Kybernetika 58 no. 3, 400-425, 2022

Predictor control for wave PDE/nonlinear ODE cascaded system with boundary value-dependent propagation speed

Xiushan Cai, Yuhang Lin, Junfeng Zhang and Cong LinDOI: 10.14736/kyb-2022-3-0400


This paper investigates predictor control for wave partial differential equation (PDE) and nonlinear ordinary differential equation (ODE) cascaded system with boundary value-dependent propagation speed. A predictor control is designed first. A two-step backstepping transformation and a new time variable are employed to derive a target system whose stability is established using Lyapunov arguments. The equivalence between stability of the target and the original system is provided using the invertibility of the backstepping transformations. Stability of the closed-loop system is established by Lyapunov arguments.


predictor control, cascaded system, wave dynamics, boundary value-dependent, backstepping transformation


93Cxx, 93Dxx


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