In this paper, an impulsive adaptive observer is proposed for online estimates of a class of hybrid cascade systems with uncertain parameters. The hybrid cascade system is formed by an ordinary differential equation (ODE) coupled with a partial differential equation (PDE) with uncertain parameters. In the hybrid cascade system, the state of the connection point between the two subsystems cannot be directly available, which makes it difficult to obtain online estimates of the inaccessible states. To deal with the complex observation problem, an impulsive adaptive observer is designed using the backstepping approach and the extended Kalman observer. In addition, the convergence of the proposed observer is examined. The backstepping transformation plays a crucial role in the convergence proof. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.

在本文中，提出了一种脉冲自适应观测器，用于对一类具有不确定参数的混合级联系统进行在线估计。混合级联系统由常微分方程 (ODE) 与参数不确定的偏微分方程 (PDE) 耦合而成。在混合级联系统中，两个子系统之间连接点的状态不能直接获得，这使得难以获得不可访问状态的在线估计。针对复杂的观测问题，利用反步法和扩展卡尔曼观测器设计了脉冲自适应观测器。此外，还检查了建议观察者的收敛性。反步变换在收敛证明中起着至关重要的作用。最后，