驻留时间有限的semi-Markov跳变广义系统的滑模控制及其在二阶多智能体系统中的应用

The modes of semi-Markov jumping singular systems jump according to a semi-Markov chain. The sliding mode control of these systems is still an open problem, and one of the difficulties is how to realize the reachability of the sliding mode surface. For the challenging problem, this project is devoted to investigating the new method of sliding mode control and its application for semi-Markov jumping singular systems with the finite sojourn time obeying arbitrary probability distribution. The focuses in detail are as follows: A new-type discretization Lyapunov function with jumping modes and sojourn time is established, and the stochastic admissibility and robust stability are researched for semi-Markov jumping singular systems. A new method to construct a multidimensional sliding mode surface and hierarchical sliding mode controller is emphatically considered. The sliding mode control theory, including the existence, final reachability and robust stability of the sliding mode dynamics, and the sliding mode control theory based observers are researched. A stochastic numerical calculation is considered, and the numerical calculation and simulation of semi-Markov jumping singular systems are researched. The application of the proposed new method of sliding mode control is founded to the consensus problem of second-order multi-agent systems with semi-Markov jumping topology in order to provide new theory support for the collaborative control of multi-agent systems.

Semi-Markov跳变广义系统的模态跳变遵循semi-Markov链，该系统的滑模控制还有许多问题需要解决，其中一个关键难题是如何实现滑模面的可达性。本项目力争解决该难题，研究驻留时间有限且服从任意概率分布的semi-Markov 跳变广义系统的滑模控制新方法及其应用。包括：构造与模态和驻留时间相关的新型离散化Lyapunov函数，研究semi-Markov跳变广义系统的随机容许性和鲁棒稳定性；重点讨论多维滑模面和递阶滑模控制器的构造新方法，研究semi-Markov跳变广义系统的滑模控制理论（滑模的存在性、最终可达性和鲁棒稳定性）和基于观测器的滑模控制理论；讨论随机数值计算方法，研究semi-Markov跳变广义系统的数值计算和仿真模拟。将滑模控制新方法应用到semi-Markov跳变拓扑结构的二阶多智能体系统的一致性研究中，为多智能体系统的协同控制研究提供新的理论支持。

受分数布朗运动干扰的semi-Markov跳变广义滞后系统的模态跳变遵循semi-Markov链，该类系统的广义随机有限时间有界性和滑模控制有许多问题需要解决。本项目解决了其中两个关键难题。一个是通过构造与Hurst指数相关的新型二重积分型Lyapunov函数解决了由分数布朗运动的样本路径连续性和长记忆性造成的系统不稳定问题。另一个是通过构造与跳变模态无关的滑模面函数和与Hurst指数相关的滑模控制器解决了滑模面存在性和可达性问题。本项目主要完成了以下研究内容：（1）给出了受分数布朗运动干扰的semi-Markov跳变广义滞后系统的正则性、无脉冲性及广义随机有限时间有界性分析及镇定控制方法，将所提方法结论应用到了机械臂的实际控制研究中。（2）给出了受分数布朗运动干扰的semi-Markov跳变广义滞后系统的滑模面函数构造方法和滑模控制设计方法，将所提方法结论应用到了垂直起降飞行器的实际控制研究中。（3）编写了判别该类系统广义随机有限时间有界性的程序。利用随机Euler方法和随机Runge-Kutta方法编写了开环系统及闭环系统的随机数值计算程序。（4）初步给出了semi-Markov跳变拓扑结构下多智能体系统的一致性研究结论。