A fusion control strategy, including probability density function (PDF) compensation and gain-scheduled control, is proposed for discrete-time stochastic systems with randomly occurring nonlinearities. Usually, it is difficult to drive the tracking error strictly to zero in a random environment. So the proposed method aims to stabilize the closed-loop system in the exponentially mean square sense and guarantee the distribution of output error as close to the expected PDF as possible. The parameters of the gain-scheduled controller are obtained by solving appropriate linear matrix inequalities, and the parameters of the PDF compensator are updated in real time according to the Kullback–Leibler divergence between the PDF of output error and the desired one. The proposed method has the characteristics of low conservativeness and easy to implement. The effectiveness of the proposed method is shown by two examples.

针对具有随机非线性的离散时间随机系统，提出了一种融合控制策略，包括概率密度函数（PDF）补偿和增益调度控制。通常，在随机环境中很难将跟踪误差严格控制为零。因此，所提出的方法旨在使闭环系统稳定在指数均方意义上，并确保输出误差的分布尽可能接近预期的PDF。通过求解适当的线性矩阵不等式，可以获得增益调度控制器的参数，并根据输出误差PDF与所需误差之间的Kullback-Leibler差异实时更新PDF补偿器的参数。该方法具有保守性低，易于实现的特点。