权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

An Optimization Approach for Nonlinear Optimal Feedback Control Design and Uncertainty Propagation

非线性最优反馈控制设计和不确定性传播的优化方法

基本信息

批准号：
1826990
负责人：
Puneet Singla
金额：
$ 31.78万
依托单位：
Pennsylvania State Univ University Park
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-08-15 至 2019-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1826990&HistoricalAwards=false
关键词：
Optimization Approach Nonlinear Optimal Feedback

项目摘要

The multi-resolution articulation abilities of the next-generation autonomous systems, used in advanced robotics, rehabilitation, tele-operation, manufacturing and infrastructure applications are made possible by unique designs and complex mechanisms. These next generation robotic systems can benefit greatly by the development of computationally efficient tools to synthesize optimal feedback control laws to achieve specified output signal statistics in presence of model and sensing uncertainties. To support commercial applications such as package delivery, it is imperative that the robotic systems operating in uncertain environments negotiate specific waypoints with prescribed tolerance. This unique challenge of routing the vehicles operating in uncertain environments involves a strong coupling between the uncertainty propagation and control. Successful negotiation of this challenge is contingent on the development of stable optimal feedback control laws, while accounting for the uncertainties that pervade dynamical systems. The fundamental formalisms that underpin this research are widely applicable to the control of next generation robotic systems and unmanned vehicles. The project includes plans to integrate research into educational efforts involving graduate and undergraduate students, including expanding efforts to reach under-represented populations in science and engineering. Outreach activities include the technical interchange meetings with local school teachers and instituting robotics related tutorial courses to motivate middle and high school students.The focus of the research is to investigate a unified approach to stable optimal feedback control laws and uncertainty propagation methods by developing computationally efficient solutions to the Hamilton Jacobi Bellman (HJB) and Fokker-Planck-Kolmogorov (FPK) partial differential equations (PDEs), respectively. Recent advances in sparse approximation and non-product quadrature rules are exploited to solve the HJB and FPK equations. The intellectual merits are drawn from advancing the state of knowledge in uncertainty quantification, optimal control theory, and numerical analysis, and integrating them effectively to realize a scalable framework for study of dynamical systems. The Conjugate Unscented Transformation (CUT) technique in conjunction with sparse approximation methods forms an enabling tool to drive the uncertainty propagation and optimal feedback control realization processes. This research culminates in the development of nonlinear stable feedback control laws for uncertain dynamic systems, impacting various estimation and control problems in engineering. The proposed research will be demonstrated on several benchmark problems, along with two key applications involving optimal momentum transfer in control of gyroscopic systems and surveillance of a ground region with the help of unmanned vehicles.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.

通过独特的设计和复杂的机制，下一代自主系统的多分辨率连接能力，用于先进的机器人，康复，远程操作，制造和基础设施应用。这些下一代机器人系统可以大大受益于计算效率的工具的发展，以合成最优反馈控制律，以实现指定的输出信号统计模型和传感不确定性的存在。为了支持商业应用，如包裹递送，在不确定环境中操作的机器人系统必须以规定的公差协商特定的航路点。这种独特的挑战，路由的车辆在不确定的环境中运行，涉及到不确定性传播和控制之间的强耦合。成功的谈判，这一挑战是取决于稳定的最优反馈控制律的发展，同时占弥漫动力系统的不确定性。支撑这项研究的基本形式主义广泛适用于下一代机器人系统和无人驾驶车辆的控制。该项目包括将研究纳入涉及研究生和本科生的教育工作的计划，包括扩大努力，以接触科学和工程领域代表性不足的人口。外展活动包括与当地学校教师的技术交流会议和建立机器人相关的辅导课程，以激励初中和高中学生。研究的重点是通过开发计算有效的解决方案，汉密尔顿雅可比贝尔曼（HJB）和福克-普朗克-科尔莫戈罗夫（FPK）偏微分方程，研究稳定的最佳反馈控制律和不确定性传播方法的统一方法（PDE）。稀疏逼近和非积求积规则的最新进展被用来解决HJB和FPK方程。知识的优点是从推进不确定性量化，最优控制理论和数值分析的知识状态，并有效地整合它们，以实现一个可扩展的框架，研究动态系统。共轭无迹变换（CUT）技术结合稀疏近似方法形成了一个使能工具，以驱动不确定性传播和最优反馈控制实现过程。这项研究的高潮是不确定动态系统的非线性稳定反馈控制律的发展，影响工程中的各种估计和控制问题。拟议的研究将在几个基准问题上得到证明，沿着两个关键应用，涉及陀螺系统控制中的最佳动量传递和无人驾驶车辆帮助下的地面区域监视。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。