计及随机传感器时滞的不确定半Markov跳变系统鲁棒滑模控制

Robust sliding mode control for uncertain semi-Markov jump systems with random sensor time delay

中文关键词  半Markov跳变系统  滑模控制  鲁棒控制  模态依赖Luenberger观测器  随机传感器时滞

英文关键词  semi-Markov jump systems  sliding mode control  robust control  mode-dependent Luenberger observer  random sensor time delay

中文摘要

      在实际系统中, 系统参数与结构随机变化、未知外界干扰、传感器时滞等现象时有发生并严重影响了系统 的稳定运行. 为了解决这一问题, 本文提出计及随机传感器时滞的一类不确定半Markov跳变系统鲁棒滑模控制方 法, 其中系统的传感器时滞通过使用Bernoulli随机分布进行描述. 考虑系统状态信息不可测量条件下, 文章设 计模态依赖Luenberger 观测器去估计半Markov 跳变系统的运行状态. 然后, 本文构造一个积分滑模面并借助随机 Lyapunov理论, 提出两种半Markov跳变系统的随机稳定性分析方法. 进而, 文章提出基于观测器的滑模控制方法使 得系统状态能够在有限时间内到达滑模面上以及滑模动态在H∞性能指标γ下是随机稳定的. 最后, 通过一种基于 他励直流电动机模型的数值仿真例子验证所设计的滑模控制方法的有效性与正确性.

英文摘要

      In practical systems, random changes of system parameters and structures, unknown external disturbance, sensor time delay and other phenomena occur from time to time, which seriously affect the stable operation of the system. In order to solve this problem, this paper proposes a robust sliding mode control method for a class of uncertain semi- Markov jump systems with stochastic sensor time delay, in which the sensor time delay is described by Bernoulli stochastic distribution. Considering that the system state information cannot be measured, the mode-dependent Luenberger observer is designed to estimate the operating state of the semi-Markov jump system. Then, an integral sliding mode surface is constructed and two stochastic stability analysis methods for semi-Markov jump systems are proposed based on stochastic Lyapunov theory. Furthermore, the observer-based sliding mode control method is proposed to make the system states reach the sliding mode surface in finite time and the sliding mode dynamic is stochastically stable with H∞ performance index γ. Finally, the effectiveness and correctness of the proposed sliding mode control method are verified by a numerical simulation example based on the separately excited DC motor model.