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

稀疏性促进动力系统大规模网络的优化设计该提案为大规模动力系统网络的设计引入了新的方法。这种类型的系统出现在各种应用中，从分布式发电到协调无人驾驶飞行器和部署机器人代理团队，到控制风力涡轮机和车辆周围的流体流动，再到控制超大型望远镜中的分段镜。多自由度系统面临的主要挑战之一是发展分析和计算方法以便于分析和设计。子系统之间的相互作用经常导致复杂的动力响应，而通过单独分析子系统无法预测这些响应。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会网络中信息的传播，说明了在高动态秩序系统中出现的复杂且看似不可预测的行为。拟议工作的更广泛影响范围从提高电力系统的性能和抑制停电到传感器网络和多代理系统的系统设计。该提案的教育方面是开发一门关于网络分析和设计的新入门课程。这门课程的目标是吸引来自不同工程系的高年级、本科生和一年级研究生。其智力优势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将结合控制理论、优化和压缩感知的工具和思想，在网络性能和控制器稀疏性之间实现最佳折衷。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，通过将最优控制问题正则化，并以分布式控制器中的通信要求为代价来引入稀疏性。与以前的努力不同，这一处罚将反映这样一个事实，即应该在一组特定的坐标中执行稀疏性。在确定了控制器结构之后，结构化优化设计步骤将在所确定的结构上优化网络性能。除了稀疏反馈综合，PI还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。尽管通常情况下，找到该问题的解决方案需要棘手的组合搜索，但该奖项将利用稀疏表示的最新发展将其视为半定规划(SDP)。虽然生成的SDP可以使用通用解算器求解，但PI将开发定制算法来利用问题结构并降低计算复杂性。这种定制的解算器将能够处理大型问题，而这是通用解算器无法处理的。

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.