Finite-time boundedness of uncertain Hamiltonian systems via sliding mode control approach

This paper seeks to address the problem of finite-time stabilization for a class of uncertain Hamiltonian systems via sliding mode control approach. A novel sliding function in connection with the state and energy function of the considered system is constructed, and then, a suitable controller is designed to drive the state trajectories onto the specified sliding surface before the given finite-time. Moreover, the finite-time boundedness of the closed-loop system over both reaching phase and sliding motion phase are analyzed and the corresponding conditions are obtained. Furthermore, two optimization problems are formed to enhance the performance of finite-time boundedness, which will be solved via genetic optimization algorithm. Finally, a simulation example is provided to illustrate the proposed control strategy.