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优控制问题。最佳控制涉及找到用户指定的动态系统输入，该系统将产生最佳可能的结果，即某些性能指标尽可能小或尽可能大。通常，结果还必须满足额外的约束，捕获系统不能或不得违反的物理限制或操作要求。在受到显着随机影响的不确定系统中，性能和约束都可以通过概率来表征。其中一种表述涉及“机会约束”，要求特定的不良事件必须足够不可能——例如，两架飞机在彼此不安全距离内通过的概率必须小于给定阈值。不幸的是，机会约束常常导致计算上难以处理的公式。该项目旨在通过四个领域的创新来克服这一障碍，即 1）以机会约束形式表示不确定性，2）机会约束的计算上易于处理的近似，3）连续最优控制问题的有效离散化，以及 4 ）最优控制问题的结构化，以便仅使用本地信息就可以将其分割到许多不同的处理器中。这些创新将被整合到一个统一的框架中，放大它们的优势，并最终能够准确有效地解决复杂的不确定最优控制问题。这项工作的结果将有利于搜索、救援和侦察任务的快速多智能体轨迹规划，以及涉及人体运动、空中交通管制、水下航行器控制和高超音速飞行器任务规划的应用。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研究所向高中生和教师进行推广。目前，机会约束控制几乎完全由鲁棒模型预测控制主导，总是涉及线性动力学和凸多面体机会约束，主要由高斯随机参数组成。 相比之下，该项目将轨迹设计视为不确定环境中的非线性机会约束最优控制问题。将研究以下关键方面： (a) 不确定环境的建模及其对状态和控制变量的概率约束的贡献； (b) 非线性、非凸和潜在高维机会约束的可扩展半解析近似，涉及基于分裂伯恩斯坦近似和马尔可夫链蒙特卡罗的非高斯概率测量； (c) 高精度、低维变阶高斯求积方法，用于离散机会约束最优控制问题所产生的连续优化问题； (d)一种新颖的大规模非线性规划问题求解器，用于快速准确地求解变阶高斯求积离散化所产生的问题。该领域的工作可以为自主路径规划做出重大贡献，并可扩展到多智能体系统。 这将需要将联合机会约束有效且准确地转换为计算上有吸引力的形式，这些形式可以被证明与最初规定的机会约束一致并收敛。这项研究将为机会约束最优轨迹设计的直接解决方案奠定基础，通过使用变阶正交配置方法离散转录问题，使用非线性编程例程解决，该例程采用强大的反向通信架构，实现并行处理和最先进的非线性规划算法。