一类不确定随机线性系统的滑模变结构控制

Sliding Mode Variable Structure Control for a Class of Uncertain Stochastic Linear System

针对一类随机线性系统中模型参数不确定的情况,充分考虑到系统状态的相互作用,通过鲁棒控制理论确定滑动面,设计了满足一定状态性能指标的滑模控制律.首先对不含控制量的子系统在不确定的情况下设计了鲁棒反馈控制律,获得了随机稳定的闭环控制子系统;再根据滑模变结构控制理论得到最终的控制律,并在随机系统满足随机I^to微分的前提下,基于Lyapunov方法证明了滑模的可达性和不确定随机系统闭环鲁棒稳定性.数字仿真结果验证了该算法的有效性.

A variable structure uncertain condition. After the control algorithm is presented for a class of linear stochastic system with algorithm fully considering the interaction among system states, a sliding mode hyperplane is designed with the robust control theory. First, the robust feedback control is designed for the uncertain sub system without control input, and then the final control is obtained based on the sliding mode control theory. On the condition that the stochastic system satisfies Ito differential, it is proved with Lyapunov method that the sliding mode hyperplane is reachable and the uncertain stochastic system is asymptotically stable by variable structure control. The numerical results show the effectiveness of the proposed control algorithm.