Abstract: The control problem of a class of Hamiltonian systems with parameter coupling was studied. Firstly, the complex dynamic behavior of the system under certain parameters was verified by drawing Lyapunov exponent diagram, chaotic attractor diagram and time domain waveform diagram. Secondly, sliding mode control method, adaptive backstepping control method and high frequency robust control method were used to design the controller, and the state of the chaotic system was stabilized to the equilibrium point. Finally, the effectiveness of the designed controller was verified by numerical simulation of MATLAB software, and its control effect was compared.

Key words: coupled Hamiltonian system, sliding mode control, adaptive backstepping control, high frequency robust control, Lyapunov exponent