共享随机丢包信道下多输入系统均方可镇定–调度与控制协同设计

Mean square stabilization of multi-input systems over shared packet loss channels via the co-design of scheduling and control

中文关键词  网络化控制系统  随机丢包  均方可镇定  协同设计  调度

英文关键词  networked control systems  random packet loss  mean square stabilization  co-design  scheduling

中文摘要

      借助有限容量信道进行设备间信息交互的网络化系统, 其整体性能依赖于控制策略和通信机制. 本文基于 调度与控制协同设计思想, 解决多个输入在共享数量有限的通信信道场景下, 所面临的网络化系统反馈控制镇定问 题. 其中, 每个通信信道建模为随机丢包模型. 首先, 根据多控制器系统性质, 将多输入系统通过共享信道状态反馈 可镇定问题, 转化为切换线性系统在一个调度周期内可镇定问题. 其次, 针对多个输入共享单个随机丢包信道的情 况, 采用等价转变思想, 将闭环系统的稳定性问题转化为易于求解的线性算子的稳定性问题. 进一步, 根据系统旺纳 姆分解技术和系统最优补灵敏度, 构造出适当的调度策略和控制器, 从而推导出网络化系统可镇定的充分条件, 该 条件用丢包率与系统不稳定度关系来表示. 然后, 将上述结论推广到多个输入共享多个随机丢包信道情况. 接下来, 根据控制不等式理论、线性编码和解码技术, 给出均匀调度策略下网络化系统可镇定时丢包率需要满足的条件. 最 后, 通过数值算例和仿真结果, 验证了所得结论的合理性.

英文摘要

      The networked system uses limited capacity channels to complete the information exchange between various devices, and its overall performance depends not only on the control strategy, but also on the communication mechanism. Based on the idea of scheduling and control co-design, this paper solves the network stabilization problem where multiple inputs must share a small number of communication channels, where each communication channel is modeled as a random packet loss model. Firstly, based on the properties of multi-controller systems, the stabilization problem of multi-input systems through shared channel is transformed into that of switched linear systems in a scheduling period. Secondly, the stability of the closed-loop system is transformed into that of linear operators which is easy to solve by using the idea of equivalent transformation for the case of sharing a single random packet loss channel. According to the Wonham decomposition technique and the optimal supplementary sensitivity of the system, the appropriate scheduling strategy and controller are constructed, and then the sufficient conditions expressed by the relationship between packet loss rate and the instability of the system are obtained. Thirdly, the above conclusions are extended to the case of sharing multiple random packet loss channels. Then, according to the majorization theory, linear coding techniques, the conditions of packet loss rate are given when the networked system can be stabilized under uniform scheduling strategy. Finally, numerical examples and simulation verify the rationality of the conclusion.