On Event-Based Sampling for $\mathcal{H}_2$-Optimal Control
arXiv: Optimization and Control(2017)
摘要
We consider the problem of finding an event-based sampling scheme that optimizes the trade-off between sampling rate and $mathcal{H}_2$ performance of a linear time-invariant system driven by white noise. We base our analysis on a recently presented sampled-data controller structure, which has been proven to be $mathcal{H}_2$-optimal for any given sampling sequence. We show that optimization of the sampling scheme is related to an elliptic convection-diffusion type partial differential equation over a domain with free boundary, a so called Stefan problem. A closed form of the optimal sampling scheme is presented for the multidimensional integrator case, together with a numerical method for obtaining it in the second order general case. In the integrator case, we prove that the optimal event-based sampling scheme will always outperform periodic sampling, and present tight bounds on the improvement. Also, we give numerical examples demonstrating the performance improvement for both the integrator case and a more general case.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络