In this study, a nonlinear robust control policy is designed together with a state observer in order to manage the novel coronavirus disease (COVID-19) outbreak having an uncertain epidemiological model with unmeasurable variables. This nonlinear model for the COVID-19 epidemic includes eight state variables (susceptible, exposed, infected, quarantined, hospitalized, recovered, deceased, and insusceptible populations). Two plausible scenarios are put forward in this article to control this epidemic before and after its vaccine invention. In the first scenario, the social distancing and hospitalization rates are employed as two applicable control inputs to diminish the exposed and infected groups. However, in the second scenario after the vaccine development, the vaccination rate is taken into account as the third control input to reduce the susceptible populations, in addition to the two objectives of the first scenario. The proposed feedback control measures are defined in terms of the hospitalized and deceased populations due to the available statistical data, while other unmeasurable compartmental variables are estimated by an extended Kalman filter (EKF). In other words, the susceptible, exposed, infected, quarantined, recovered, and insusceptible individuals cannot be identified precisely because of the asymptomatic infection of COVID-19 in some cases, its incubation period, and the lack of an adequate community screening. Utilizing the Lyapunov theorem, the stability and bounded tracking convergence of the closed-loop epidemiological system are investigated in the presence of modeling uncertainties. Finally, a comprehensive simulation study is conducted based on Canada’s reported cases for two defined timing plans (with different treatment rates). Obtained results demonstrate that the developed EKF-based control scheme can achieve desired epidemic goals (exponential decrease of infected, exposed, and susceptible people).

在这项研究中，非线性鲁棒控制策略与状态观察器一起设计，以管理具有不确定流行病学模型和不可测量变量的新型冠状病毒病 (COVID-19) 爆发。这种 COVID-19 流行病的非线性模型包括八个状态变量（易感、暴露、感染、隔离、住院、康复、死亡和不易感人群）。本文提出了两种似是而非的情景，以在疫苗发明前后控制这种流行病。在第一种情况下，社会距离和住院率被用作两个适用的控制输入，以减少暴露和感染群体。然而，在疫苗开发之后的第二种情况下，除了第一个方案的两个目标之外，疫苗接种率被视为减少易感人群的第三个控制输入。由于可用的统计数据，建议的反馈控制措施是根据住院和死亡人口定义的，而其他不可测量的区室变量则通过扩展卡尔曼滤波器 (EKF) 进行估计。换句话说，由于 COVID-19 在某些情况下的无症状感染、其潜伏期以及缺乏足够的社区筛查，无法准确识别易感者、暴露者、感染者、隔离者、康复者和不易感者。利用李亚普诺夫定理，在存在建模不确定性的情况下，研究了闭环流行病学系统的稳定性和有界跟踪收敛性。最后，根据加拿大报告的病例，针对两个确定的时间计划（具有不同的治疗率）进行了全面的模拟研究。获得的结果表明，所开发的基于 EKF 的控制方案可以实现预期的流行病目标（感染者、暴露者和易感人群呈指数下降）。