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

这个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，从而系统使用关于它们的状态和环境的反馈，帮助决定未来的优化行动方案，以及其中使用诸如潜在的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，使跟踪和站点保持等控制目标能够在规定的有限时间期限内实现。使用应用数学来控制生态机器人系统将促进科学进步，因为它导致了更有效的方法来了解污染、石油泄漏或其他环境压力对复杂、动态和无结构海洋环境的影响。这项工作将与两名博士生合作，他们在工程和数学领域的研究将帮助他们为各种潜在的职业生涯做好准备。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情况。这种外展有助于激励一批多样化的、合格的学生干部考虑从事工程或数学职业。该项目的应用部分将专注于算法开发和海洋机器人。此外，这项研究将有可能应用于其他具有事件触发控制、安全或时间约束以及不确定性的环境，如可再生能源网络或智能交通系统。该项目将使用三种策略，帮助解决具有通信或状态约束或优化要求的非线性控制系统的控制理论方面的重大挑战。第一个将为有时间期限的系统设计事件或自触发反馈控制，其触发是根据输出测量计算的，并确定何时重新计算控制以避免不希望的操作模式，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最后期限，因此不太适合工程应用。这将建立在非首席研究员在事件触发非线性控制理论方面的先前工作的基础上，该理论为各种类型的非线性系统开发了几个建设性的设计工具。第二个将在事件或自触发控制下开发稳健的前向不变性方法，帮助预测和量化控制系统在不违反容限和安全界限的情况下所能容忍的不确定性程度。这将建立在首席调查员之前的工作基础上，该工作计算了海洋机器人曲线跟踪中允许的不确定度的界限。第三种是基于有限时间学习的自适应动态规划，它逼近最优策略，以帮助克服传统动态规划中出现的维度诅咒。这将建立在非首席研究员先前在自适应动态规划方面的工作基础上，该工作提出了从输入状态或输入-输出数据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，在水下海洋机器人中，事件触发将处理断断续续的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并评估数学算法。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.