Sparsity-promoting optimal design of large-scale networks of dynamical systems

大规模动力系统网络的稀疏性优化优化设计

• 批准号: 1407958
• 负责人: Mihailo Jovanovic
• 金额: $ 38.97万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-15 至 2017-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1407958&HistoricalAwards=false
• 关键词: Sparsity; promoting; optimal; design; large

Sparsity-promoting optimal design of large-scale networks of dynamical systemsThe proposal introduces new methods for the design of large-scale networks of dynamical systems. Systems of this type arise in applications ranging from distributed power generation, to coordination of unmanned aerial vehicles and deployment of teams of robotic agents, to control of fluid flows around wind turbines and vehicles, to control of segmented mirrors in extremely large telescopes. One of the major challenges in systems with large number of degrees of freedom is the development of analytical and computational methods for their tractable analysis and design.Interactions between subsystems often induce complex dynamical responses that cannot be predicted by analyzing subsystems in isolation. Blackouts in power networks, congestion in transportation networks, spatio-temporal oscillations in biochemical networks, turbulence in fluid flows, and the spread of information in social networks illustrate the complex and seemingly unpredictable behavior that arises in systems of high dynamical order. The broader impacts of the proposed work range from improved performance and suppression of blackouts in power systems to systematic design of sensor networks and multi-agent systems. The educational aspect of the proposal is to develop a new introductory course on analysis and design of networks. This course will be aimed at attracting students from diverse engineering departments at senior undergraduate and first year graduate levels.The intellectual merit lies in the development of theory and techniques for structure identification and optimal design of large networks of dynamical systems. The PI will combine tools and ideas from control theory, optimization, and compressive sensing to achieve an optimal tradeoff between network performance and controller sparsity. The proposed approach involves both structure identification and structured optimal design steps. In the structure identification step, sparsity will be induced by regularizing an optimal control problem with a penalty on communication requirements in the distributed controller. In contrast to previous efforts, this penalty will reflect the fact that sparsity should be enforced in a specific set of coordinates. After having identified a controller structure, the structured optimal design step will optimize the network performance over the identified structure. Alongside the sparse feedback synthesis, the PI will address the critical question of optimal sensor and actuator selection in large-scale networks.Although, in general, finding the solution to this problem requires an intractable combinatorial search, this award will draw upon recent developments in sparse representations to cast it as a semidefinite program (SDP). While the resulting SDP can be solved using general-purpose solvers, the PI will develop customized algorithms to exploit the problem structure and reduce computational complexity. Such customized solvers will be capable of dealing with large problems.that general-purpose solvers are not able to handle.

稀疏促进优化设计的大规模网络的动力系统的建议介绍了新的方法设计的大规模网络的动力系统。这种类型的系统出现在各种应用中，从分布式发电，到无人驾驶飞行器的协调和机器人代理团队的部署，到控制风力涡轮机和车辆周围的流体流动，到控制超大望远镜中的分段反射镜。大自由度系统的主要挑战之一是发展易于分析和设计的分析和计算方法。子系统之间的相互作用往往会导致复杂的动力响应，这些响应不能通过孤立地分析子系统来预测。电力网络中的停电、交通网络中的拥堵、生化网络中的时空振荡、流体流动中的湍流以及社交网络中的信息传播，都说明了在高度动态秩序的系统中出现的复杂且看似不可预测的行为。所提出的工作范围从提高性能和抑制电力系统停电的传感器网络和多代理系统的系统设计的更广泛的影响。建议的教育方面是开发一个新的网络分析和设计入门课程。本课程的目标是吸引不同工程系的高年级本科生和研究生一年级的学生，其智力价值在于发展大型动力系统网络的结构识别和优化设计的理论和技术。PI将结合联合收割机的工具和思想，从控制理论，优化和压缩感知，以实现网络性能和控制器稀疏之间的最佳权衡。所提出的方法包括结构识别和结构优化设计步骤。在结构识别步骤中，稀疏性将通过正则化最优控制问题来诱导，并对分布式控制器中的通信要求进行惩罚。与以前的努力相比，这种惩罚将反映这样一个事实，即稀疏性应该在一组特定的坐标中强制执行。在识别了控制器结构之后，结构化的最优设计步骤将在所识别的结构上优化网络性能。除了稀疏反馈综合，PI将解决大规模网络中最佳传感器和执行器选择的关键问题。虽然，在一般情况下，找到这个问题的解决方案需要一个棘手的组合搜索，这个奖项将借鉴稀疏表示的最新发展，把它作为一个半定规划（SDP）。虽然由此产生的SDP可以使用通用求解器来求解，但PI将开发定制算法来利用问题结构并降低计算复杂性。这种定制的求解器将能够处理通用求解器无法处理的大型问题。