An LMI approach to structured sparse feedback design in linear control systems
An LMI approach to structured sparse feedback design in linear control systems
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线性控制系统中结构化稀疏反馈设计的 LMI 方法
DOI：
10.23919/ecc.2013.6669578
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
P. Shcherbakov
中科院分区：
文献类型：
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作者：
Boris Polyak;M. Khlebnikov;P. Shcherbakov
考虑线性系统中的经典状态反馈设计，该系统受性能规范的约束，并附加要求控制输入向量u = Kx具有尽可能多的零条目。相应的增益K称为行稀疏控制器。我们提出了一种近似求解这类非凸问题的方法，即在LMI约束下的矩阵范数的最小化。本文的新颖之处在于问题的表述本身和代理的构建。两个主要贡献是用于静态输出反馈的低维输出设计，以及通过LQR说明的次优设计。初步数值实验的结果是双重的。首先，在许多测试问题中，控件的数量大大减少，而性能没有明显损失。其次，通过我们的方法获得的非零条目的数量非常接近或与最小可能的数量一致。该方法可以进一步扩展到处理稀疏公式中的许多最优鲁棒控制问题。
Consider the classical state feedback design in the linear system ẋ = Ax + Bu subject to performance specifications with an additional requirement that the control input vector u = Kx has as many zero entries as possible. The corresponding gain K is referred to as a row-sparse controller. We propose an approach to approximate solution of this kind of nonconvex problems by formulating the proper convex surrogate,-the minimization of a certain matrix norm subject to LMI constraints. The novelty of the paper is the problem formulation itself and the construction of the surrogate. The two main contributions are the design of low-dimensional output to be used in static output feedback, and suboptimal design illustrated via LQR. The results of preliminary numerical experiments are twofold. First, in many test problems, the number of controls was considerably reduced without significant loss in performance. Second, the number of nonzero entries obtained by our method is either very close to or coincide with the minimum possible amount. The approach can be further extended to handle numerous problems of optimal and robust control in sparse formulation.