Synthesis of H2 optimal static structured controllers: Primal and dual formulations
Synthesis of H2 optimal static structured controllers: Primal and dual formulations
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H2 最优静态结构控制器的综合：原始公式和对偶公式
DOI：
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发表时间：
2009
期刊：
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通讯作者：
M. Jovanović
中科院分区：
文献类型：
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作者：
Fu Lin;M. Fardad;M. Jovanović
研究了关联大系统的H2最优静态结构反馈增益的设计问题。分布式控制器的设计与访问少量的子系统的测量施加特定的稀疏约束的反馈增益。对于这个非凸约束最优控制问题，我们研究了原始和对偶公式，以获得最优性界。我们利用稀疏性结构存在于大规模系统中实现一个有效的拟牛顿算法来解决原始问题。我们采用次梯度方法来解决对偶问题，并获得了性能指标的最优值的下界。令人惊讶的是，在许多实际问题中，解决原始问题的上限和解决对偶问题的下限几乎是相同的，这表明在这些应用中缺乏对偶差距，并且实际上已经获得了全局最优的结构增益。
We consider the design of H2 optimal static structured feedback gains for large-scale interconnected systems. The design of distributed controllers with access to measurements of a small number of the subsystems imposes particular sparsity constraints on the feedback gains. For this nonconvex constrained optimal control problem, we study both the primal and dual formulations to obtain optimality bounds. We exploit the sparsity structure present in large-scale systems by implementing an efficient quasi-Newton algorithm to solve the primal problem. We employ the subgradient method to solve the dual problem and obtain a lower bound for the optimal value of the performance index. Surprisingly, in many problems of practical interest, the upper bounds from solving primal problems and the lower bounds from solving dual problems are almost identical, suggesting the lack of duality gap in these applications and that the globally optimal structured gains have in fact been attained.