In this study, the probabilistic-constrained outlier-resistant tracking control problem is investigated for a class of stochastic nonlinear systems subject to measurement outliers, randomly occurring faults and stochastic nonlinearities. The measurement outliers (e.g. the abnormal values of sensor measurements), which are mainly caused by sensor outages, faults or some unpredictable sudden but sharp disturbances, would inevitably bring certain negative effects on control performance if not tackled appropriately. Different from the commonly used saturation-function-based method, new type of event-trigger-based outlier-resistant communication scheme is proposed in this paper. Based on the proposed scheme, not only those “unnecessary” measurements are not permitted for transmission, but also the measurement outliers are discarded. The main purpose of the current study is to design a novel tracking control scheme such that both the ${\mathcal{H}}_{\infty }$ control performance and specific probabilistic constraint (i.e., the probability of the tracking error falling in a prescribed set is larger than a preset value) are satisfied simultaneously. Furthermore, a finite-horizon probabilistic-constrained ${\mathcal{H}}_{\infty }$ tracking control algorithm is developed to co-design the controller gain matrices and parameters of the event-triggered communication scheme. Finally, one example is utilized to illustrate the efficiency of the theoretical results.

在这项研究中，针对一类受测量异常值、随机发生的故障和随机非线性影响的随机非线性系统，研究了概率约束异常值抵抗跟踪控制问题。测量异常值（如传感器测量值的异常值）主要由传感器断电、故障或一些不可预测的突然而剧烈的扰动引起，如果处理不当，不可避免地会对控制性能带来一定的负面影响。与常用的基于饱和函数的方法不同，本文提出了一种新型的基于事件触发的抗离群点通信方案。基于所提出的方案，不仅那些“不必要”的测量不允许传输，而且测量异常值也被丢弃。${\mathcal{H}}_{\infty }$同时满足控制性能和特定概率约束（即跟踪误差落在规定集合内的概率大于预设值）。此外，有限范围的概率约束${\mathcal{H}}_{\infty }$开发跟踪控制算法以协同设计事件触发通信方案的控制器增益矩阵和参数。最后，通过一个例子来说明理论结果的有效性。