分方程寻求广义的Lyapunov函数构建体，其中可以包括当前方法的扩展，以构建严格的Lyapunov函数，以实现普通微分方程的严格函数，以实现更困难的双曲线偏微分方程案例。第二种策略将涉及将强大的预测控制作为积分延迟方程的解决方案，而在扰动的一阶双曲偏微分方程方面是双重表示。结合Lyapunov函数构建体，这可以为相应的偏微分方程提供预测控制的非线性普通微分方程和鲁棒性结果。第三个策略将使用强大的正向不变性，该策略涉及指定状态约束以促进计算最大允许扰动集以确保在不确定性下进行安全操作。该项目将通过最先进的工程应用来指导，以帮助确保所有项目结果的实际实用性。普通的微分方程应用将涉及神经肌肉电刺激，这是一种康复方法，可以帮助恢复患有运动神经元疾病的人类的运动，并控制一类用于浴膜调查或监测水质的自主海洋机器人。部分微分方程应用程序将涉及用于制造平板显示或光刻术中的激光脉冲塑形系统，以及可以帮助减轻石油生产中剥落的不利影响的多相流量系统。