Adaptive predefined-time robust control for nonlinear time-delay systems with different power Hamiltonian functions

Shutong Liu; Renming Yang; Shutong Liu; Renming Yang

doi:10.3934/math.20231441

AIMS Mathematics

2023, Volume 8, Issue 12: 28153-28175. doi: 10.3934/math.20231441

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Research article

Adaptive predefined-time robust control for nonlinear time-delay systems with different power Hamiltonian functions

Shutong Liu ,
Renming Yang ^,

Department of Information Science and Electrical Engineering, Shandong Jiaotong University, Jinan 250357, China

Received: 24 July 2023 Revised: 14 September 2023 Accepted: 27 September 2023 Published: 13 October 2023
MSC : 93B52, 93C10

The article studies $ H_\infty $ control as well as adaptive robust control issues on the predefined time of nonlinear time-delay systems with different power Hamiltonian functions. First, for such Hamiltonian systems with external disturbance and delay phenomenon, we construct the appropriate Lyapunov function and Hamiltonian function of different powers. Then, a predefined-time $ H_\infty $ control approach is presented to stabilize the systems within a predefined time. Furthermore, when considering nonlinear Hamiltonian system with unidentified disturbance, parameter uncertainty and delay, we devise a predefined-time adaptive robust strategy to ensure that the systems reach equilibrium within one predefined time and have better resistance to disturbance and uncertainty. Finally, the validity of the results is verified with a river pollution control system example.
- nonlinear time-delay system,
- adaptive robust control,
- predefined-time control,
- Hamiltonian method
Citation: Shutong Liu, Renming Yang. Adaptive predefined-time robust control for nonlinear time-delay systems with different power Hamiltonian functions[J]. AIMS Mathematics, 2023, 8(12): 28153-28175. doi: 10.3934/math.20231441

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Abstract

The article studies $ H_\infty $ control as well as adaptive robust control issues on the predefined time of nonlinear time-delay systems with different power Hamiltonian functions. First, for such Hamiltonian systems with external disturbance and delay phenomenon, we construct the appropriate Lyapunov function and Hamiltonian function of different powers. Then, a predefined-time $ H_\infty $ control approach is presented to stabilize the systems within a predefined time. Furthermore, when considering nonlinear Hamiltonian system with unidentified disturbance, parameter uncertainty and delay, we devise a predefined-time adaptive robust strategy to ensure that the systems reach equilibrium within one predefined time and have better resistance to disturbance and uncertainty. Finally, the validity of the results is verified with a river pollution control system example.

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