Asynchronous sliding mode control for Markovian jumping systems in finite-time intervals
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摘要: 针对马尔科夫跳变系统，讨论有限时间区间内异步滑模控制及其有限时间有界问题. 针对系统存在状态不可测的非同步现象，基于隐马尔科夫模型，设计了模式相关滑模控制器，使得系统状态轨迹在规定的有限时间内被驱动到滑模面上. 采用有限时间分析法，得到滑模动力学在到达阶段和滑动运动阶段的有限时间有界准则，获得异步控制器增益矩阵解的充分条件. 最后，通过单连杆机器人手臂模型证明所得结果的有效性.Abstract: The problem of asynchronous sliding mode control in finite-time intervals was studied for Markovian jumping systems. A mode-dependent sliding mode surface function was designed based on the hidden Markov model for the unmeasurable non-synchronization phenomenon. A sliding mode controller was designed to drive the state trajectory of the system to the specified sliding mode surface in a specified finite-time. Through the finite-time analysis method, the finite-time boundedness criterion of sliding mode dynamics in the arrival stage and sliding motion stage was gained, sufficient conditions for the solution of the asynchronous controller gain matrix were obtained. Finally, a single-link robot arm model was used to demonstrate the effectiveness of the results.
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图 4 带有控制器
${\boldsymbol{u}}(t)$ 的系统响应曲线Figure 4. System response curve with
${\boldsymbol{u}}(t)$ 
图 5 不带有控制器加权函数
${{\boldsymbol{x}}^{\rm{T}}}(t){\boldsymbol{R}}{\boldsymbol{x}}(t)$ 的变化曲线Figure 5. Curve of state function
${{\boldsymbol{x}}^{\rm{T}}}(t){\boldsymbol{R}}{\boldsymbol{x}}(t)$ without controller
图 6 带有控制器加权函数
${{\boldsymbol{x}}^{\rm{T}}}(t){\boldsymbol{R}}{\boldsymbol{x}}(t)$ 的变化曲线Figure 6. Curves of state function
${{\boldsymbol{x}}^{\rm{T}}}(t){\boldsymbol{R}}{\boldsymbol{x}}(t)$ with controller -
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