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摘要: 对于具有未知参数的LQG(Linear quadratic Gaussian)问题,提出了一种次优对偶控制方法,用Kalman滤波处理过程噪声和测量噪声,用前一时刻的后验概率对Cost-to-go进行线性近似,然后,用动态规划获得了次优控制律.最后,用一个例子说明了本文设计的控制器的实施过程.结果表明,该控制律具有良好的对偶性质,并能在学习和控制之间实现较好平衡.
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关键词:
- LQG (Linear quadratic Gaussian) /
- 动态规划 /
- 对偶控制 /
- 最优控制
Abstract: For the LQG problem with unknown parameters, a novel suboptimal dual control approach is proposed in this paper. First, Kalman filter is used to deal with the noises of process and measurement and posterior probabilities at the previous moment are used to linearly approximate the cost-to-go at the present moment. Then dynamic programming is adopted to obtain a suboptimal control law. Finally, an example is presented to illustrate the implementation process of the developed controller. The result shows that this control law has good dual property and achieves a better balance between learning and control.-
Key words:
- LQG (Linear quadratic Gaussian) /
- dynamic programming /
- dual control /
- optimal control
1) 本文责任编委 方海涛 -
表 1 不同不确定参数下Monte Carlo仿真性能指标比较
Table 1 Performance index of Monte Carlo runs comparison for different uncertainty parameters
最优控制 非对偶控制1 非对偶控制2 对偶控制 30.1702 5.1102×105 379.9141 38.6375 表 2 两个控制律性能比较
Table 2 Performance comparison for two control laws in example
控制律 DUL控制 对偶控制 统计平均值 56.4350 39.2685 最大值 148.6953 126.3292 标准差 27.9879 21.2748 -
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