In this article, a new iterative spiking adaptive dynamic programming (SADP) method based on the Poisson process is developed to solve optimal impulsive control problems. For a fixed time interval, combining the Poisson process and the maximum likelihood estimation (MLE), the three-tuple of state, spiking interval, and probability of Poisson distribution can be computed, and then, the iterative value functions and iterative control laws can be obtained. A property analysis method is developed to show that the value functions converge to optimal performance index function as the iterative index increases from zero to infinity. Finally, two simulation examples are given to verify the effectiveness of the developed algorithm.

中文翻译：

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离散时间非线性系统基于泊松过程的尖峰自适应动态规划

在本文中，开发了一种基于泊松过程的迭代尖峰自适应动态规划（SADP）方法来解决最优脉冲控制问题。对于固定的时间区间，结合泊松过程和最大似然估计（MLE），可以计算泊松分布的状态、尖峰区间和概率三元组，进而得到迭代值函数和迭代控制律获得。开发了一种属性分析方法，以表明随着迭代指数从零增加到无穷大，价值函数收敛到最优性能指数函数。最后通过两个仿真例子验证了所开发算法的有效性。