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

促进稀疏性的大型动力系统网络优化设计本文介绍了大型动力系统网络设计的新方法。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。在具有大量自由度的系统中，主要挑战之一是为其易于处理的分析和设计开发分析和计算方法。子系统之间的相互作用通常会引起复杂的动态响应，这些响应无法通过单独分析子系统来预测。电力网络的停电、交通网络的拥堵、生化网络的时空振荡、流体流动的湍流以及社会网络中信息的传播，说明了高动态秩序系统中出现的复杂且看似不可预测的行为。所提出的工作的广泛影响范围从改善电力系统的性能和抑制停电到传感器网络和多智能体系统的系统设计。教育方面的建议是开发一门新的网络分析和设计入门课程。本课程旨在吸引来自不同工程院系的大四本科生和研究生一年级的学生。智力上的优势在于发展了大型动力系统网络结构辨识和优化设计的理论和技术。PI将结合控制理论、优化和压缩感知的工具和思想，以实现网络性能和控制器稀疏性之间的最佳权衡。该方法包括结构识别和结构优化设计两个步骤。在结构识别步骤中，通过正则化一个最优控制问题来产生稀疏性，该问题会对分布式控制器中的通信要求造成惩罚。与以前的努力相反，这种惩罚将反映这样一个事实，即应该在特定的坐标集中强制执行稀疏性。在确定了控制器结构之后，结构化优化设计步骤将在确定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优传感器和执行器选择的关键问题。虽然，一般来说，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，将其作为一个半确定规划（SDP）。虽然生成的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大型问题。通用解算器无法处理的问题。

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.