Monte Carlo Statistical Prediction Method for Optimal Control of Linear Hybrid Systems
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摘要: 针对含扩散项的线性混杂切换系统优化控制问题, 为降低优化求解的计算复杂性, 提出了Monte Carlo统计预测方法. 首先通过数值求解技术把连续时间优化控制问题转化为离散时间的Markov决策过程问题; 然后在若干有限状态子空间内, 利用反射边界技术来求解相应子空间的最优控制策略; 最后根据最优控制策略的结构特性, 采用统计预测方法来预测出整个状态空间的最优控制策略. 该方法能有效降低求解涉及大状态空间及多维变量的线性混杂切换系统优化控制的计算复杂性, 文末的仿真结果验证了方法的有效性.
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关键词:
- 线性混杂系统 /
- 最优控制 /
- 数值解 /
- Monte Carlo统计预测
Abstract: To reduce the computational complexity of optimal control of linear hybrid switching diffusion systems, a new Monte Carlo statistical prediction method is proposed. Firstly, the original optimal control problem in continuous time is approximated by a Markov decision problem in discrete time using numerical method; secondly, the numerical optimal control policies in some random sub-state spaces are obtained by reflecting boundary technique; and finally, the optimal control policy on the entire state space is predicted by statistical prediction based on the structure of the optimal control policy. The method can decrease the computational complexity and can be extended to cases of high dimension and large state space. Numerical examples illustrate and confirm the effectivity of the proposed method.
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