A new finite time control method to nonlinear systems with uncertain dynamics and time-varying powers

The existing researches mainly focused on control issues of systems with constant powers. In practical engineering, it shows that some dynamic systems have time-varying powers, which result in the inapplicability of many reported methods. Besides, nonlinear systems constantly suffer from uncertain dynamics. This article discusses the control issue of systems which possess uncertain dynamics and time-varying powers. By introducing a new Lyapunov function which contains quadratic components and high-order components and raising a novel recursive design strategy, we successfully design a semi-global practical finite time controller which allows uncertain dynamics and larger range of system powers. Numerical and practical examples show that the presented strategy is valid.