Variational Method and Computation for H∞ Control
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摘要: 通过将未来时段(t,tf]H∞状态反馈问题的泛函指标和过去时段[0,t)H∞滤波问题的泛函指标组合在一起,可以得到整个时段[0,tf]的H∞ 量测反馈问题的泛函指标,从而可以将变分法进一步用于研究H∞量测反馈问题。在过去时段与未来时段的连接点,即当前时刻t,有两个连接条件:一个是估计状态x(t)必须是未来时段状态向量估计的初始条件,另一个关于协态向量λ(t)的连接条件则可以由变分原理导出。进一步的推证表明:最优参数γcr-2所满足的第三个条件依然是最小瑞利商。因此精细积分方法可以用于H∞量测反馈控制问题最优参数的计算,此前该方法已用来计算H∞状态反馈和H∞滤波问题中的最优参数γcr-2。Abstract: The variational approach is further applied to the measurement feedback H∞ control problems.Based on the induced norm description of the system Г,the variational functionals Jc and Jp of state feedback H∞ control for the future time interval(t,tf],and of H∞ filter for the past time interval[0,t),respectively,are combined together to generate the variational functional of the measurement feedback for the whole time interval[0,tf].The connection condition at the present time t is that the estimated state vector x(t) must be continuously extended to be the initial condition of the future state vector estimation.Another connection condition for the dual vector K(t)can be naturally derived from the variational principle.The equations thus derived show that the third condition for the optimal parameter γcr-2 is again a bound of the smallest Rayleigh quotient.Therefore,the precise integration method developed formerly to determine the optimal parameter γcr-2 of H∞ control and of H∞ filter respectively can be further applied to the determination of the optimal parameter.
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Key words:
- H∞ control /
- Rayleigh quotient /
- variational principle /
- precise integration
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