Abstract In this work, the generalized value iteration with a discount factor is developed for optimal control of discrete-time nonlinear systems, which is initialized with a positive definite value function rather than zero. The convergence analysis of the discounted value function sequence is provided. The condition for the discount factor is given to guarantee the stability of the controlled plants. With this operation, the iterative control policy that asymptotically stabilizes the closed-loop system can be determined. The introduction of a discount factor has eased some conditions that the system dynamics and the initialization of the generalized value iteration need to fulfill. It is not required that the initial control policy is stabilizing. In the iteration process, under some conditions, if the system is asymptotically stable at the current iteration, then it can be guaranteed that the iterative control policies after this current iteration step also are stabilizing. It is convenient and practical to evaluate the asymptotic stability of the closed-loop system using the iterative control policy. A numerical example with physical background is carried out to validate the present results.

中文翻译：

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具有稳定性分析的折扣最优控制的广义值迭代

摘要 在这项工作中，为离散时间非线性系统的最优控制开发了具有折扣因子的广义值迭代，该系统用正定值函数而不是零初始化。提供了贴现值函数序列的收敛性分析。给出折扣因子的条件是为了保证受控设备的稳定性。通过该操作，可以确定渐近稳定闭环系统的迭代控制策略。折扣因子的引入缓解了系统动力学和广义值迭代初始化需要满足的一些条件。不需要初始控制策略是稳定的。在迭代过程中，在某些条件下，如果系统在本次迭代渐近稳定，则可以保证本次迭代后的迭代控制策略也是稳定的。使用迭代控制策略评估闭环系统的渐近稳定性是方便和实用的。进行了具有物理背景的数值示例以验证当前结果。