复杂受限的semi-Markov跳变系统控制与滤波

复杂难测的实际运行环境会导致机器人系统参数发生突变以及信息获取困难，所以研究复杂受限的semi-Markov跳变系统的控制与滤波问题具有重要的理论和实际意义。本项目通过对实际问题的提炼，总结出系统模态转移信息受限、系统状态测量信息受限、系统模态信息受限等几类受限情形。考虑上述受限情形，提出非齐次semi-Markov跳变系统的稳定和镇定性分析、输出反馈控制器设计和异步滤波器设计等问题研究框架。一方面，本项目将通过对不完全信息的合理补偿和估计等方法，降低控制器设计时因信息不完全带来的影响；另一方面，为降低结果的保守性，采用驻留时间依赖的Lyapunov函数、隐semi-Markov模型、投影定理等方法，给出结构更为简单灵活的控制器和滤波器设计方法，并将理论成果应用到移动机器人系统上。以期提出一套较为完整的基于受限信息下的移动机器人系统控制与滤波理论及方法，并为实际应用提供技术支持。

The complex and unmeasurable actual operation environment will lead to the abrupt change of robot system parameters and the difficulty in obtaining information. Therefore, it is of great theoretical and practical significance to study the control and filtering problems of semi-Markov jump system under complex and limited environment. By refining the practical problems, this project summed up some kinds of constrained situations, such as system mode transfer information limitation, system state measurement information limitation, system mode information limitation and so on. In consideration of the above constrained situations, the research frameworks of the stability and stabilization analysis, output feedback controller design and asynchronous filter design of the nonhomogeneous semi-Markov jump system are proposed respectively. On the one hand, this project will reduce the influence caused by incomplete information during controller design via reasonable compensation and estimation of incomplete information. On the other hand, in order to reduce the conservativeness of the results, the time-dependent Lyapunov function, hidden semi-Markov model, projection theorem and other methods are adopted to present a more simple and flexible controller and filter design method, and the theoretical results are applied to the mobile robot system. In order to provide technical support for practical application, a relatively complete set of mobile robot system control and filtering theory method based on limited information is proposed.