Adaptive observer for ODE-PDE cascade systems subject to nonlinear dynamics and uncertain parameters

• Published in: Nonlinear dynamics Vol. 111; no. 18; pp. 17317 - 17336
• Main Authors: Ji, Chunting, Zhang, Zhengqiang
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.09.2023; Springer Nature B.V
• Subjects: Automotive Engineering; Classical Mechanics; Control; Decoupling; Design; Dynamical Systems; Engineering; Errors; Mathematical functions; Mechanical Engineering; Nonlinear dynamics; Original Paper; Parabolic differential equations; Parameter estimation; Parameter uncertainty; Partial differential equations; Sensors; Vibration; Nonlinear dynamics; ODE-PDE cascade systems; Uncertainty; Adaptive observer
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-023-08780-5

In this article, state and parameter estimation problems are investigated for ODE-PDE coupled systems, for which the parabolic PDE sensor includes nonlinear dynamics and parameter uncertainty. The major difficulty we face is that the link point among the ODE part and the PDE part is not convenient to measurable. For this reason, the objective of this paper is to build an adaptive observer to provide online estimates of states and unknown parameters on the basis that only boundary state is available for measurement. First of all, the observer error system is converted to a tractable target error system by applying the decoupling transformation. Then, the least-squares parameter adaptive law is built. Under an ad hoc persistent excitation condition, the exponentially decaying of the observer error system is demonstrated by applying Lyapunov–Krasovskii functional. Finally, the effectiveness of the theoretical results is confirmed by a simulation example.