Optimization of spatially distributed systems with spatially local controllers and partial connectivity
Optimization of spatially distributed systems with spatially local controllers and partial connectivity
复制标题
具有空间局部控制器和部分连通性的空间分布式系统的优化
DOI：
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发表时间：
2014
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通讯作者：
M. Demetriou
中科院分区：
文献类型：
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作者：
M. Demetriou
针对一类偏微分方程提出了两种不同的网络化分布式控制器设计方法。这样的工作试图通过选择由互连的控制单元的网络控制空间分布的过程来降低控制器的复杂性。这种方法减少了使用集中式控制器的需要，集中式控制器必须通过分布式传感器融合传感信息，然后通过空间分布的致动器将控制器分配给空间分布的过程。在第一种方法中，控制器单元用于实现本地控制器的控制器增益，沿着的致动器和传感器的位置和网络的连通性进行了优化，通过制定的优化问题到一个适当选择的性能测量的闭环系统的最小化问题。这需要一个参数化的运营商李雅普诺夫方程的形式，其最优解提供了最佳的（比例）控制器增益，最佳位置的执行器和传感器，以及最佳的网络连接。第二种方法认为，使用Lyapunov重新设计方法提取其适应的分布式控制器的增益的适应。所提出的控制器的适定性和收敛性能进行了总结，并提出了研究所提出的工作的各个方面的数值研究。
This paper presents two different design approaches of networked distributed controllers for a class of partial differential equations. Such a work attempts to reduce controller complexity by opting to control a spatially distributed process by a network of interconnected control units. This approach reduces the need to use a centralized controller that must fuse sensory information by the distributed sensors and then dispense the controllers to the spatially distributed process via the spatially distributed actuators. In the first approach, the controller gains used to implement the local controllers by the controller units, along with the actuator and sensor location and the network connectivity are optimized by formulating the optimization problem into a minimization problem of an appropriately chosen performance measure of the closed-loop system. This takes the form of a parameterized operator Lyapunov equation whose optimal solution provides the optimal (proportional) controller gains, the optimal locations of the actuators and sensors, and the optimal network connectivity. The second approach considers the adaptation of the gains of the distributed controllers using Lyapunov-redesign methods to extract their adaptation. The well-posedness and convergence properties of the proposed controllers are summarized and numerical studies examining various aspects of the proposed work are presented.