Collaborative Research: Designs and Theory for Interval Contractors and Reference Governors with Aerospace Applications

合作研究：间隔承包商和参考调速器与航空航天应用的设计和理论

• 批准号: 2308282
• 负责人: Michael Malisoff
• 金额: $ 21万
• 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: 2023
• 资助国家: 美国
• 起止时间: 2023-08-01 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2308282&HistoricalAwards=false
• 关键词: Collaborative; Research; Designs; Theory; Interval

This project will produce mathematical methods for the control of important classes of dynamical systems that are used in aerospace engineering. The controls will be modeled as forcing functions, which represent the admissible forces that can be applied to the dynamics. The focus will be on producing formulas for controls that ensure that desirable prescribed control objectives are met for dynamical systems that contain significant input or state constraints. Input constraints are restrictions on forces that can be applied to the systems, such as maximum allowable thrusts for an aerial vehicle. State constraints are restrictions on the allowable states of the systems, which can arise from obstacle avoidance requirements or the need to keep the pitch or roll of an aerial vehicle in safe ranges. The research is amenable to significant engineering applications with either incomplete information about the systems' states or surroundings, or where there are time deadlines or latencies when achieving prescribed control goals. Latencies in mathematical models are important for modeling the delayed effects of applying forces to dynamical systems. The potential applications include using aerospace engineering methods for national defense, for search and rescue, or for drones that can deliver medical supplies in developing countries that may not yet have well equipped runways. The methods will be tested in numerical simulations, using mathematical models of quadrotors and fixed wing aircraft, and then in real time in an aerospace engineering lab and outdoors using flying platforms. In addition to generating fundamental knowledge that can enhance the performance of aerospace systems in national defense or other significant domains, the project will train PhD students at the interface of aerospace engineering and mathematics. This will help increase the population of US applied mathematicians who can collaborate with engineers and who can use state-of-the-art mathematical techniques to help solve important societal problems.The project will pursue three research strategies. One strategy will develop interval contractors, which are iterative techniques for estimating solutions of uncertain dynamical systems under incomplete information about the current state of the dynamics, focusing on how uncertainty in state and input measurements affect the contraction of the intervals and deriving conditions under which the intervals contract to small enough tubes around unknown time-varying functions in finite time. This strategy will build on the investigators' preliminary results that illustrate significant improvement in tracking in aerospace models that is achievable when interval contractors are used in conjunction with state augmentation methods and convexity arguments to transform polynomial state constraints into more easily handled linear constraints. A second strategy will develop finite time extremum seeking methods, which identify extrema of uncertain functions using sampled or delayed measurements and where the identification process uses interval contractors, and which are therefore a significant departure from standard optimization methods where the objective function is assumed to be known. A third strategy will be robust reference governors, which are add-on schemes for control systems that prevent input or state violations while maintaining the performance of controls that were designed in the absence of input or state constraints. This strategy will focus on using interval contractors to ensure finite time convergence, under unknown delays in continuous and discrete time and perturbed sampled measurements that can model the effects of image processing. The project would prove theorems that provide sufficient conditions for the methods to satisfy prescribed convergence properties with a view towards findings rates of convergence, which is a significant departure from research in the engineering community that was mainly experimental. The applications will include propellant slosh mitigation, automatic safe landing, and source seeking.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.

该项目将产生数学方法，以控制航空航天工程中使用的重要类动力系统类别。控件将建模为强迫函数，该功能代表可应用的功能，可以应用于动力学。重点将放在为控件生成公式上，以确保对包含重要输入或状态约束的动态系统满足理想的规定控制目标。输入限制是对可以应用于系统的力的限制，例如航空车辆的最大允许推力。状态限制是对系统允许状态的限制，这可能是由于避免障碍的要求或需要保持航空车辆在安全范围内的螺距或滚动的需求。这项研究适合重要的工程应用程序，具有有关系统状态或周围环境的不完整信息，或者在实现规定的控制目标时的时间截止日期或潜伏期。数学模型中的潜伏期对于建模将力施加到动态系统的延迟影响很重要。潜在的应用包括使用航空航天工程方法进行国防，进行搜救，或用于在发展中国家提供医疗用品的无人机，这些国家可能还没有设备齐全的跑道。该方法将使用数值模拟，使用四型和固定机翼飞机的数学模型进行测试，然后在航空航天工程实验室和户外使用飞行平台实时测试。除了产生基本知识以增强航空航天系统在国防或其他重要领域的性能外，该项目还将在航空航天工程和数学的界面上培训博士生。这将有助于增加我们应用数学家的人口，他们可以与工程师合作，并可以使用最先进的数学技术来帮助解决重要的社会问题。该项目将采取三种研究策略。一种策略将开发间隔承包商，这是迭代技术，用于估算有关动力学当前状态的不完整信息的不确定动力系统解决方案的解决方案，重点介绍了状态和输入测量的不确定性如何影响间隔的收缩，并在有限的时间内围绕未知时间的小管汇总到不知名的小管中的条件，这些条件在这些条件下会产生。该策略将建立在研究人员的初步结果的基础上，该结果说明了航空航天模型中跟踪的显着改善，当间隔承包商与状态增强方法结合使用时，可以实现，并且可以将多项式约束转换为更容易处理的线性约束。第二种策略将开发有限的时间超值寻求方法，该方法使用采样或延迟测量值确定不确定功能的极端功能，以及识别过程使用间隔承包商，因此与假定目标函数已知的标准优化方法有很大的不同。第三个策略将是强大的参考调查员，它们是控制系统的附加方案，可防止输入或状态违规，同时保持在没有输入或状态约束的情况下设计的控件的性能。该策略将集中于使用间隔承包商来确保有限的时间收敛，在连续和离散的时间和扰动的采样测量中，可以模拟图像处理的效果。该项目将证明定理为满足规定的融合特性提供足够条件的定理，以朝着融合的发现率视图，这与工程界的研究显着不同，这主要是实验性的。这些申请将包括缓解推进剂SLOSH，自动安全着陆和来源寻求。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响评估标准通过评估来支持的。