Convex Optimization Approaches to Information Structured Decentralized Control
Convex Optimization Approaches to Information Structured Decentralized Control
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DOI：
10.1109/tac.2018.2830112
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发表时间：
2018-04
影响因子：
6.8
通讯作者：
Yin Wang;Jose A. Lopez;M. Sznaier
中科院分区：
文献类型：
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作者：
Yin Wang;Jose A. Lopez;M. Sznaier
本文考虑稀疏约束下的输出反馈控制器综合问题。这个问题通常是NP难的，除非被控对象满足二次不变性。我们的主要结果表明，即使这个属性不成立，易于处理的凸松弛与最优性证书可以通过使用多面体李雅普诺夫函数重铸成一个多项式优化的问题。将这些想法与秩最小化工具相结合，导致计算上有吸引力的算法。作为一种替代方案，我们提出了第二次放松，具有较低的计算复杂度，基于找到所需的控制动作的最佳稀疏估计。这些结果说明了几个例子。
This paper considers the problem of synthesizing output feedback controllers subject to sparsity constraints. This problem is known to be generically NP-hard, unless the plant satisfies the quadratic invariance property. Our main results show that, even if this property does not hold, tractable convex relaxations with optimality certificates can be obtained by recasting the problem into a polynomial optimization through the use of polyhedral Lyapunov functions. Combining these ideas with rank minimization tools leads to a computationally attractive algorithm. As an alternative, we present a second relaxation, with lower computational complexity, based on finding the best sparse estimate of a desired control action. These results are illustrated with several examples.