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首页> 外文期刊>IEEE Transactions on Automatic Control >Sparsity Promotion in State Feedback Controller Design
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Sparsity Promotion in State Feedback Controller Design

机译：状态反馈控制器设计中的稀疏性提升

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摘要

A globally convergent algorithm for synthesis of sparse optimal state feedback (SOSF) control of linear time-invariant (LTI) systems is proposed. This problem is known to be NP-hard due to its combinatorial nature. A structured norm controller design problem is intrinsically non-convex, even if a fixed structure is known in advance. The proposed algorithm minimizes the norm performance index, and simultaneously regularizes the sparsity of the control structure using the norm. It guarantees that the solution converges to a stationary point of the original problem. The algorithm is implemented using Linear Matrix Inequalities (LMIs) which are efficient, reliable and extendable to other control problems. The performance of the proposed algorithm is illustrated with application to several examples. The results are also compared with Alternating Direction Method of Multiplier (ADMM) for sparse LQR design (as a special case of the norm problem). In most instances, the appropriate selection of the control structure leads to a near optimal performance index with a substantially reduced number of communication links.
机译：提出了一种全局收敛的线性时不变（LTI）系统的稀疏最优状态反馈（SOSF）控制综合算法。由于其组合性质，已知此问题是NP难题。结构化的规范控制器设计问题本质上是非凸的，即使预先知道固定结构也是如此。所提出的算法使规范性能指标最小化，并同时使用规范来规范控制结构的稀疏性。它保证了解决方案收敛到原始问题的固定点。该算法使用有效，可靠且可扩展到其他控制问题的线性矩阵不等式（LMI）来实现。将该算法应用于几个示例进行了说明。还将结果与用于稀疏LQR设计（作为规范问题的特例）的乘数交变方向法（ADMM）进行比较。在大多数情况下，对控制结构的适当选择会导致接近最佳的性能指标，并且通信链路的数量会大大减少。

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