基于轨迹灵敏度的随机网络控制系统不敏感控制

This project is dedicated to cope with the finite-frequency insensitive control problem based on trajectory sensitivity for stochastic networked-control systems. The designed controllers have low sensitivity to stochastic trivial additive/multiplicative controller coefficient variations. At the same time, the drawback that the transfer function sensitivity approach involving the closed-loop system’s transfer function will not be applied to stochastic networked-control systems will be resolved by using trajectory sensitivity approach. First of all, by modeling the stochastic networked-control systems with networked induced delay and consecutive packet dropouts as stochastic time-delay systems, a frequency dependent insensitive control strategy based on combining trajectory sensitivity approach and delay finite-frequency technology is provided. Then, the relationship among controller coefficient variation bounds, networked characteristic parameters, system performances and sensitivity performance is investigated. The convex optimization conditions are also given to simultaneously optimize the system performance and sensitivity performance. Then, the sum of trajectory sensitivities is adopted to deal with the non-convex optimization problem of the controller design with respect to multiplicative controller coefficient variations. In addition, approach is investigated to solve the problem that the sum of trajectory sensitivities will fail to obtain individual controller coefficient sensitivity. Reduction of computational complexity and conservativeness are also considered simultaneously. The research project has important significance for the development of sensitivity theory and network control theory as well as the improvement of practical engineering systems’ reliability and safety.

本项目拟在有限频域内研究基于轨迹灵敏度的随机网络控制系统不敏感控制问题，实现对随机出现的微小的加性/乘性区间型控制器参数变化具有较低的灵敏度，同时采用轨迹灵敏度法解决已有的传递函数灵敏度法因涉及闭环系统传递函数而不适用于随机网络控制系统的缺陷。首先，将具有网络诱导时延和连续数据丢包的随机网络控制系统建模为随机时延系统，结合轨迹灵敏度法和时延有限频技术，提出频率相关的不敏感控制策略，研究控制器参数变化界、网络特征参数及系统稳定性和敏感性之间的关系，给出同时优化系统性能和轨迹灵敏度性能的凸优化条件。其次，采用轨迹灵敏度求和的方法解决乘性控制器参数变化的情况下控制器设计的非凸优化问题，同时研究解决由此引起的无法获得单个控制器参数灵敏度的方法，兼顾考虑降低计算复杂度和减小设计的保守性。该项研究对敏感性理论和网络控制理论的发展以及对改进实际工程系统的可靠性和安全性都具有重要意义。

本项目针对具有区间型的加性/乘性区间有界控制器参数变化的网络控制系统设计不敏感控制和网络化车辆队列的队列稳定性问题进行深入和系统的科学研究。研究集中在三个方面。首先对单一线性系统在具有加性区间型控制器参数摄动的情况下，采用灵敏度函数法和参数摄动转换法设计了不敏感动态输出反馈控制器和基于观测器的不敏感输出反馈控制器，并同时优化系统性能。同时提出了解决输出反馈控制器设计中出现的非凸性问题的方法。其次，针对不管是基于参数灵敏度技术还是轨迹灵敏度技术都难于直接处理的含有量化的网络化多智能体系统的不敏感控制问题，将区间型参数变化问题转化为较易解决的参数摄动问题，给出了分布式不敏感状态反馈控制器设计策略。最后，针对网络化车辆队列的队列稳定性问题，给出了分布式自适应滑模控制策略。. 本项目共发表学术论文26篇，大部分发表在国际权威学术期刊和会议上，其中SCI收录13篇，包括控制领域国际顶尖期刊IEEE Transactions on Intelligent Transportation Systems (长文2篇)，IEEE Transactions on Vehicular Technology (长文1篇)，IEEE Transactions on Control of Network Systems (长文1篇)和International Journal of Robust and Nonlinear Control等，并发表了8篇国际会议论文，同时申请了发明专利和实用新型各一项。基于本项目成果，项目负责人获得了职称的晋升，同时项目组负责人和团队成员分别获得国家自然科学基金面上项目和青年项目各一项。