A Convex Computational Framework for Understanding and Controlling Nonlinear Systems

用于理解和控制非线性系统的凸计算框架

基本信息

批准号：
1931270
负责人：
Matthew Peet
金额：
$ 26.78万
依托单位：
Arizona State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-09-01 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1931270&HistoricalAwards=false
关键词：
Convex Computational Framework Understanding Controlling

项目摘要

Complicated engineered systems have become increasingly common and autonomous, with examples including underwater vehicles, UAVs, and self-driving cars, as well as less visible systems such as power inverters, battery storage devices, network routers, and data storage devices. Extended periods of autonomy inevitably lead to such unexpected changes as: altered or degraded system configuration; failures of actuators or sensors; and evolution of the working environment. Without an automated mechanism for identification of and adaptation to such changes, it is likely that the technological foundation of our society will become increasingly unreliable. The goal of the project is to improve autonomy in complicated systems. Specifically, optimization algorithms are used to learn the environment, analyze this information, and design control strategies. Based on fundamental theory of how dynamical systems operate, these algorithms provide a rigorous basis for cognizance and adaptability. The impact of this work will be a more safe and reliable technological infrastructure, both on earth and in space. Increasing the reliability and duration of autonomous systems will lead to, for example, faster and cheaper exploration of space, safer transportation networks, and more reliable communication networks.Recently, Sum-of-Squares (SOS) algorithms have become a powerful tool for understanding nonlinear dynamical systems. The power of SOS lies in its convex parametrization of non-quadratic Lyapunov functions. Unfortunately, however, this convex formulation assumes the dynamics are known and has not been extended to estimating the Region of Attraction (ROA), Minimum Invariant Set (MIS), and Forward Reachability (FRS). At the core of this project is the novel observation that the ROA/MIS/FRS problems can be expressed using sub- or super-solutions to a value function defined by the solution to a Hamilton-Jacobi-Bellman (HJB) equation. The first part of the project exploits this equivalence to show that the ROA/MIS/FRS problems can be posed as SOS optimization problems wherein the objective is volume minimization or maximization of sublevel sets of a sub/super-value function. The second part of the project uses new convex volume metrics to solve these SOS volume optimization problems. The third part of the project considers the case where the dynamics are unknown and uses trajectory data to directly estimate the ROA and FRS without use of a dynamic model. The algorithms are also applied to control of spacecraft attitude dynamics.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.

复杂的工程系统已经变得越来越普遍和自主，包括水下车辆，无人机和自动驾驶汽车在内的示例，以及较低的可见系统，例如电源逆变器，电池存储设备，网络路由器和数据存储设备。延长的自主性不可避免地会导致出乎意料的变化：更改或退化的系统配置；执行器或传感器的失败；和工作环境的发展。如果没有自动化的机制来识别和适应这种变化，我们社会的技术基础可能会变得越来越不可靠。该项目的目的是提高复杂系统中的自主权。具体而言，优化算法用于学习环境，分析此信息和设计控制策略。基于动态系统如何运行的基本理论，这些算法为认知和适应性提供了严格的基础。这项工作的影响将是地球和太空中更安全和可靠的技术基础设施。增加自主系统的可靠性和持续时间将导致例如，更快，更便宜的空间探索，更安全的运输网络以及更可靠的通信网络。 SOS的力量在于其非二次lyapunov函数的凸参数化。但是，不幸的是，该凸公式假设该动力学是已知的，并且尚未扩展到估计吸引区域（ROA），最小不变集（MIS）和正向达到性（FRS）。该项目的核心是新的观察结果，即ROA/MIS/FRS问题可以使用hamilton-Jacobi-Bellman（HJB）方程的解决方案定义的值函数来表达。该项目的第一部分利用了这种等效性，以表明ROA/MIS/FRS问题可以作为SOS优化问题，其中该目标是体积最小化或最大化子/超级价值函数的Sublevel集合。该项目的第二部分使用新的凸量指标来解决这些SOS体积优化问题。该项目的第三部分考虑了动力学未知并使用轨迹数据直接估算ROA和FRS而无需使用动态模型的情况。该算法还用于控制航天器态度动力学。该奖项反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响标准，被认为值得通过评估来获得支持。

项目成果

期刊论文数量（18）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

SOSTOOLS Version 4.00 Sum of Squares Optimization Toolbox for MATLAB

DOI：
发表时间：
2013-10
期刊：
影响因子：
0
作者：
A. Papachristodoulou;James Anderson;G. Valmórbida;S. Prajna;Peter J Seiler;P. Parrilo;M. Peet;Declan S. Jagt
通讯作者：
A. Papachristodoulou;James Anderson;G. Valmórbida;S. Prajna;Peter J Seiler;P. Parrilo;M. Peet;Declan S. Jagt

Efficient Data Structures for Representation of Polynomial Optimization Problems: Implementation in SOSTOOLS