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

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.