代数黎卡提不等式与多目标优化

ALGEBRAIC RICCATI INEQUALITY AND MULTIPLE PERFORMANCE OPTIMIZATION

本文证明了 H∞ 次优设计问题可以归结为两个代数黎卡提不等式的解 .代数黎卡提不等式形式的特点在于 :如果存在一个正定解 ,那么就可能存在一族正定解 .也就是说 ,我们可以进行多目标优化 ,例如我们可以基于代数黎卡提不等式来设计 H∞ /H2 混合次优控制器 ,并给出了数值实例来说明本文结论的有效性 .

In this paper, the authors propose that H ∞ sub optimization design problem can be solved by solving two algebraic Riccati inequalities. The advantage of using Algebraic Riccati Inequality is that there may be a set of solutions if there is one solution. In other words, we may have the chance to optimize system's multiple performance indexes at the same time. For example, we can design H ∞/H 2 mixed sub optimization controller based on Algebraic Riccati Inequality. More over, an application example is given to illustrate the main results.