Adaptive Finite-Time Control for High-Order Nonlinear Systems With Multiple Uncertainties and its Application

The globally finite-time control issue is concerned in this note for high-order nonlinearly parameterized systems with unknown control gain and external disturbances. A novel control strategy combining adaptive control technique with sign function can well deal with serious uncertainties and unknown control gain. Without any nonlinear growth assumptions, a unified and systematic design procedure is employed to derive an adaptive state-feedback controller with the help of the adding a power integrator method and backstepping technique. Then, by finite-time stability analysis and Lyapunov functions, the proposed controller ensures that the closed-loop system is globally practically finite-time stable (PFTS). Two simulation examples, including a mass-spring mechanical system and a numerical example, are applied to verify the performance and effectiveness of the designed schemes.