不确定非齐次semi-Markov跳变系统的约束预测控制研究

齐次semi-Markov(SM)跳变系统能够有效描述系统随机突变现象，在工业机械臂和无人机系统控制中得到了广泛应用。齐次SM过程驱动下各工作模态间的跳变转移概率由当前模态滞留时间概率分布和内嵌转移概率共同决定，然而在实际系统中，模态内嵌转移概率具有时变性，即非齐次SM过程普遍存在，这给系统稳定性分析与控制综合带来了困难。因此本项目将以不确定非齐次SM跳变系统稳定判据为核心，围绕工程中的约束问题展开控制方法的研究。主要研究内容包括：(1)引入正定松弛变量，重构系统随机稳定性判据，并设计约束预测控制器；(2)构建滞留时间内模态依赖不变集空间，在每个工作模态空间下设计约束鲁棒预测控制器，兼顾鲁棒性；(3)设计模态依赖动态事件触发机制预测控制算法，提高系统控制性能的同时节约网络通信和计算资源。本项目有望建立一套不确定非齐次SM跳变系统约束预测控制器设计方法，并将其应用到变负载无人机控制系统中。

Homogeneous semi-Markov (SM) jump systems is considered as a stochastic system which effectively describes the random mutation of systems, such as industrial manipulator systems and unmanned aerial vehicle (UAV) systems. The transition probability of each operating mode is driven by a homogeneous SM process, which is determined by the distribution of sojourn-time in current mode and the embedded transition probability of two adjacent modes. However, in practical systems, the embedded transition probability is time-varying rather than constant, which is difficult to obtain accurately. That means the non-homogeneous SM process is widespread, which leads to significant difficulties while performing stability analysis and control synthesis of non-homogeneous SM system. Therefore, this project will focus on the stability criterion of uncertain non-homogeneous SM jump system, and carry out the control method research on the constrained problem, which exists widely in engineering. The main research contents are given as follows :(1) The stochastic stability criterion of the system is re-established by designing positive definite relaxation variables, and the model predictive controller is designed; (2) A mode-dependent invariant set space is constructed, and a constrained robust predictive controller is designed for each operating mode space by taking the robust performance into account. (3) The mode-dependent dynamic event-trigger mechanism is constructed, and then the dynamic event-trigger based model predictive control algorithm is proposed to improve the system control performance and reduce the waste of network resources. The goal of this project is to estabilish the novel model predictive controller for constrained uncertain non-homogeneous SM systems and then apply the obtained results to variable load UAV systems.