This paper aims to solve the model-free linear quadratic regulator problem for discrete-time Markov jump linear systems without requiring an initial stabilizing control policy. We propose both model-based and model-free successive over relaxation algorithms to learn the optimal control policy of discrete-time Markov jump linear systems. The model-free value iteration algorithm is a special case of our model-free algorithm when the relaxation factor equals one. A sufficient condition on the relaxation factor is provided to guarantee the convergence of our algorithms. Moreover, it is proved that our model-free algorithm can obtain an approximate optimal solution when the transition probability matrix is unknown. Finally, a numerical example is used to illustrate our results.

中文翻译：

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离散时间马尔可夫跳跃系统的无模型 LQR 控制的连续过松弛


本文旨在解决离散时间马尔可夫跳跃线性系统的无模型线性二次调节器问题，而无需初始稳定控制策略。我们提出了基于模型和无模型的连续松弛算法，以学习离散时间马尔可夫跳跃线性系统的最佳控制策略。当松弛因子等于 1 时，无模型值迭代算法是无模型算法的一种特例。提供了关于松弛因子的充分条件来保证我们算法的收敛性。此外，证明当转移概率矩阵未知时，我们的无模型算法可以得到近似的最优解。最后，使用一个数值示例来说明我们的结果。