This paper addresses the current sensorless finite time control for the buck-boost converter with unknown constant power load.The low frequency oscillation caused by negative impedance of constant power loads can adversely affect the stability of buck-boost converters.First,to reconstruct unavailable inductor current and unknown power load,a reduced-order generalized parameter estimation based observer with finite time convergence is designed on the basis of dynamic regression extension and mixing techniques,which is able to reformulate the state observation as parameter estimation.Second,the nonlinear system is converted into a linear one via a feedback linearization approach,and a Fast Terminal Sliding Mode Controller (FTSMC) is designed to stabilize the system.Subsequently,a current sensorless finite time controller is proposed by combining the FTSMC with the generalized parameter estimation based observer.Then the finite time stability of the closed-loop system is proved by the finite time stability result of the cascaded system.Finally,the effectiveness of the proposed current sensorless finite time control scheme is verified by simulation and experiment results.