Collaborative Research: Designs and Theory for Event-Triggered Control with Marine Robotic Applications

该项目将设计数学方法来控制海洋机器人和其他工程应用领域中出现的动力系统的行为。这些方法将需要事件触发的反馈控制，从而系统使用关于其状态和周围环境的反馈，帮助决定未来的优化行动方案，以及使用诸如潜在违反约束的事件来确定何时改变控制。该项目将寻求有限时间控制方法，使跟踪和位置保持等控制目标能够在规定的有限时间期限内实现。利用应用数学来控制生态机器人系统将促进科学进步，通过更有效的方法来了解污染，石油泄漏或其他环境压力在复杂，动态和非结构化海洋环境中的影响。这项工作将与两个博士合作。学生在工程和数学的接口的研究将有助于他们准备各种各样的潜在职业。调查人员还将向路易斯安那州或纽约的小学生介绍该项目的基本方面。这种推广活动可以帮助激励多元化，合格的学生干部考虑追求工程或数学的职业生涯。该项目的应用部分将侧重于算法开发和海洋机器人。此外，该研究将有可能应用于其他设置与事件触发控制，安全或定时约束，和不确定性，如可再生能源网络或智能交通系统。该项目将有助于解决控制理论的重大挑战，非线性控制系统与通信或状态约束或优化要求，使用三种策略。第一个将为具有时间截止日期的系统设计事件或自触发反馈控制，其触发根据输出测量计算，并确定何时重新计算控制以避免不期望的操作模式，目标是确保有限时间收敛。这将有助于克服使用标准反馈控制的障碍，标准反馈控制要求用户连续或频繁地重新计算控制值，而不优化成本标准或满足时间期限，因此不太适合工程应用。这将建立在非领导调查员的事件触发的非线性控制理论，开发了几个建设性的设计工具，为各类非线性系统的先前工作。第二个将开发事件或自触发控制下的鲁棒前向不变性方法，这有助于预测和量化控制系统可以容忍的不确定性程度，而不会违反公差和安全界限。这将建立在首席研究员先前的工作基础上，该工作计算了海洋机器人曲线跟踪中允许的不确定性的界限。第三个是基于有限时间学习的自适应动态规划，它近似于最优策略，以帮助克服传统动态规划中出现的维数灾难。这将建立在非首席研究员在自适应动态规划方面的先前工作的基础上，该工作提出了从输入状态或输入输出数据中学习次优控制器的计算算法。这项工作将包括水下海洋机器人的应用和实验，其中事件触发将科普间歇性通信和有限的电力资源。真实的物理海洋机器人平台将用于探索数值方面和评估数学算法。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

This project will devise mathematical methods to control the behavior of dynamical systems that arise in the field of marine robotics and other engineering applications. The methods will entail event-triggered feedback control, whereby the systems use feedback about their states and their surroundings, help decide future optimizing courses of action, and where events like potential violations of constraints are used to determine when to change the controls. The project will seek finite-time control methods, which enable control objectives such as tracking and station keeping to be realized by prescribed finite-time deadlines. Using applied mathematics to control ecological robotic systems will promote scientific progress, by leading to more effective ways to understand the effects of pollutions, oil spills, or other environmental stresses in complex, dynamic, and unstructured marine environments. The work will be collaborative with two Ph.D. students whose research at the interface of engineering and mathematics will help prepare them for a wide variety of potential careers. The investigators will also deliver presentations on elementary aspects of the project to grade school students in Louisiana or New York. This outreach can help inspire a diverse, qualified cadre of students to consider pursuing careers in engineering or mathematics. The project's applied part will focus on algorithmic development and marine robots. Additionally, this research will have the potential for applications in other settings with event-triggered controls, safety or timing constraints, and uncertainties, such as renewable energy networks or intelligent transportation systems.The project will help address significant challenges in control theory for nonlinear control systems with communication or state constraints or optimization requirements, using three strategies. The first will design event- or self-triggered feedback controls for systems with time deadlines, whose triggers are computed from output measurements, and which determine when to recompute the control to avoid undesirable operating modes, with the goal of ensuring finite time convergence. This will help overcome the obstacles to using standard feedback controls, which require the user to continuously or frequently recompute control values without optimizing cost criteria or meeting time deadlines, and which therefore are less suitable in engineering applications. This will build on the nonlead investigator's prior work in event-triggered nonlinear control theory that developed several constructive design tools for various classes of nonlinear systems. The second will develop robust forward invariance methods under event- or self-triggered controls, which help predict and quantify the degree of uncertainty that control systems can tolerate without violating tolerance and safety bounds. This will build on the lead investigator's prior work that computed bounds on allowable uncertainties in marine robotic curve tracking. The third involves finite time learning-based adaptive dynamic programming that approximates optimal policies, to help overcome the curse of dimensionality that arises in traditional dynamic programming. This will build on the nonlead investigator's prior work in adaptive dynamic programming that proposed computational algorithms to learn suboptimal controllers from input-state or input-output data. The work will include applications to, and experiments with, underwater marine robots, where event-triggering will cope with intermittent communication and constrained power resources. Real physical marine robotic platforms will be used to explore numerical aspects and to evaluate the mathematical algorithms.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.