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This paper addresses the finite-time adaptive tracking control problem for a class of pure feedback nonlinear systems whose nonaffine functions may not be differentiable. By properly modeling the nonaffine function, the design difficulty of the pure feedback structure is overcome without using the median value theorem. In our design procedure, an finite-time adaptive controller is elaborately developed using the decoupling technology, which eliminates the limitation assumption on the partial derivatives of nonaffine functions. Furthermore, the constructed controller can stabilize the system within a finite-time so that all signals in the closed-loop system are semiglobally uniformly finite-time bounded (SGUFB), while ensuring the tracking performance. Finally, the simulation results prove the effectiveness of the proposed method.

Finite-Time Adaptive Tracking Control for a Class of Pure-Feedback Nonlinear Systems with Disturbances via Decoupling Technique