马尔可夫跳变系统的奇异自适应滑模控制

Singular adaptive sliding mode control for Markovian jump systems

该文采用奇异系统方法研究了转移速率部分已知的、具有匹配非线性和匹配外部扰动的连续时间马尔可夫跳变系统的自适应积分滑模控制问题.首先,按照奇异系统方法设计积分型滑模面,进而结合原系统及滑模动力学可得奇异马尔可夫跳变系统;其次,以线性矩阵不等式的形式给出了保证所得奇异马尔可夫跳变系统随机容许性的充分条件;紧接着在这一条件下,结合自适应控制来保证状态轨迹对积分滑模面的可达性;最后通过仿真案例验证了所得结果的有效性.

In this paper,the problem of adaptive sliding mode control for continuous-time Markovian jump systems with partially known transition probabilities and matched nonlinearities and matched external disturbances is investigated by using a singular system method.Firstly,the integral-type sliding mode surface is designed according to the singular system approach and the singular Markovian jump system is obtained by combining the original system and the sliding mode dynamics.Secondly,sufficient conditions to guarantee the stochastic admissibility of singular Markovian jump systems are given in the form of linear matrix inequalities.Then,the adaptive control is combined to ensure the reaching conditions of the state trajectory.Finally,the effectiveness of the results is verified by a simulation case.