A Novel Framework for the Efficient and Accurate Solutions of Complex Chance-Constrained Optimal Control Problems

一种高效、准确地解决复杂机会约束最优控制问题的新框架

• 批准号: 1563225
• 负责人: Anil Rao
• 金额: $ 40万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1563225&HistoricalAwards=false
• 关键词: Novel; Framework; Efficient; Accurate; Solutions

This project will create a novel integrated computational framework for formulating and solving optimal control problems in the presence of uncertainty. Optimal control is concerned with finding the user-specified inputs to a dynamic system that will produce the best possible outcome, in the sense that some performance measure is made as small or as large as possible. Typically the outcome must also satisfy additional constraints, capturing physical limitations or operating requirements that the system cannot or must not violate. In uncertain systems subject to significant random influence, both performance and constraints may be characterized probabilistically. One such formulation involves "chance constraints," requiring that a specified undesirable event must be sufficiently unlikely -- for example, the probability that two aircraft will pass within an unsafe distance of each other must be less than a given threshold. Unfortunately chance constraints often lead to formulations that are computationally intractable. This project aims to overcome this obstacle through innovations in four areas, namely 1) the representation of uncertainty in the form of chance constraints, 2) the computationally tractable approximation of chance constraints, 3) the efficient discretization of continuous optimal control problems, and 4) the structuring of the optimal control problem so that it can be split among many different processors using only local information. These innovations will be integrated into a unified framework, amplifying their benefits and ultimately enabling accurate and efficient solution of complex uncertain optimal control problems. Results from this of this work will benefit rapid multi-agent trajectory planning for search, rescue and reconnaissance missions, as well as applications involving human motion, air-traffic control, underwater vehicle control, and hypersonic vehicle mission planning. Educational activities will include outreach to high school students and teachers through the University of Florida Student Science Training Program and Summer Science Institute.Presently, chance-constrained control is almost exclusively dominated by robust model predictive control, invariably involving linear dynamics and convex polyhedral chance constraints, mostly comprising Gaussian random parameters. In contrast, this project will pose trajectory design as a nonlinear chance-constrained optimal control problem in an uncertain environment. The following key aspects will be studied: (a) modeling of the uncertain environment and its contribution to probabilistic constraints on the state and control variables; (b) scalable semi-analytical approximation of nonlinear, nonconvex and potentially high dimensional chance constraints involving non-Gaussian probability measures based on split-Bernstein approximations and Markov chain Monte Carlo; (c) highly accurate and low-dimensional variable-order Gaussian quadrature methods for discretizing the continuous optimization problem arising from the chance-constrained optimal control problem; and (d) a novel large-scale nonlinear programming problem solver for rapidly and accurately solving problems arising from the variable-order Gaussian quadrature discretization. Work in this area can lead to significant contributions in autonomous path planning, extendable to multi-agent systems. This will require efficient and accurate conversion of the joint chance constraints into computationally attractive forms that can be shown to be consistent with and convergent to the originally prescribed chance constraints. This research will lay the foundation for the direct solution of chance-constrained optimal trajectory design by discretizing the transcribed problem using a variable order orthogonal collocation method, solved using an nonlinear programming routine that employs a powerful reverse communication architecture, enabling parallel processing together with a state-of-the-art nonlinear programming algorithm.

该项目将创建一个新颖的集成计算框架，用于在存在不确定性的情况下制定和解决最佳控制问题。最佳控制涉及找到将用户指定的输入到动态系统中，该输入将产生最佳结果，从某种意义上说，某些性能度量是尽可能小的或尽可能大的。通常，结果还必须满足其他限制，捕获系统不能或不得违反的物理限制或操作要求。在受到重大随机影响的不确定系统中，性能和约束都可以概率地表征。一种这样的公式涉及“机会约束”，要求指定的不良事件必须足够不可能 - 例如，两架飞机将在彼此不安全距离内通过的概率必须小于给定的阈值。不幸的是，机会限制通常会导致计算上棘手的制剂。该项目的目的是通过四个领域的创新来克服这一障碍，即1）以机会约束的形式表示不确定性，2）机会约束的计算可处理的近似值，3）有效地离散持续的最佳控制问题，以及4）4）最佳控制问题的结构仅在许多不同的处理器中分布在许多不同的处理器之间。这些创新将集成到一个统一的框架中，扩大其收益，并最终实现复杂不确定的最佳控制问题的准确有效解决方案。这项工作的结果将使搜索，救援和侦察任务的快速多代理轨迹计划以及涉及人类运动，空中交通控制，水下车辆控制和超音速车辆任务计划的应用。教育活动将包括通过佛罗里达大学学生科学培训计划和夏季科学学院向高中生和老师的宣传。偶然受限的控制几乎完全由强大的模型预测性控制，始终涉及线性动力学和凸多面部性的偶然性约束，最多构成高斯随机参数。 相比之下，该项目将在不确定的环境中作为非线性机会约束的最佳控制问题构成轨迹设计。将研究以下关键方面：（a）对不确定环境的建模及其对状态和控制变量概率约束的贡献； （b）基于分裂伯恩斯坦近似值和马尔可夫链蒙特卡洛（Markov Chain Monte Carlo）的非线性，非凸和潜在的高维频率限制的可扩展半分析近似； （c）高度准确且低维的可变级高斯正交方法，用于离散偶然受限的最佳控制问题引起的连续优化问题； （d）一种新型的大规模非线性编程问题求解器，用于快速，准确地解决由可变阶的高斯正交离散化引起的问题。在这一领域的工作可以导致自主路径规划中的重大贡献，可扩展到多代理系统。 这将需要将关节机会约束的有效，准确的转换为计算吸引力的形式，这些形式可以证明与最初规定的机会约束相一致并收敛。这项研究将通过使用可变顺序正交式搭配方法离散转录问题的直接解决方案的直接解决方案，从而使用非线性编程程序来解决，该程序采用强大的反向通信体系结构，从而使并行处理与先行的非线性编程Algorithm一起解决。