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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，例如水下航行器，无人机和自动驾驶汽车，以及不太明显的系统，如电源逆变器，电池存储设备，网络路由器和数据存储设备。延长自主期不可避免地会导致意外变化，例如：系统配置改变或退化;执行器或传感器故障;以及工作环境的演变。如果没有一个自动化的机制来识别和适应这些变化，我们社会的技术基础可能会变得越来越不可靠。该项目的目标是提高复杂系统的自主性。具体而言，优化算法用于学习环境，分析这些信息，并设计控制策略。基于动力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在地球和空间建立一个更加安全和可靠的技术基础设施。提高自治系统的可靠性和持续时间将导致更快和更便宜的空间探索，更安全的交通网络和更可靠的通信网络。最近，平方和（SOS）算法已成为理解非线性动力系统的强大工具。SOS的力量在于它的非二次李雅普诺夫函数的凸参数化。然而，不幸的是，这种凸公式假设的动态是已知的，并没有被扩展到估计的吸引区（罗阿），最小不变集（MIS），和前向可达性（FRS）。在这个项目的核心是新的观察，罗阿/MIS/FRS问题可以表示使用子或超级解决方案的值函数定义的解决方案的哈密尔顿-雅可比-贝尔曼（HJB）方程。该项目的第一部分利用这种等价性表明，罗阿/MIS/FRS的问题可以构成SOS优化问题，其中的目标是体积最小化或最大化的子级集的子/超值函数。该项目的第二部分使用新的凸体积度量来解决这些SOS体积优化问题。该项目的第三部分考虑的情况下，动态是未知的，并使用轨迹数据直接估计的罗阿和FRS，而不使用的动态模型。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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