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Robust controller synthesis via non-linear matrix inequalities

机译:非线性矩阵不等式的鲁棒控制器综合

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Over the last several years fixed-structure multiplier versions of mixed structured singular value (MSSV) theory have been developed and have led to the development of linear matrix inequalities (LMIs) for the analysis of robust stability andperformance. These LMIs have in turn led to the development of bilinear matrix inequalities BMIs for the synthesis of robust controllers. The BMI formulation in practice requires the multiplier to lie in the span of a stable basis, potentially introducing significant conservatism. This paper uses the LMI approach to MSSV analysis to develop an approach to robust controller synthesis that is based on the stable factors of the multipliers and does not require the multipliers to be restricted to a basis. Itis shown that this approach requires the solution of non-linear matrix inequalities (NMIs). A continuation algorithm is presented for the solution of NMIs. This algorithm may be used to solve NMIs in general and its usefulness is not limited to the robust controller synthesis problem alone. The primary computational burden of the continuation algorithm is the solution of a series of LMIs. The use of this algorithm is demonstrated by designing a robust controller for a benchmark problem.
机译:在过去的几年中,已经开发出混合结构奇异值(MSSV)理论的固定结构乘数形式,并导致线性矩阵不等式(LMI)的发展,用于分析鲁棒稳定性和性能。这些LMI进而导致了用于合成鲁棒控制器的双线性矩阵不等式BMI的发展。在实践中,BMI的制定要求乘数处于一个稳定的基础之内,可能会带来重大的保守主义。本文使用LMI方法对MSSV进行分析,以开发一种基于乘法器稳定因子的鲁棒控制器综合方法,而无需将乘法器限制为基础。结果表明,该方法需要求解非线性矩阵不等式(NMI)。提出了一种求解NMI的连续算法。一般而言,该算法可用于解决NMI,其实用性不仅限于鲁棒的控制器综合问题。连续算法的主要计算负担是一系列LMI的解决方案。通过设计用于基准问题的鲁棒控制器来演示该算法的使用。

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